Quick recall · 191 cards
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Which one of the following thermodynamic quantities is not a state function?
D · Work
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Which of the following clearly defines availability or exergy?
A · it is the maximum useful work obtainable from a system as it reaches the dead state
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Energy is ____ conserved and exergy is ____ conserved.
B · always, not generally
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For a closed system undergoing a process between two specified states, the decrease in availability (or exergy) of the system is always:
A · equal to the irreversibility of the system
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The exergy of an isolated system can ____
C · never increase
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The Clausius inequality holds good for
B · any cycle
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A reversible process is performed in such a way that
D · all of the mentioned
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Irreversibility of a process may be due to
C · both of the mentioned
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A heat transfer process approaches reversibility as the temperature difference between two bodies approaches
B · zero
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Which of the following can be a cause of irreversibility?
D · all of the mentioned
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Which of the following is true?
D · all of the mentioned
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The Clausius inequality holds good for
B · any cycle
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For a reversible isothermal isobaric process, which of the following quantities remains constant or has a specific property?
B · Gibbs free energy G decreases or remains minimum
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Which one of the following thermodynamic quantities is NOT a state function?
D · Work
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Which of the following best describes the first law of thermodynamics?
B · Energy can neither be created nor destroyed, only transformed
The first law of thermodynamics states that energy can neither be created nor destroyed, only transformed from one form to another.
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The first law of thermodynamics for a closed system can be expressed as \( \Delta U = Q - W \). What does \( W \) represent in this equation?
B · Work done by the system
In the first law for closed systems, \( W \) represents the work done by the system on the surroundings.
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In a closed system undergoing a cyclic process, the net heat transfer is 500 kJ. What is the net work done by the system over the cycle?
B · 500 kJ
For a cyclic process, the change in internal energy \( \Delta U = 0 \). Hence, net heat transfer equals net work done by the system.
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Which of the following statements is TRUE regarding the first law of thermodynamics for a closed system?
C · Energy can be transferred only as heat or work
Energy transfer in a closed system occurs only via heat or work; mass does not cross the system boundary.
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Refer to the diagram below of a piston-cylinder device. If 200 kJ of heat is added and the piston does 150 kJ of work on the surroundings, what is the change in internal energy of the gas inside the cylinder?
A · 50 kJ increase
Using first law: \( \Delta U = Q - W = 200 - 150 = 50 \) kJ increase.
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In a closed system, which of the following quantities is a state function?
C · Internal energy
Internal energy is a state function, depending only on the state of the system, not the path.
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A rigid tank contains 3 kg of an ideal gas at 300 K and 200 kPa. If 50 kJ of heat is removed, what happens to the internal energy of the gas?
B · Decreases by 50 kJ
Since volume is constant, no work is done. Heat removed decreases internal energy by 50 kJ.
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During a process in a closed system, 120 kJ of work is done on the system and 80 kJ of heat is lost by the system. What is the net change in internal energy?
A · 40 kJ increase
Work done on system is positive, heat lost is negative: \( \Delta U = Q - W = -80 - (-120) = 40 \) kJ increase.
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In an open system (control volume), which of the following energy terms must be considered in the first law energy balance?
B · Mass flow energy, heat transfer, and work done
In open systems, energy associated with mass flow (enthalpy, kinetic, potential) along with heat and work must be considered.
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Which of the following is NOT true for the first law of thermodynamics applied to an open system?
D · Enthalpy is not considered in energy balance
Enthalpy is a key property used in open system energy balances to account for flow energy.
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In a steady flow process, the energy balance equation includes all except:
A · Change in internal energy of the control volume
In steady flow, the internal energy of the control volume does not change with time.
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Which of the following energy interactions is NOT considered work in thermodynamics?
D · Heat transfer
Heat transfer is a form of energy transfer but not work.
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In a thermodynamic process, which of the following is a path function?
C · Work
Work depends on the path taken during the process, hence it is a path function.
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A gas undergoes a process where 100 kJ of heat is added and 60 kJ of work is done by the gas. What is the change in internal energy?
B · 40 kJ increase
Using first law: \( \Delta U = Q - W = 100 - 60 = 40 \) kJ increase.
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Which of the following statements is TRUE about heat and work in thermodynamics?
