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Steam power cycles – Rankine cycle

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Quick recall · 215 cards
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“Heat cannot by itself flow from a body at a lower temperature to a body at a higher temperature” is a statement or consequence of
A · The second law of thermodynamics
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The pressure and temperature at which three phases of a pure substance coexist is called:
B · Triple point
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On a p-T diagram, the triple point of a pure substance is represented as:
C · A point
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The graphical representation of the transformation of 1 kg of ice into 1 kg of superheated steam at constant pressure is best depicted using which diagram?
C · t-h diagram (temperature-enthalpy diagram)
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One mole of an ideal gas at STP occupies how many litres?
C · 22.4 litres
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Which of the following is the ideal gas equation?
D · PV = nRT
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Under conditions of fixed temperature and amount of gas, which of the following statements correctly represent Boyle's law?
D · All of the above
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The ideal gas law predicts that the molar volume (volume of one mole) of gas equals:
D · RT/P
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Under ideal conditions, isothermal, isobaric, isochoric and adiabatic processes are ________.
C · Quasi-static processes
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In a Carnot cycle, the working medium receives heat at a _____________ temperature.
B · higher
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In a Carnot cycle, what is the working fluid?
B · an ideal gas
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The efficiency of the Carnot engine is determined by:
C · both source and sink
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Which one of the following statements regarding a Rankine cycle is FALSE?
B · Reduction in thermal efficiency
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Assume a turbine to be part of a simple Rankine cycle. The density of water at the inlet to the pump is 1000 kg/m³. Ignoring kinetic and potential energy effects, the specific work (in kJ/kg) supplied to the pump is:
C · 2.930
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What is the primary effect of regeneration in a Rankine cycle?
B · Reduces fuel consumption and improves thermal efficiency
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For the same compression ratio and for the same heat added, which cycle is more efficient?
A · Otto cycle is more efficient than Diesel Cycle
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Otto cycle efficiency is higher than Diesel cycle efficiency for the same compression ratio and heat input because in Otto cycle __________
A · combustion is at constant volume
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For the same compression ratio of Otto, Diesel and Dual cycle, which has the highest efficiency?
B · Otto cycle
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During a refrigeration cycle, heat is rejected by the refrigerant in a:
B · Condenser
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In a vapour compression system, the condition of refrigerant before entering the compressor is:
C · Dry saturated vapour
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The highest temperature during the cycle in a vapour compression system occurs after:
A · Compression
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In a vapour compression system, the lowest temperature during the cycle occurs after:
C · Expansion
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The sub-cooling in a refrigeration cycle:
B · Increases C.O.P
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Why is a gas turbine considered to operate on the Brayton cycle?
B · B. Combustion causes no increase in volume.
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An open cycle gas turbine engine is best described by which of the following statements?
B · B. Working fluids are taken in, transformed, and then discarded.
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Which of the following best states the Zeroth Law of Thermodynamics?
A · If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other
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Two bodies A and B are separately in thermal equilibrium with a third body C. According to the Zeroth Law, what can be concluded about bodies A and B?
B · A and B are in thermal equilibrium with each other
According to the Zeroth Law, if A and B are each in thermal equilibrium with C, then A and B are in thermal equilibrium with each other, implying they have the same temperature.
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Which of the following is a direct implication of the Zeroth Law of Thermodynamics?
A · Definition of temperature as a measurable property
The Zeroth Law allows the definition of temperature as a fundamental and measurable property, since thermal equilibrium implies equality of temperature.
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The First Law of Thermodynamics is essentially a statement of which principle?
A · Conservation of energy
The First Law states that energy can neither be created nor destroyed, only transformed, which is the principle of conservation of energy.
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In a closed system undergoing a process, the First Law of Thermodynamics can be expressed as \( \Delta U = Q - W \). What do the symbols represent?
A · \( \Delta U \): change in internal energy, \( Q \): heat added to the system, \( W \): work done by the system
In the First Law, \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.
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A gas in a piston-cylinder device absorbs 500 J of heat and does 200 J of work on the surroundings. What is the change in internal energy of the gas?
A · 300 J increase
Using \( \Delta U = Q - W = 500 - 200 = 300 \) J, the internal energy increases by 300 J.
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For a cyclic process, what is the net change in internal energy according to the First Law of Thermodynamics?
A · Zero
In a cyclic process, the system returns to its initial state, so the net change in internal energy \( \Delta U = 0 \).
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Which statement correctly describes the Second Law of Thermodynamics?
A · Entropy of an isolated system never decreases
The Second Law states that entropy, a measure of disorder, of an isolated system never decreases; it either increases or remains constant.
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Which of the following is an example of an irreversible process illustrating the Second Law of Thermodynamics?
A · Free expansion of gas into vacuum
Free expansion into vacuum is irreversible because it increases entropy and cannot spontaneously reverse, illustrating the Second Law.
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The Kelvin-Planck statement of the Second Law of Thermodynamics implies that:
A · It is impossible to construct a heat engine that converts all heat into work without any other effect
The Kelvin-Planck statement says no heat engine can have 100% efficiency; some heat must be rejected, reflecting the Second Law.
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Which of the following best describes the Zeroth Law of Thermodynamics?
A · If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other
The Zeroth Law states that if two systems are in thermal equilibrium with a third system, they must be in thermal equilibrium with each other, establishing the concept of temperature.
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Which practical device relies fundamentally on the Zeroth Law of Thermodynamics?
A · Thermometer
Thermometers measure temperature by reaching thermal equilibrium with the system, a concept based on the Zeroth Law.
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Two bodies A and B are in thermal equilibrium with a third body C, but A and B are not in thermal equilibrium with each other. What does this imply about the Zeroth Law?
D · There is an error in the measurement or assumption
According to the Zeroth Law, if A and B are each in thermal equilibrium with C, they must be in thermal equilibrium with each other. If not, it indicates an error in measurement or assumptions.
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The First Law of Thermodynamics is a statement of which fundamental principle?
A · Conservation of energy
The First Law states that energy cannot be created or destroyed, only transformed, which is the principle of conservation of energy.
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A system absorbs 500 J of heat and does 200 J of work on its surroundings. What is the change in internal energy of the system?
B · +300 J
Using the First Law: \( \Delta U = Q - W = 500 - 200 = +300 \) J
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In an adiabatic process, which of the following is true according to the First Law of Thermodynamics?
A · Heat transfer \( Q = 0 \), so \( \Delta U = -W \)
In an adiabatic process, no heat is exchanged (\( Q=0 \)), so the change in internal energy equals the negative of work done by the system.
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A gas in a closed system undergoes a cyclic process absorbing 400 J of heat and doing 400 J of work. What is the net change in internal energy after one complete cycle?
A · Zero
For a cyclic process, the internal energy returns to its initial value, so \( \Delta U = 0 \).
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Which statement best reflects the Second Law of Thermodynamics?
A · Entropy of an isolated system never decreases
The Second Law states that entropy, a measure of disorder, of an isolated system never decreases.
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Which of the following devices violates the Second Law of Thermodynamics if it operated as described?
A · A heat engine converting all absorbed heat into work
No heat engine can convert all absorbed heat into work without losses, as per the Second Law.
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Which of the following statements about entropy is correct?
A · Entropy is a measure of system disorder and always increases in spontaneous processes
Entropy quantifies disorder and tends to increase in spontaneous, irreversible processes.
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A heat engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. What is the maximum theoretical efficiency of this engine according to the Second Law?
A · 50%
Carnot efficiency \( \eta = 1 - \frac{T_c}{T_h} = 1 - \frac{300}{600} = 0.5 = 50\% \).
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Which of the following processes is irreversible according to the Second Law of Thermodynamics?
A · Free expansion of a gas into vacuum
Free expansion into vacuum is spontaneous and irreversible, increasing entropy.
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Assertion (A): The entropy of a perfect crystal at absolute zero is zero. Reason (R): At absolute zero, the system is in a state of perfect order with only one microstate accessible. Choose the correct option:
A · A is true, R is true, and R is the correct explanation of A.
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Which of the following correctly describes the phase of steam at a pressure below saturation pressure and temperature above saturation temperature?
C · Superheated steam
Steam at a pressure below saturation pressure and temperature above saturation temperature is in the superheated state.
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At constant pressure, when steam changes from saturated liquid to saturated vapor, which property changes significantly?
B · Specific volume
During phase change at constant pressure, temperature remains constant but specific volume changes significantly as liquid converts to vapor.
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Refer to the diagram below showing a 3D p-v-T surface of steam. Which region corresponds to the wet steam phase?
A · Region under the saturation dome
Wet steam exists under the saturation dome where liquid and vapor coexist in equilibrium.
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Which statement best describes the shape of the p-v-T surface for steam near the critical point?
B · The saturation dome disappears and the surface becomes continuous
At the critical point, the saturation dome disappears and the p-v-T surface becomes continuous with no distinct phase boundary.
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Refer to the diagram below of the p-v-T surface of steam. Which curve represents the saturated liquid line?
A · Left boundary of the saturation dome
The saturated liquid line forms the left boundary of the saturation dome, representing states where steam is saturated liquid.
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Which of the following correctly identifies the critical point on the saturation dome of steam?
A · Point where saturated liquid and saturated vapor lines meet
The critical point is where saturated liquid and saturated vapor lines meet, beyond which distinct liquid and vapor phases do not exist.
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Refer to the saturation dome diagram below. What happens to the latent heat of vaporization as the critical point is approached?
C · It decreases and becomes zero at the critical point
Latent heat of vaporization decreases as the critical point is approached and becomes zero at the critical point.
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Which of the following is NOT typically found in steam tables?
D · Thermal conductivity of steam
Steam tables provide thermodynamic properties like specific volume, enthalpy, and entropy but do not include thermal conductivity.
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Refer to the Mollier diagram (h-s chart) below. If steam moves from state 1 to state 2 along a constant entropy line, what type of process is this?
C · Isentropic process
A process along a constant entropy line (vertical line on h-s chart) is isentropic, meaning entropy remains constant.
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When using steam tables, which property remains constant during an isobaric heating of saturated liquid to saturated vapor?
A · Pressure
During isobaric heating from saturated liquid to saturated vapor, pressure remains constant while temperature and specific volume change.
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Which thermodynamic relation involving steam properties is used to calculate the change in enthalpy with respect to pressure at constant temperature?
B · Clausius-Clapeyron equation
The Clausius-Clapeyron equation relates the change in pressure and temperature during phase change and is used to calculate enthalpy changes.
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Which of the following equations correctly expresses the Clapeyron equation for phase change of steam?
A · \( \frac{dP}{dT} = \frac{L}{T \Delta v} \)
The Clapeyron equation is given by \( \frac{dP}{dT} = \frac{L}{T \Delta v} \), where \(L\) is latent heat, \(T\) temperature, and \(\Delta v\) change in specific volume.
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What is the primary purpose of steam tables in engineering thermodynamics?
A · To provide properties of steam at various pressures and temperatures
Steam tables provide thermodynamic properties such as pressure, temperature, enthalpy, entropy, and specific volume of steam at various states, which are essential for analysis and design.
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Which of the following properties is NOT typically found in standard steam tables?
C · Thermal conductivity
Steam tables generally list thermodynamic properties such as enthalpy, entropy, pressure, temperature, and specific volume, but not thermal conductivity.
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In the saturated steam tables, the term \( x \) represents:
B · Quality of steam
The quality \( x \) denotes the dryness fraction or the ratio of mass of vapor to the total mass in a saturated mixture.
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Which of the following best describes the use of steam tables for property determination?
B · They help find thermodynamic properties at given pressure and temperature
Steam tables allow engineers to find thermodynamic properties such as enthalpy, entropy, and specific volume for steam at specified pressures and temperatures.
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At a pressure of 0.5 MPa and temperature of 200°C, which steam property is closest to the specific enthalpy (\( h \)) of superheated steam?
B · 2700 kJ/kg
At 0.5 MPa and 200°C, superheated steam enthalpy is approximately 2700 kJ/kg according to standard superheated steam tables.
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A steam sample at 0.2 MPa has an enthalpy of 2700 kJ/kg. Using steam tables, determine the phase of steam.
C · Superheated steam
At 0.2 MPa, enthalpy of saturated vapor is less than 2700 kJ/kg; hence, the steam with 2700 kJ/kg enthalpy is superheated.
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Which phase of steam corresponds to the state where the temperature is at saturation and quality \( x = 0 \)?