D · Both heat and work are path functions
Heat and work depend on the path taken during a process and are therefore path functions.
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Refer to the P-V diagram below showing a process from state 1 to state 2. Which of the following statements is correct regarding work done during this process?
A · Work done by the system equals the area under the curve from 1 to 2
Work done by the system during expansion or compression is the area under the P-V curve between the two states.
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Which of the following is a state function in thermodynamics?
C · Enthalpy
Enthalpy is a state function depending only on the state of the system.
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During an isochoric process in a closed system, which of the following is zero?
B · Work done
In an isochoric (constant volume) process, boundary work is zero because volume does not change.
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Refer to the diagram below of a control volume with steady flow. Which term represents the net work done by the system?
C · Shaft work output
Shaft work output is the net work done by the system in steady flow devices.
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In the steady flow energy equation, which of the following terms is usually negligible in most engineering applications?
D · Change in potential energy
Change in potential energy is often negligible compared to other energy terms in steady flow processes.
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Refer to the flowchart below representing energy interactions in a turbine. Which arrow represents the work output?
B · Work output from the turbine shaft
The work output from the turbine shaft is the useful work extracted from the fluid.
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A real gas in a piston-cylinder device expands from 5 bar and 400 K to 1 bar and 300 K. Which property must be known to accurately apply the first law?
C · Real gas internal energy or enthalpy data
For real gases, internal energy or enthalpy data from tables or equations of state are needed for accurate energy calculations.
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During a steady flow process of an ideal gas, the inlet velocity is 20 m/s and outlet velocity is 80 m/s. If the enthalpy drop is 150 kJ/kg, what is the kinetic energy change per unit mass?
A · 3 kJ/kg increase
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Which device converts heat energy into mechanical work under steady flow conditions?
B · Turbine
A turbine converts heat energy (enthalpy) of the fluid into mechanical work.
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In a heat exchanger operating under steady state, which of the following is TRUE according to the first law?
B · Heat is transferred between two fluids without work
Heat exchangers transfer heat between fluids without work or mass accumulation.
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Refer to the piston-cylinder diagram below. If the gas inside is compressed from 0.1 m³ to 0.05 m³ at constant pressure of 200 kPa, what is the work done on the gas?
A · 10 kJ done on the gas
Work done on gas = \( P \Delta V = 200 \times (0.05 - 0.1) = -10 \) kJ (negative work done by gas means 10 kJ done on gas).
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Which of the following devices typically requires work input to increase fluid pressure under steady flow?
B · Compressor
Compressors require work input to increase the pressure of a fluid.
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In a nozzle, the fluid velocity increases from 50 m/s to 250 m/s. Assuming no heat transfer and negligible potential energy change, what happens to the fluid enthalpy?
B · Decreases
Increase in velocity corresponds to a decrease in enthalpy due to conversion of enthalpy to kinetic energy.
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In a closed system, 500 kJ of work is done on the system and 200 kJ of heat is lost to the surroundings. If the internal energy of the system increases by 100 kJ, what is the net energy transfer?
A · 300 kJ into the system
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A gas in a piston-cylinder device undergoes a process where 250 kJ of work is done by the gas and 100 kJ of heat is added. If the internal energy decreases by 80 kJ, what is the net heat transfer?
A · 170 kJ added
First law: \( \Delta U = Q - W \). Rearranged: \( Q = \Delta U + W = -80 + 250 = 170 \; kJ \) added. But since 100 kJ is already added, net heat transfer is 170 kJ added in total.
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Refer to the diagram below showing a closed system undergoing a cyclic process on a P-V diagram. The area enclosed by the cycle is 500 kJ. What is the net work done by the system during the cycle?
A · 500 kJ done by the system
In a cyclic process, the net work done by the system equals the area enclosed by the P-V diagram. Positive area means work is done by the system.
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Refer to the flow process schematic below of a nozzle where steam enters at 2 MPa, 400 °C, and 20 m/s and leaves at 1 MPa and 300 °C. Assuming adiabatic flow, what is the velocity at the outlet?
C · 350 m/s
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Which of the following energy forms is NOT typically considered in the first law analysis of a steady-flow open system?
D · Nuclear energy
Nuclear energy is not considered in classical thermodynamic first law analyses of engineering systems; kinetic, potential, and internal energies are standard forms included.
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In an energy balance for a closed system, which of the following terms is always zero?
C · Mass flow across system boundary
In a closed system, no mass crosses the system boundary, so mass flow term is zero.
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Which of the following is a path function in thermodynamics?
C · Work
Work and heat are path functions; internal energy, enthalpy, and pressure are state functions.
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During a process in a closed system, 120 kJ of heat is added and 80 kJ of work is done by the system. If the internal energy increases by 30 kJ, what is the sign and magnitude of the net work done on the system?
B · 80 kJ work done by system
Work done by system is positive; given 80 kJ work done by system, so net work done on system is negative 80 kJ (work done by system).
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Refer to the diagram below of a piston-cylinder device where the gas expands from volume 0.1 m³ to 0.3 m³ at constant pressure of 200 kPa. Calculate the work done by the gas.
B · 40 kJ
Work done by gas at constant pressure: \( W = P \Delta V = 200 \times 10^3 \times (0.3 - 0.1) = 40,000 \; J = 40 \; kJ \).
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The specific heat at constant pressure \( C_p \) for an ideal gas is related to specific heat at constant volume \( C_v \) by which of the following relations?
B · \( C_p = C_v + R \)
For ideal gases, \( C_p = C_v + R \), where \( R \) is the gas constant.
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An ideal gas undergoes a process where its internal energy increases by 100 kJ and enthalpy increases by 150 kJ. What is the work done by the gas if the process occurs at constant pressure?
A · 50 kJ done by gas
At constant pressure, \( W = P \Delta V = \Delta H - \Delta U = 150 - 100 = 50 \; kJ \) done by the gas.
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Which of the following statements about specific heats of an ideal gas is TRUE?
A · Specific heats vary significantly with temperature
Specific heats for ideal gases vary with temperature but are often assumed constant over small temperature ranges.
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For an ideal gas, the change in internal energy depends primarily on which property?
B · Temperature
Internal energy of an ideal gas depends mainly on temperature.
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In a steady-flow process, the mass flow rate remains constant but the pressure and temperature of the fluid change with time. This process is classified as:
B · Unsteady flow process
If properties change with time at a point, the process is unsteady flow.
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Refer to the diagram below showing a control volume with varying inlet and outlet conditions over time. Which parameter must remain constant for the process to be steady flow?
A · Mass flow rate
Steady flow requires constant mass flow rate through the control volume.
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In an unsteady flow process, which of the following quantities changes with time inside the control volume?
B · Energy stored
Unsteady flow involves accumulation or depletion of mass or energy inside the control volume, so energy stored changes with time.
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A compressor compresses air from 100 kPa and 300 K to 500 kPa. If the process is adiabatic and reversible, which of the following assumptions is valid?
A · Isentropic process
Adiabatic and reversible process is isentropic.
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Which ideal gas assumption allows the use of \( PV = mRT \) to relate pressure, volume, and temperature?
D · All of the above
Ideal gas assumptions include negligible molecular volume, no intermolecular forces, and elastic collisions.
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For an ideal gas, the enthalpy change is related to temperature change by which of the following?
B · \( \Delta h = C_p \Delta T \)
Enthalpy change for ideal gas is \( \Delta h = C_p \Delta T \).
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An ideal gas expands from 1 m³ to 2 m³ at constant temperature. What is the change in internal energy?
A · Zero
For ideal gases, internal energy depends only on temperature. At constant temperature, \( \Delta U = 0 \).
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During a steady-flow process, the enthalpy of the fluid decreases by 100 kJ/kg and the velocity increases from 20 m/s to 60 m/s. What is the heat transfer per kg if the process is adiabatic?
A · 0 kJ/kg
Adiabatic means no heat transfer, so heat transfer is 0 kJ/kg.
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Which device converts fluid energy into mechanical work under steady-flow conditions?
B · Turbine
A turbine extracts work from fluid flow under steady conditions.
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In an ideal gas, the ratio of specific heats \( \gamma = \frac{C_p}{C_v} \) is 1.4. If \( C_v = 0.72 \; kJ/kg\cdot K \), what is \( C_p \)?
B · 1.01 kJ/kg\cdot K
\( C_p = \gamma C_v = 1.4 \times 0.72 = 1.008 \; kJ/kg\cdot K \), approximately 1.01.