C · Saturated liquid
Quality \( x = 0 \) indicates saturated liquid at saturation temperature and pressure.
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At 0.1 MPa pressure, what is the approximate temperature of saturated steam?
A · 99.61°C
At 0.1 MPa (1 bar), the saturation temperature is approximately 99.61°C.
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Refer to the phase diagram below. Which region corresponds to superheated steam?

Temperature (°C)Pressure (MPa)Saturated RegionCompressed LiquidSuperheated Steam
B · Right of the saturated curve (light blue area)
Superheated steam exists to the right of the saturated vapor curve where steam temperature is higher than saturation temperature at given pressure.
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Which property of superheated steam increases significantly with temperature at constant pressure?
A · Specific volume
At constant pressure, increasing temperature in superheated steam increases specific volume significantly.
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At 0.5 MPa and 300°C, what is the approximate entropy of superheated steam?
B · 6.5 kJ/kg·K
From superheated steam tables, entropy at 0.5 MPa and 300°C is approximately 6.5 kJ/kg·K.
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Refer to the superheated steam table excerpt below. At 0.4 MPa and 250°C, what is the specific enthalpy (\( h \))?

Pressure (MPa)Temperature (°C)Specific Enthalpy (kJ/kg)
0.42002776
0.42502850
0.43002920
B · 2850 kJ/kg
At 0.4 MPa and 250°C, the specific enthalpy is 2850 kJ/kg as per the table.
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Which statement correctly describes compressed liquid water properties compared to saturated liquid at the same temperature?
B · Compressed liquid has lower specific volume than saturated liquid
Compressed liquid (subcooled liquid) has a lower specific volume than saturated liquid at the same temperature because it is under higher pressure.
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At 0.1 MPa and 90°C, water is in compressed liquid state. Which property is closest to that of saturated liquid at 0.1 MPa?
B · Specific volume is slightly less
In compressed liquid state, specific volume is slightly less than saturated liquid at the same pressure and temperature below saturation.
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Refer to the compressed liquid properties table below. At 0.5 MPa and 80°C, what is the approximate specific enthalpy?

Pressure (MPa)Temperature (°C)Specific Enthalpy (kJ/kg)
0.560250
0.580335
0.5100420
B · 335 kJ/kg
At 0.5 MPa and 80°C, the specific enthalpy of compressed liquid water is approximately 335 kJ/kg.
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Which of the following interpolation methods is most appropriate for estimating steam properties between two known values in steam tables?
A · Linear interpolation
Linear interpolation is commonly used to estimate steam properties between two tabulated values due to its simplicity and reasonable accuracy.
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Refer to the steam table excerpt below. Estimate the specific enthalpy at 0.9 MPa by linear interpolation between 0.8 MPa and 1.0 MPa.

Pressure (MPa)\( h_f \) (kJ/kg)
0.8721.1
1.0762.5
A · 741.8 kJ/kg
Using linear interpolation: \( h_f = 721.1 + \frac{0.9-0.8}{1.0-0.8} \times (762.5 - 721.1) = 721.1 + 0.5 \times 41.4 = 741.8 \) kJ/kg.
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Which interpolation technique is more accurate for steam property estimation when the property varies non-linearly with pressure or temperature?
A · Quadratic interpolation
Quadratic interpolation accounts for curvature in data and provides better accuracy for non-linear variations than linear interpolation.
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Which of the following best describes the Mollier diagram (h-s chart)?
A · A plot of enthalpy versus entropy for steam
The Mollier diagram is a graphical representation of enthalpy (h) versus entropy (s) for steam and is widely used in thermodynamic analysis.
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Which axis represents entropy in a Mollier diagram for steam?
A · Horizontal axis
In the Mollier diagram, entropy is plotted on the horizontal axis while enthalpy is on the vertical axis.
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Refer to the Mollier diagram below. Which region corresponds to saturated liquid?

Entropy (kJ/kg·K)Enthalpy (kJ/kg)Saturated Liquid LineSaturated Vapor Line
A · Left curve of the dome
The left curve of the dome in the Mollier diagram represents the saturated liquid line.
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Which of the following properties can be directly read from a Mollier diagram for a given steam state?
A · Enthalpy and entropy
The Mollier diagram plots enthalpy versus entropy, so these properties can be directly read for a given state.
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Refer to the Mollier diagram below. A steam state is marked at entropy \( s = 6.5 \) kJ/kg·K and enthalpy \( h = 2800 \) kJ/kg. What is the likely phase of steam?

State PointEntropy (kJ/kg·K)Enthalpy (kJ/kg)
B · Superheated steam
The state point lies to the right of the saturated dome indicating superheated steam.
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Which process is represented by a vertical line in the Mollier diagram?
B · Isenthalpic process
A vertical line in the Mollier diagram represents constant enthalpy (isenthalpic) process.
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In the Mollier diagram, an isentropic expansion process is represented by:
B · A horizontal line
Isentropic process means constant entropy, so it is represented by a horizontal line (constant \( s \)) on the Mollier diagram.
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Which of the following is a typical application of the Mollier diagram in thermodynamic problems?
A · Determining enthalpy changes during turbine expansion
The Mollier diagram is widely used to determine enthalpy and entropy changes during expansion or compression processes in turbines and compressors.
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Which of the following processes can be analyzed effectively using the Mollier diagram?
A · Isentropic expansion in turbines
Mollier diagram is particularly useful for analyzing isentropic expansion and compression processes in turbines and compressors.
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In the Mollier diagram, the saturated liquid line and saturated vapor line correspond respectively to:
A · Left and right boundaries of the dome
The saturated liquid line forms the left boundary and the saturated vapor line forms the right boundary of the dome in the Mollier diagram.
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Which statement best describes the relationship between steam tables and the Mollier diagram?
A · Steam tables provide numerical data, Mollier diagram provides graphical representation of the same data
Steam tables provide tabulated numerical values of steam properties, while the Mollier diagram graphically represents these properties for easier visualization and analysis.
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Which property pair is common to both steam tables and Mollier diagram for steam?
A · Enthalpy and entropy
Both steam tables and Mollier diagrams provide enthalpy and entropy values for steam states.