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Which of the following is NOT an assumption of the ideal gas model?
D · Gas molecules have permanent dipole moments
Ideal gas model assumes no intermolecular forces, so permanent dipole moments are not considered.
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According to Clausius statement of the Second Law of Thermodynamics, which of the following is impossible?
A · Heat cannot flow spontaneously from a colder body to a hotter body without external work.
Clausius statement says that heat cannot spontaneously flow from cold to hot without work input, which is a fundamental restriction of the second law.
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Which of the following is an implication of the Second Law of Thermodynamics?
A · All natural processes are irreversible.
The second law implies that natural processes tend to increase entropy and are irreversible; complete conversion of heat to work is impossible.
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A heat engine absorbs 500 kJ of heat from a high-temperature reservoir and rejects 300 kJ to a low-temperature reservoir. What is the thermal efficiency of the engine?
A · 40%
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Which of the following factors does NOT affect the thermal efficiency of an ideal heat engine operating between two reservoirs?
A · Temperatures of the heat source and sink
For an ideal (Carnot) engine, efficiency depends only on reservoir temperatures, not on working fluid or heat input amount.
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A heat engine operates between reservoirs at 600 K and 300 K. What is the maximum possible efficiency?
A · 50%
Carnot efficiency \( \eta = 1 - \frac{T_{cold}}{T_{hot}} = 1 - \frac{300}{600} = 0.5 = 50\% \).
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Refer to the diagram below showing a heat engine cycle on a P-v diagram. Which area represents the net work output of the cycle?
A · Area enclosed by the cycle curve
The net work output of a cycle on a P-v diagram is represented by the area enclosed by the cycle path.
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A refrigerator removes 200 kJ of heat from the cold space and rejects 250 kJ to the surroundings. What is the coefficient of performance (COP) of the refrigerator?
A · 4.0
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Which of the following correctly defines the coefficient of performance (COP) of a heat pump?
A · COP = \( \frac{Q_{H}}{W} \), where \( Q_{H} \) is heat delivered to the hot reservoir
For heat pumps, COP is defined as heat delivered to the hot space divided by work input.
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A refrigerator operates between 270 K and 300 K. What is the maximum possible COP of this refrigerator?
A · 9
Maximum COP for refrigerator \( = \frac{T_{L}}{T_{H} - T_{L}} = \frac{270}{300 - 270} = \frac{270}{30} = 9 \). Correction: The correct answer is 9, so option A is correct.
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Refer to the T-s diagram below for a Carnot refrigerator operating between 280 K and 310 K. What is the coefficient of performance (COP) of this refrigerator?
A · 9.33
COP of Carnot refrigerator \( = \frac{T_{L}}{T_{H} - T_{L}} = \frac{280}{310 - 280} = \frac{280}{30} = 9.33 \).
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Which of the following statements about the Carnot cycle is TRUE?
A · It is the most efficient cycle operating between two temperature reservoirs.
The Carnot cycle is reversible and represents the maximum efficiency achievable between two temperature reservoirs, independent of working fluid.
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Refer to the P-v diagram below of a Carnot heat engine. Which process corresponds to isothermal expansion?
A · Process 1-2
In Carnot cycle, process 1-2 is isothermal expansion at high temperature where heat is absorbed.
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Which of the following best describes irreversibility in thermodynamic processes?
A · A process that generates entropy and cannot be reversed without external work
Irreversible processes generate entropy and cannot be reversed without additional work input.
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In a closed system, entropy generation occurs due to which of the following?
A · Friction and unrestrained expansion
Entropy generation occurs in irreversible processes such as friction and free expansion.
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Refer to the T-s diagram below showing an irreversible process between states 1 and 2. Which statement is TRUE regarding entropy change?
A · Entropy of the system increases and entropy is generated.
In an irreversible process, entropy of the system increases and entropy generation is positive.
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Which of the following is a key difference between practical and ideal heat engines?
A · Practical engines have irreversibilities causing lower efficiency than ideal engines.
Practical engines have losses and irreversibilities that reduce efficiency compared to ideal reversible engines.
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A practical refrigerator has a COP of 3.5 while the Carnot refrigerator operating between the same temperatures has a COP of 5. What is the percentage efficiency of the practical refrigerator relative to Carnot?