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Refer to the diagram below showing a portion of the Mollier diagram and steam table data. Which method would be more accurate for determining enthalpy at entropy \( s = 6.8 \) kJ/kg·K?

Entropy (kJ/kg·K)Enthalpy (kJ/kg)
A · Using steam tables with interpolation
Steam tables with interpolation provide more precise numerical values than graphical estimation from the Mollier diagram.
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Which of the following is an advantage of using the Mollier diagram over steam tables?
A · Quick visual estimation of thermodynamic processes
The Mollier diagram allows quick graphical analysis and visualization of thermodynamic processes, although steam tables provide more precise numerical data.
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Refer to the Mollier diagram below. If a steam state moves horizontally from left to right, which property remains constant?

Entropy (kJ/kg·K)Enthalpy (kJ/kg)
B · Enthalpy
Horizontal movement means enthalpy remains constant while entropy changes.
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Steam at 2.5 MPa and 350°C is throttled to 0.1 MPa. Using steam tables and the Mollier diagram, determine the change in enthalpy and entropy. Which of the following statements is true?
A · Enthalpy remains constant; entropy increases by 0.3 kJ/kg·K
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Steam at 4 MPa and 450°C expands isentropically to 0.1 MPa. Using the Mollier diagram, determine the exit temperature and quality of steam. Which of the following is correct?
A · Exit temperature = 140°C, quality = 0.90
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Steam at 5 MPa and 400°C is throttled to 0.1 MPa. Using steam tables and Mollier diagram, determine the entropy change and final dryness fraction. Which of the following is correct?
A · Entropy increases by 0.25 kJ/kg·K, dryness fraction = 0.85
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Steam at 3 MPa and 400°C is throttled to 0.1 MPa. Using steam tables and Mollier diagram, determine the entropy change and final dryness fraction. Which of the following is correct?
A · Entropy increases by 0.20 kJ/kg·K, dryness fraction = 0.87
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Steam at 6 MPa and 500°C expands isentropically to 0.1 MPa. Using the Mollier diagram, determine the enthalpy and entropy at turbine exit. Which of the following is correct?
C · h_exit = 2300 kJ/kg, s_exit = 7.2 kJ/kg·K
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Which of the following is the correct form of the Ideal Gas Equation?
A · \( PV = nRT \)
The Ideal Gas Equation is commonly expressed as \( PV = nRT \), where \(P\) is pressure, \(V\) is volume, \(n\) is number of moles, \(R\) is universal gas constant, and \(T\) is temperature.
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The Ideal Gas Equation can also be written as \( PV = mRT_s \). What does \( R_s \) represent in this equation?
B · Specific gas constant
In the form \( PV = mRT_s \), \( R_s \) is the specific gas constant which is related to the universal gas constant by \( R_s = \frac{R}{M} \), where \(M\) is molar mass.
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If the pressure of an ideal gas is doubled while keeping the temperature constant, what happens to its volume according to the Ideal Gas Law?
B · Volume halves
At constant temperature, pressure and volume are inversely proportional (Boyle's Law), so doubling pressure halves the volume.
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The universal gas constant \( R \) has a value of approximately:
A · 8.314 J/mol·K
The universal gas constant \( R \) is approximately 8.314 J/mol·K.
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The specific gas constant \( R_s \) for a gas is related to the universal gas constant \( R \) and molar mass \( M \) by which of the following relations?
B · \( R_s = \frac{R}{M} \)
The specific gas constant \( R_s \) is given by \( R_s = \frac{R}{M} \), where \( M \) is molar mass in kg/mol.
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A gas has a universal gas constant \( R = 8.314 \) J/mol·K and molar mass \( M = 28 \) g/mol. What is its specific gas constant \( R_s \) in J/kg·K?
B · 297.6
Convert molar mass to kg/mol: \( 28 \text{ g/mol} = 0.028 \text{ kg/mol} \). Then \( R_s = \frac{8.314}{0.028} = 297.6 \) J/kg·K.
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According to the Ideal Gas Law, if the volume and temperature of a gas are kept constant, what is the relationship between pressure and number of moles?
B · Pressure is directly proportional to number of moles
At constant volume and temperature, pressure is directly proportional to the number of moles \( n \) as per \( PV = nRT \).
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An ideal gas is compressed isothermally to half its original volume. What happens to its pressure?
B · Pressure doubles
For isothermal process, \( PV = constant \). Halving volume doubles pressure.
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A gas occupies 2 m\(^3\) at 300 K and 100 kPa. If the temperature is increased to 600 K at constant pressure, what is the new volume?
D · 4 m\(^3\)
At constant pressure, volume is proportional to temperature (Charles's Law). \( V_2 = V_1 \times \frac{T_2}{T_1} = 2 \times \frac{600}{300} = 4 \) m\(^3\).
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The molar mass of a gas is important in gas calculations because it allows conversion between:
B · Number of moles and mass
Molar mass converts between mass \( m \) and number of moles \( n \) via \( n = \frac{m}{M} \).
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A gas sample has a mass of 5 kg and molar mass of 20 kg/kmol. How many moles of gas are present?
A · 0.25 kmol
Number of moles \( n = \frac{m}{M} = \frac{5}{20} = 0.25 \) kmol.
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An ideal gas at 300 K and 1 atm pressure occupies 1 m\(^3\). If the gas is compressed to 0.5 m\(^3\) and temperature raised to 600 K, what is the final pressure?
A · 2 atm
Using \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \), \( P_2 = P_1 \times \frac{V_1}{V_2} \times \frac{T_2}{T_1} = 1 \times \frac{1}{0.5} \times \frac{600}{300} = 2 \) atm.
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A cylinder contains 2 kmol of an ideal gas at 300 K and 200 kPa. Calculate the volume occupied by the gas. (Use \( R = 8.314 \) kJ/kmol·K)
B · 24.94 m\(^3\)
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Which of the following is the correct form of the Ideal Gas Equation?
A · \( PV = nRT \)
The ideal gas equation is typically expressed as \( PV = nRT \), where \( n \) is the number of moles.
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If the pressure of an ideal gas is doubled while keeping temperature constant, what happens to its volume according to the ideal gas law?
B · Volume halves
According to \( PV = nRT \), if temperature and amount of gas are constant, pressure and volume are inversely proportional.
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Which of the following is NOT a correct form of the ideal gas equation?