A · 70%
Percentage efficiency = \( \frac{3.5}{5} \times 100 = 70\% \).
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Refer to the T-s diagrams below comparing an ideal and a practical heat engine cycle. Which of the following is TRUE?
A · The practical cycle has larger entropy generation and lower efficiency.
Practical cycles have irreversibilities causing entropy generation and reduced efficiency compared to ideal cycles.
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Which of the following statements about T-s diagrams is TRUE for second law analysis?
A · The area under the process curve represents heat transfer.
In T-s diagrams, the area under the process curve corresponds to heat transfer (\( Q = \int T dS \)).
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Refer to the P-v diagram below of a real engine cycle. Which of the following indicates irreversibility?
A · Hysteresis or area loss compared to ideal cycle
Irreversibility in P-v diagrams is shown by hysteresis or area loss compared to ideal cycles.
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Refer to the T-s diagram below of a heat engine cycle. Which process corresponds to isentropic compression?
C · Process 3-4
In a Carnot cycle, process 3-4 is isentropic compression where entropy remains constant.
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In a thermodynamic process, which of the following indicates irreversibility?
B · Entropy generation is positive
Irreversibility in a process leads to positive entropy generation, indicating loss of useful energy.
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A heat engine absorbs 500 kJ of heat from a high-temperature reservoir and rejects 300 kJ to a low-temperature reservoir. What is the thermal efficiency of the engine?
A · 40%
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Refer to the diagram below showing a schematic of a simple heat engine. If the heat input is 800 kJ and the work output is 320 kJ, what is the heat rejected to the sink?
B · 480 kJ
From energy balance, \( Q_{in} = W_{out} + Q_{out} \) so \( Q_{out} = Q_{in} - W_{out} = 800 - 320 = 480 \) kJ.
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Which of the following factors does NOT affect the thermal efficiency of a heat engine?
D · Mass flow rate of the working fluid
Thermal efficiency depends on temperatures and heat flows, not directly on mass flow rate, which affects power output but not efficiency.
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A heat engine operates between reservoirs at 600 K and 300 K. What is the maximum possible efficiency according to Carnot's theorem?
A · 0.5
Carnot efficiency \( \eta = 1 - \frac{T_C}{T_H} = 1 - \frac{300}{600} = 0.5 \) or 50%.
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Refer to the T-S diagram below of a Carnot cycle. Which process corresponds to the isentropic expansion?
A · Process 1-2
In a Carnot cycle T-S diagram, isentropic processes are vertical lines (constant entropy). Process 1-2 is vertical indicating isentropic expansion.
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A refrigerator extracts 200 kJ of heat from the cold space and rejects 300 kJ to the surroundings. What is its coefficient of performance (COP)?
C · 2.0
COP of refrigerator \( = \frac{Q_L}{W} = \frac{Q_L}{Q_H - Q_L} = \frac{200}{300 - 200} = 2.0 \). But 2.0 is option C, so correctAnswer should be C.
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Which of the following statements about the coefficient of performance (COP) of a heat pump is TRUE?
B · COP of a heat pump is the ratio of heat delivered to the hot reservoir to the work input
COP of a heat pump is defined as \( \frac{Q_H}{W} \), heat delivered to hot reservoir divided by work input.
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Refer to the schematic diagram below of a vapor-compression refrigeration cycle. Which component is responsible for rejecting heat to the surroundings?
C · Condenser
The condenser rejects heat from the refrigerant to the surroundings.
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Which of the following expressions correctly represents the COP of an ideal refrigerator operating between temperatures \( T_L \) and \( T_H \)?
B · \( \frac{T_L}{T_H - T_L} \)
COP of an ideal (Carnot) refrigerator is \( \frac{T_L}{T_H - T_L} \).
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For a Carnot heat engine operating between 900 K and 300 K, what is the work output if the heat absorbed from the hot reservoir is 1200 kJ?
A · 800 kJ
Carnot efficiency \( \eta = 1 - \frac{300}{900} = \frac{2}{3} \). Work output \( W = \eta Q_{in} = \frac{2}{3} \times 1200 = 800 \) kJ.
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Refer to the P-V diagram below of a Carnot cycle. Which process represents the isothermal compression?
C · Process 3-4
In a Carnot cycle P-V diagram, isothermal compression is the process where volume decreases at constant temperature, usually process 3-4.
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Which of the following best describes entropy generation in an irreversible process?
C · Entropy generation is positive indicating irreversibility
Entropy generation is always positive in irreversible processes, indicating lost work potential.
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Refer to the entropy generation illustration below. Which process shows the highest irreversibility?
C · Process C with entropy generation of 0.5 kJ/K
Higher entropy generation indicates higher irreversibility; process C has the highest positive entropy generation.
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Which of the following is NOT a cause of irreversibility in thermodynamic processes?
D · Isentropic compression
Isentropic compression is an ideal reversible process and does not cause irreversibility.
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A heat engine has a thermal efficiency of 40% and rejects 600 kJ of heat to the sink. What is the heat absorbed from the source?
A · 1000 kJ
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Refer to the schematic below of a heat pump system. If the heat delivered to the hot reservoir is 500 kJ and the work input is 125 kJ, what is the COP of the heat pump?
A · 4.0
COP of heat pump \( = \frac{Q_H}{W} = \frac{500}{125} = 4.0 \).
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Which of the following is TRUE regarding the performance comparison of real and Carnot heat engines operating between the same two reservoirs?
C · Carnot efficiency is the maximum possible efficiency achievable
Carnot efficiency sets the upper limit for efficiency; real engines have lower efficiency due to irreversibilities.
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A refrigerator has a COP of 3. If it removes 600 kJ of heat from the refrigerated space, what is the work input to the refrigerator?
A · 200 kJ
COP \( = \frac{Q_L}{W} \Rightarrow W = \frac{Q_L}{COP} = \frac{600}{3} = 200 \) kJ.
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Which of the following best describes the entropy change of the universe for a reversible process?
C · Zero
For a reversible process, the entropy change of the universe is zero.
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Refer to the entropy generation illustration below. If the entropy generation for a process is 0.3 kJ/K and the heat transfer to the surroundings is 100 kJ at 300 K, what is the entropy change of the system?
A · -0.33 kJ/K
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In performance analysis, which of the following is a direct consequence of irreversibility in a heat engine?
C · Decrease in thermal efficiency
Irreversibility causes losses that reduce the thermal efficiency of the engine.
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A heat engine rejects 400 kJ of heat to the sink and produces 600 kJ of work. What is the heat absorbed from the source?
A · 1000 kJ
Energy balance: \( Q_{in} = W + Q_{out} = 600 + 400 = 1000 \) kJ.
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A heat engine working between 500 K and 300 K has an entropy generation rate of 0.02 kW/K. If the heat input is 1000 kW, calculate the work output and the efficiency of the engine.
A · Work output = 333 kW, Efficiency = 0.333
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Which of the following best defines a thermodynamic potential?
A · A state function used to determine equilibrium and spontaneity in thermodynamic systems
Thermodynamic potentials are state functions that help determine equilibrium conditions and spontaneity of processes in thermodynamics.
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Thermodynamic potentials are important because they allow us to:
B · Predict phase changes and chemical reactions at constant temperature and pressure
Thermodynamic potentials like Gibbs free energy are used to predict phase changes and chemical reaction spontaneity at constant temperature and pressure.
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Which of the following statements about thermodynamic potentials is TRUE?
B · Gibbs free energy is minimized at constant temperature and pressure
Gibbs free energy reaches a minimum at equilibrium for processes occurring at constant temperature and pressure.
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The internal energy \( U \) of a system is a function of which natural variables?
B · Entropy and volume
Internal energy \( U \) is naturally expressed as a function of entropy \( S \) and volume \( V \), i.e., \( U = U(S,V) \).
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Given the fundamental thermodynamic relation \( dU = TdS - PdV \), what does the term \( TdS \) represent physically?
B · Heat added to the system
The term \( TdS \) represents the heat added to the system in a reversible process.
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For an ideal gas, the internal energy depends primarily on which property?
B · Temperature
For an ideal gas, internal energy depends only on temperature and is independent of pressure and volume.
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Consider a system where the internal energy \( U \) is known. Which of the following expressions correctly represents the differential form of \( U \)?
B · \( dU = TdS - PdV \)
The correct differential form of internal energy is \( dU = TdS - PdV \), where \( T \) is temperature and \( P \) is pressure.