A · \( PV = mRT \)
The ideal gas equation must include temperature \( T \); \( PV = mR \) is incomplete and incorrect.
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The universal gas constant \( R_u \) has a value approximately equal to:
A · 8.314 J/mol·K
The universal gas constant \( R_u \) is 8.314 J/mol·K, used in molar form of the ideal gas equation.
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The specific gas constant \( R \) for a gas is related to the universal gas constant \( R_u \) by which of the following relations?
A · \( R = \frac{R_u}{M} \)
The specific gas constant \( R \) is the universal gas constant divided by the molecular weight \( M \) of the gas.
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Given that the universal gas constant \( R_u = 8.314 \) J/mol·K and molecular weight of oxygen \( M = 32 \) kg/kmol, what is the specific gas constant \( R \) for oxygen?
B · 259 J/kg·K
Specific gas constant \( R = \frac{R_u}{M} = \frac{8.314}{0.032} = 259.8 \) J/kg·K approximately.
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Which of the following correctly expresses the relationship between the universal gas constant \( R_u \), specific gas constant \( R \), and molecular weight \( M \)?
A · \( R_u = R \times M \)
The universal gas constant is the product of specific gas constant and molecular weight: \( R_u = R \times M \).
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If the molecular weight of a gas is doubled, what happens to its specific gas constant \( R \), assuming \( R_u \) remains constant?
B · It halves
Since \( R = \frac{R_u}{M} \), doubling \( M \) halves \( R \).
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In an engineering problem, an ideal gas at 300 K and 1 atm occupies 2 m\(^3\). Using the ideal gas equation, what is the pressure if the volume is compressed to 1 m\(^3\) at constant temperature?
C · 2 atm
At constant temperature, pressure and volume are inversely proportional, so pressure doubles when volume halves.
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An ideal gas undergoes an isothermal expansion from 1 m\(^3\) to 3 m\(^3\) at 300 K. If initial pressure is 3 atm, what is the final pressure?
A · 1 atm
Using \( P_1 V_1 = P_2 V_2 \), \( P_2 = \frac{P_1 V_1}{V_2} = \frac{3 \times 1}{3} = 1 \) atm.
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Which of the following is a limitation of the ideal gas model?
A · It assumes no intermolecular forces
The ideal gas model assumes no intermolecular forces and zero molecular volume, which limits its accuracy at high pressures and low temperatures.
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Which assumption is NOT made in the ideal gas model?
D · Gas molecules have significant volume affecting pressure
Ideal gas molecules are assumed to have negligible volume; significant volume affecting pressure is not an assumption of the ideal gas model.
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An engineer uses the ideal gas equation to estimate gas behavior at very high pressure. Which of the following is a likely consequence?
D · The estimate will be invalid due to molecular interactions
At very high pressures, molecular volume and interactions become significant, violating ideal gas assumptions and invalidating the model.
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Which of the following engineering applications commonly uses the ideal gas equation?
A · Design of gas turbines
The ideal gas equation is widely used in gas turbine design and other thermodynamic systems involving gases.
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A gas with molar mass 28.97 kg/kmol is heated from 300 K to 600 K at constant pressure. Given Cp = 29 J/mol·K and R = 8.314 J/mol·K, calculate the change in enthalpy per kg of gas. Which of the following is correct?
A · A) ΔH = Cp (T2 - T1) / M = 29 * 300 / 0.02897 J/kg
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Assertion (A): The specific gas constant R for a gas is inversely proportional to its molar mass. Reason (R): R = R_universal / M, where M is molar mass of the gas. Choose the correct option:
A · A) Both A and R are true and R is the correct explanation of A
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An ideal gas with γ = 1.4 is compressed adiabatically from 100 kPa and 300 K to 500 kPa. Calculate the final temperature T2. Which of the following formulas correctly gives T2?
A · A) T2 = T1 (P2/P1)^{(γ-1)/γ}
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An ideal gas expands isothermally from volume V1 to V2 at temperature T. Given the universal gas constant R and number of moles n, which expression correctly represents the entropy change ΔS of the gas?
A · A) ΔS = n R ln(V2/V1)
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In an isochoric process, which of the following parameters remains constant?
B · Volume
An isochoric process is characterized by constant volume, meaning the volume does not change during the process.
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During an isochoric heating process of an ideal gas, what happens to the pressure and temperature?
C · Pressure increases, temperature increases
Since volume is constant in an isochoric process, heating increases temperature which causes the pressure to increase according to the ideal gas law.
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Which of the following is a typical example of an isochoric process?
B · Heating of gas in a rigid container
Heating gas in a rigid container keeps the volume fixed, making it an isochoric process.
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Refer to the diagram below showing a P-V plot of an isochoric process. What is the work done by the gas during this process?
B · Zero, since volume does not change
Work done by the gas is \( W = \int P dV \). Since volume is constant in an isochoric process, \( dV = 0 \) and work done is zero.
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In an isochoric process, the heat added to the system is equal to:
A · Change in internal energy
Since work done is zero in an isochoric process, the heat added changes only the internal energy of the system.
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Which of the following statements is TRUE for an isochoric process of an ideal gas?
C · Volume remains constant
By definition, an isochoric process occurs at constant volume.
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In an isobaric process, which thermodynamic property remains constant?
A · Pressure
An isobaric process is characterized by constant pressure throughout the process.
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During an isobaric expansion of an ideal gas, what happens to the volume and temperature?
B · Volume increases, temperature increases
At constant pressure, increasing volume requires an increase in temperature according to the ideal gas law.
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Which of the following is an example of an isobaric process?
B · Boiling water at atmospheric pressure
Boiling water at atmospheric pressure occurs at constant pressure, making it an isobaric process.
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Refer to the P-V diagram below for an isobaric process. What is the expression for work done by the gas during this process?
A · \( W = P (V_2 - V_1) \)
Work done in any process is \( W = \int P dV \). For constant pressure, \( W = P (V_2 - V_1) \).
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In an isobaric process, the heat added to the system is related to the change in which property?
B · Enthalpy
At constant pressure, heat added equals the change in enthalpy of the system.
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Which statement is TRUE for an isobaric process of an ideal gas?
B · Pressure remains constant
By definition, pressure remains constant in an isobaric process.
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In an isothermal process for an ideal gas, which of the following remains constant?
C · Temperature
An isothermal process is defined as a process occurring at constant temperature.
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During an isothermal expansion of an ideal gas, what happens to the internal energy of the gas?
C · Remains constant
For an ideal gas, internal energy depends only on temperature, which remains constant in an isothermal process.
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Which of the following expressions correctly represents the work done by an ideal gas during an isothermal process from volume \( V_1 \) to \( V_2 \)?
C · \( W = nRT \ln \frac{V_2}{V_1} \)
Work done in an isothermal process is \( W = nRT \ln \frac{V_2}{V_1} \), where temperature is constant.
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Refer to the P-V diagram below showing an isothermal expansion of an ideal gas. Which curve represents the process?
C · A hyperbolic curve
Isothermal processes for ideal gases are represented by hyperbolic curves on P-V diagrams due to \( PV = constant \).
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In an isothermal process, the heat transferred to the system is equal to:
B · Work done by the system
Since internal energy remains constant in an isothermal process, heat added equals the work done by the system.
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Which of the following processes is reversible and isothermal for an ideal gas?
B · Slow compression of gas in a piston-cylinder with heat exchange
Slow compression with heat exchange maintains constant temperature and reversibility, defining an isothermal reversible process.
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Which thermodynamic process is characterized by no change in entropy for an ideal gas?
C · Isothermal reversible
An isothermal reversible process is isentropic for an ideal gas, meaning entropy remains constant.
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Which of the following correctly describes a thermodynamic process characteristic?
A · In an adiabatic process, heat transfer is zero
An adiabatic process is defined by zero heat transfer to or from the system.
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Which of the following is TRUE for an adiabatic process of an ideal gas?
A · Heat transfer is zero
Adiabatic processes occur without heat transfer, but temperature, pressure, and volume can change.
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Which process is characterized by constant entropy for an ideal gas?
D · Isentropic
Isentropic processes are defined by constant entropy.
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Which thermodynamic process is represented by a vertical line on a P-V diagram?
B · Isochoric
A vertical line on a P-V diagram indicates constant volume, i.e., an isochoric process.
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Refer to the T-S diagram below. Which curve corresponds to an isothermal process?
A · Horizontal line
In a T-S diagram, an isothermal process occurs at constant temperature, represented by a horizontal line.
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On a P-V diagram, which process is represented by a horizontal line?
A · Isobaric
A horizontal line on a P-V diagram indicates constant pressure, i.e., an isobaric process.
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Refer to the P-V diagram below. Which process is represented by the curve labeled 'Process X' that shows a hyperbolic shape?
C · Isothermal
A hyperbolic curve on a P-V diagram represents an isothermal process where \( PV = constant \).
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In the T-S diagram, which process is represented by a vertical line?
B · Isentropic
A vertical line in a T-S diagram indicates constant entropy, i.e., an isentropic process.
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Refer to the process flow schematic below. Which process is depicted by the system where volume is fixed and heat is added?
B · Isochoric process
Heat addition at constant volume corresponds to an isochoric process.
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Calculate the work done by 2 moles of an ideal gas during an isothermal expansion from 10 L to 20 L at 300 K. (Use \( R = 8.314 \ \text{J/mol·K} \))
D · \( 4157 \ \text{J} \)
Work done \( W = nRT \ln \frac{V_2}{V_1} = 2 \times 8.314 \times 300 \times \ln(2) \approx 4157 \ \text{J} \).
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Calculate the heat added during an isobaric process where 1 mole of an ideal gas is heated from 300 K to 400 K at 1 atm. (Use \( R = 8.314 \ \text{J/mol·K} \), \( C_p = 29 \ \text{J/mol·K} \))
B · \( 870 \ \text{J} \)
Heat added \( Q = n C_p \Delta T = 1 \times 29 \times (400 - 300) = 870 \ \text{J} \).
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Calculate the work done during an isobaric expansion of 3 moles of ideal gas from 5 L to 15 L at 300 K. (Use \( R = 8.314 \ \text{J/mol·K} \), 1 atm = 101325 Pa)
A · \( 2.48 \times 10^3 \ \text{J} \)
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Calculate the change in internal energy for 1 mole of an ideal gas heated from 300 K to 400 K in an isochoric process. (Use \( C_v = 20.8 \ \text{J/mol·K} \))
A · \( 208 \ \text{J} \)
Change in internal energy \( \Delta U = n C_v \Delta T = 1 \times 20.8 \times (400 - 300) = 208 \ \text{J} \).
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Calculate the work done during an isothermal compression of 1 mole of ideal gas from 20 L to 10 L at 300 K. (Use \( R = 8.314 \ \text{J/mol·K} \))
A · \( -1728 \ \text{J} \)
Work done \( W = nRT \ln \frac{V_2}{V_1} = 1 \times 8.314 \times 300 \times \ln(\frac{10}{20}) = -1728 \ \text{J} \) (negative sign indicates work done on the gas).
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Calculate the heat transferred during an isochoric heating of 2 moles of an ideal gas from 300 K to 500 K. (Use \( C_v = 20.8 \ \text{J/mol·K} \))
C · \( 4160 \ \text{J} \)
Heat transferred \( Q = n C_v \Delta T = 2 \times 20.8 \times (500 - 300) = 4160 \ \text{J} \).
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Which of the following is a common real-life application of an isobaric process?
B · Boiling water at atmospheric pressure
Boiling water at atmospheric pressure occurs at constant pressure, an example of an isobaric process.
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Which thermodynamic process best describes the operation of a diesel engine compression stroke where volume decreases rapidly with negligible heat transfer?
D · Adiabatic
Rapid compression with negligible heat transfer is modeled as an adiabatic process.
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Which thermodynamic process occurs in a refrigerator evaporator where refrigerant absorbs heat at constant temperature?
C · Isothermal
Heat absorption at constant temperature in the evaporator is an isothermal process.
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Which of the following best describes the Carnot cycle?
A · A cycle consisting of two isothermal and two adiabatic reversible processes
The Carnot cycle is an ideal thermodynamic cycle consisting of two isothermal and two adiabatic reversible processes, representing the most efficient heat engine cycle possible.
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The working substance in a Carnot cycle operates between two thermal reservoirs at temperatures \( T_H \) and \( T_C \). Which statement is true about these temperatures?
B · Heat is absorbed at \( T_H \) and rejected at \( T_C \)
In the Carnot cycle, heat is absorbed isothermally from the hot reservoir at temperature \( T_H \) and rejected isothermally to the cold reservoir at temperature \( T_C \).
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Refer to the diagram below showing the Carnot cycle on a P-V diagram. Which process corresponds to the expansion of the working fluid at constant temperature?
A · Process 1-2 (Isothermal expansion)
In the Carnot cycle, process 1-2 is the isothermal expansion where the working fluid expands at the high temperature while absorbing heat.
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Which sequence correctly represents the four processes of the Carnot cycle?
A · Isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression
The Carnot cycle consists of isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression in that order.
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Refer to the T-S diagram below of a Carnot cycle. Which process represents the heat rejection to the cold reservoir?
A · Process 3-4 (Isothermal compression)
In the Carnot cycle T-S diagram, process 3-4 is the isothermal compression where heat is rejected to the cold reservoir at temperature \( T_C \).
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The efficiency \( \eta \) of a Carnot engine operating between temperatures \( T_H \) and \( T_C \) is given by:
A · \( \eta = 1 - \frac{T_C}{T_H} \)
The Carnot efficiency is derived as \( \eta = 1 - \frac{T_C}{T_H} \), where temperatures are absolute (Kelvin).
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Which of the following statements about Carnot efficiency is correct?
A · It represents the maximum possible efficiency any heat engine can achieve operating between two temperatures
Carnot efficiency is the theoretical maximum efficiency achievable by any heat engine operating between two reservoirs; no real engine can exceed it.
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Derive the expression for the efficiency of a Carnot engine if the heat absorbed from the hot reservoir is \( Q_H \) and heat rejected to the cold reservoir is \( Q_C \). Which of the following is correct?
A · \( \eta = \frac{Q_H - Q_C}{Q_H} \)
Efficiency is defined as work output over heat input, \( W = Q_H - Q_C \), so \( \eta = \frac{W}{Q_H} = \frac{Q_H - Q_C}{Q_H} \).
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Which of the following is a key significance of the Carnot cycle in thermodynamics?
A · It sets the upper limit on the efficiency of all heat engines
The Carnot cycle is significant because it establishes the theoretical maximum efficiency limit for all heat engines operating between two temperatures.
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Which implication follows from the Carnot theorem regarding reversible and irreversible engines operating between the same two reservoirs?
A · No irreversible engine can have efficiency greater than a reversible engine
Carnot theorem states that reversible engines have the maximum efficiency; irreversible engines operating between the same reservoirs have lower efficiency.
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In the context of the Carnot cycle, which statement about entropy change is true?
A · The total entropy change over one complete Carnot cycle is zero
The Carnot cycle is reversible; hence, the net entropy change over one complete cycle is zero.
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Which of the following best explains the role of reversibility in the Carnot cycle?
A · Reversibility ensures maximum efficiency and zero net entropy change
Reversibility in the Carnot cycle ensures no entropy generation, leading to maximum possible efficiency and zero net entropy change over the cycle.
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Which of the following correctly describes the four processes of the Carnot cycle?
B · Two isothermal and two adiabatic processes
The Carnot cycle consists of two isothermal processes (heat transfer at constant temperature) and two adiabatic processes (no heat transfer).
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During the isothermal expansion process in a Carnot cycle, which of the following statements is true?
B · The temperature remains constant while heat is absorbed
In the isothermal expansion process, the system absorbs heat at a constant temperature and does work on the surroundings.
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Refer to the schematic diagram below of a Carnot cycle. Which process corresponds to the adiabatic compression?
D · Process 4-1
In the Carnot cycle schematic, process 4-1 represents adiabatic compression where the system is compressed without heat exchange.
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The thermal efficiency \( \eta \) of a Carnot engine operating between temperatures \( T_H \) and \( T_C \) is given by:
B · \( 1 - \frac{T_C}{T_H} \)
The efficiency of a Carnot engine is \( \eta = 1 - \frac{T_C}{T_H} \), where temperatures are in absolute scale (Kelvin).
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If a Carnot engine operates between 500 K and 300 K, what is its maximum possible efficiency?
A · 0.40
Efficiency \( \eta = 1 - \frac{T_C}{T_H} = 1 - \frac{300}{500} = 0.40 \) or 40%.
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Refer to the T-S diagram below of a Carnot cycle. What is the area enclosed by the cycle on this diagram equal to?
B · Work done by the engine during one cycle
The area enclosed by the Carnot cycle on the T-S diagram represents the net work output of the cycle.
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Which of the following best explains the significance of the Carnot cycle in thermodynamics?
B · It provides a standard to compare the efficiency of real engines
The Carnot cycle sets the maximum possible efficiency for any heat engine operating between two temperatures, serving as a standard for real engines.
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Which of the following statements about the Carnot cycle's significance is true?
B · It shows that efficiency depends only on the temperature difference of reservoirs
Carnot cycle shows that maximum efficiency depends only on the temperatures of the hot and cold reservoirs, not on the working substance.
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Which of the following is an implication of Carnot's theorem for practical heat engines?
B · Irreversibility always reduces the efficiency below that of a Carnot engine
Irreversibility in practical engines causes efficiency to be less than the ideal Carnot efficiency.
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Refer to the P-V diagram below of a Carnot cycle. Which statement about reversibility and irreversibility is correct?
B · The cycle is reversible as all processes are carried out quasi-statically without friction
Carnot cycle is an ideal reversible cycle where all processes are carried out quasi-statically and without friction or dissipative effects.
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Which factor primarily causes irreversibility in a Carnot cycle when implemented in real engines?
B · Friction and unrestrained expansion
In real engines, friction and rapid (unrestrained) expansion cause irreversibility, reducing efficiency below that of the ideal Carnot cycle.
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Which process in the Otto cycle represents the constant volume heat addition?
C · Ignition of air-fuel mixture
In the Otto cycle, heat addition occurs at constant volume during the ignition of the air-fuel mixture, which is modeled as a constant volume process.
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In an ideal Otto cycle, the compression and expansion processes are assumed to be:
C · Isentropic
The compression and expansion strokes in an ideal Otto cycle are assumed to be isentropic (reversible adiabatic) processes.
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Refer to the P-V diagram below of an ideal Otto cycle. Which process corresponds to the heat rejection?
D · Process 4-1
In the Otto cycle, heat rejection occurs at constant volume during process 4-1 on the P-V diagram.
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Which of the following correctly describes the main difference between the Diesel cycle and the Otto cycle?
B · Diesel cycle has constant pressure heat addition, Otto cycle has constant volume heat addition
The Diesel cycle features heat addition at constant pressure, while the Otto cycle features heat addition at constant volume.
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In the Diesel cycle, which process represents the constant pressure heat addition?
B · Process 2-3 (constant pressure heat addition)
Heat addition in the Diesel cycle occurs during process 2-3 at constant pressure.
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Refer to the T-S diagram below of an ideal Diesel cycle. Which process corresponds to the constant pressure heat addition?
B · Process 2-3
In the Diesel cycle T-S diagram, process 2-3 is the constant pressure heat addition process.
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Which of the following best describes the dual combustion cycle (Otto-Diesel cycle)?
C · Heat addition occurs partly at constant volume and partly at constant pressure
The dual combustion cycle combines features of both Otto and Diesel cycles, with heat addition partly at constant volume and partly at constant pressure.
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Refer to the schematic diagram below of the dual combustion cycle. Which process represents the constant volume heat addition phase?
A · Process 2-3
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Which performance parameter is defined as the ratio of net work output to the heat input in a gas power cycle?
B · Thermal efficiency
Thermal efficiency is defined as the ratio of net work output to the heat input supplied to the cycle.
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Refer to the table below comparing Otto, Diesel, and Dual cycles. Which cycle generally has the highest thermal efficiency for the same compression ratio?
A · Otto cycle
For the same compression ratio, the Otto cycle generally has higher thermal efficiency than Diesel and Dual cycles because heat addition occurs at constant volume, which is more efficient.
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Given the following data for Otto and Diesel cycles operating at the same compression ratio, which statement is true regarding their mean effective pressures (MEP)?
B · Diesel cycle has higher MEP than Otto cycle
Diesel cycles generally have higher mean effective pressure due to higher compression ratios and longer combustion duration at constant pressure.
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For thermodynamic analysis of gas power cycles, which of the following assumptions is commonly made to simplify calculations?
A · Working fluid is an ideal gas with constant specific heats
Thermodynamic analysis of ideal gas power cycles often assumes the working fluid behaves as an ideal gas with constant specific heats to simplify calculations.
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Refer to the P-V diagram below showing Otto, Diesel, and Dual cycles. Which cycle's heat addition process includes both constant volume and constant pressure segments?
C · Dual combustion cycle
The dual combustion cycle uniquely combines heat addition at constant volume and constant pressure, as shown in the P-V diagram.
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In thermodynamic analysis, the mean effective pressure (MEP) is useful because it:
B · Represents an average pressure that, if acted on the piston during the power stroke, would produce the net work output
MEP is a hypothetical constant pressure that, acting on the piston during the power stroke, would produce the same net work as the actual cycle.
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Which of the following best describes the primary purpose of a vapour compression refrigeration cycle?
B · To transfer heat from a low temperature reservoir to a high temperature reservoir
The vapour compression refrigeration cycle transfers heat from a low temperature space (refrigerated space) to a high temperature environment, thus providing cooling.
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In a vapour compression refrigeration cycle, the refrigerant leaves the evaporator as:
B · Superheated vapour
The refrigerant leaves the evaporator as superheated vapour to ensure that no liquid enters the compressor, which could damage it.
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Refer to the diagram below of a basic vapour compression refrigeration cycle. Which component is responsible for increasing the pressure and temperature of the refrigerant vapour?
C · Compressor
The compressor compresses the refrigerant vapour, raising its pressure and temperature before it enters the condenser.
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Which component in the vapour compression refrigeration cycle is primarily responsible for reducing the pressure and temperature of the refrigerant?
B · Expansion valve
The expansion valve throttles the high-pressure liquid refrigerant, reducing its pressure and temperature before entering the evaporator.
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During which process in the vapour compression cycle does the refrigerant absorb heat from the refrigerated space?
C · Evaporation
In the evaporator, the refrigerant evaporates by absorbing heat from the refrigerated space, thus providing the cooling effect.
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Refer to the Pressure-Enthalpy (P-h) diagram below of a vapour compression refrigeration cycle. Which process corresponds to the throttling (expansion) process?
C · Process 3-4: Expansion (Throttling)
In the P-h diagram, the expansion process is represented by a vertical line from high pressure to low pressure at constant enthalpy, which is process 3-4.
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Which of the following expressions correctly defines the Coefficient of Performance (COP) for a refrigeration cycle?
B · COP = \( \frac{Refrigeration\ Effect}{Work\ Input} \)
COP for refrigeration is the ratio of refrigeration effect (heat absorbed in evaporator) to the work input to the compressor.
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Refer to the T-s diagram below of a vapour compression refrigeration cycle. Which process represents the isentropic compression of the refrigerant?
A · Process 1-2
In the T-s diagram, the vertical line (constant entropy) from state 1 to 2 represents the isentropic compression process in the compressor.
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Which refrigerant property is most critical for efficient heat absorption in the evaporator of a vapour compression cycle?
C · High latent heat of vaporization
A high latent heat of vaporization allows the refrigerant to absorb more heat during evaporation, improving cooling efficiency.
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Which of the following modifications to the vapour compression cycle improves the refrigeration effect by lowering the enthalpy of the refrigerant entering the expansion valve?
B · Subcooling the liquid refrigerant before the expansion valve
Subcooling the liquid refrigerant reduces its enthalpy before throttling, increasing the refrigeration effect and improving cycle efficiency.
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In an energy and mass flow analysis of a vapour compression refrigeration cycle, which of the following assumptions is generally valid for the compressor?
B · The compressor operates isentropically
The compression process is often assumed isentropic (adiabatic and reversible) for ideal analysis to simplify calculations.
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Refer to the schematic diagram below of a vapour compression refrigeration cycle with subcooling. What is the main advantage of adding a subcooler to the cycle?
C · Increases the refrigeration effect and COP
Subcooling the refrigerant liquid before expansion increases the refrigeration effect and improves the COP by reducing the enthalpy entering the expansion valve.

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