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Enthalpy \( H \) is defined as:
B · \( H = U + PV \)
Enthalpy \( H \) is defined as \( H = U + PV \), where \( U \) is internal energy, \( P \) is pressure, and \( V \) is volume.
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Which of the following is the natural variable set for enthalpy \( H \)?
C · Entropy and pressure
Enthalpy \( H \) is naturally expressed as a function of entropy \( S \) and pressure \( P \), i.e., \( H = H(S,P) \).
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Which of the following differential expressions correctly represents enthalpy \( H \)?
A · \( dH = TdS + VdP \)
The differential form of enthalpy is \( dH = TdS + VdP \), where \( T \) is temperature and \( V \) is volume.
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Helmholtz free energy \( A \) is defined as:
B · \( A = U - TS \)
Helmholtz free energy \( A \) is defined as \( A = U - TS \), where \( U \) is internal energy, \( T \) temperature, and \( S \) entropy.
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What are the natural variables of Helmholtz free energy \( A \)?
A · Temperature and volume
Helmholtz free energy \( A \) is naturally expressed as a function of temperature \( T \) and volume \( V \), i.e., \( A = A(T,V) \).
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The differential form of Helmholtz free energy \( A \) is:
A · \( dA = -SdT - PdV \)
The differential form of Helmholtz free energy is \( dA = -SdT - PdV \).
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Which of the following statements about Helmholtz free energy is correct?
C · It is minimized at constant temperature and volume
Helmholtz free energy is minimized at constant temperature and volume at equilibrium.
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Gibbs free energy \( G \) is defined as:
B · \( G = H - TS \)
Gibbs free energy \( G \) is defined as \( G = H - TS \), where \( H \) is enthalpy, \( T \) temperature, and \( S \) entropy.
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What are the natural variables of Gibbs free energy \( G \)?
B · Temperature and pressure
Gibbs free energy \( G \) is naturally expressed as a function of temperature \( T \) and pressure \( P \), i.e., \( G = G(T,P) \).
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The differential form of Gibbs free energy \( G \) is:
A · \( dG = -SdT + VdP \)
The differential form of Gibbs free energy is \( dG = -SdT + VdP \).
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At constant temperature and pressure, a spontaneous process occurs if:
B · The Gibbs free energy \( G \) decreases
At constant temperature and pressure, spontaneity is indicated by a decrease in Gibbs free energy \( G \).
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Which Maxwell relation is derived from the Helmholtz free energy \( A(T,V) \)?
A · \( \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V \)
From Helmholtz free energy \( A(T,V) \), the Maxwell relation is \( \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V \).
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Which Maxwell relation is derived from the Gibbs free energy \( G(T,P) \)?
A · \( \left( \frac{\partial S}{\partial P} \right)_T = -\left( \frac{\partial V}{\partial T} \right)_P \)
From Gibbs free energy \( G(T,P) \), the Maxwell relation is \( \left( \frac{\partial S}{\partial P} \right)_T = -\left( \frac{\partial V}{\partial T} \right)_P \).
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Which of the following is NOT a Maxwell relation?
C · \( \left( \frac{\partial V}{\partial T} \right)_P = \left( \frac{\partial S}{\partial P} \right)_T \)
The correct Maxwell relation is \( \left( \frac{\partial V}{\partial T} \right)_P = -\left( \frac{\partial S}{\partial P} \right)_T \), not positive as in option C.
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Legendre transformations are used in thermodynamics to:
B · Change the natural variables of thermodynamic potentials
Legendre transformations allow changing the natural variables of thermodynamic potentials, e.g., from \( U(S,V) \) to \( H(S,P) \).
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Which of the following is the Legendre transform of internal energy \( U(S,V) \) with respect to volume \( V \)?
A · Enthalpy \( H = U + PV \)
Enthalpy \( H \) is obtained by Legendre transforming \( U \) with respect to volume \( V \), replacing \( V \) by \( P \).
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Which thermodynamic potential is obtained by Legendre transforming internal energy \( U(S,V) \) with respect to entropy \( S \) and volume \( V \)?
C · Gibbs free energy \( G \)
Gibbs free energy \( G \) is obtained by Legendre transforming \( U \) with respect to both entropy \( S \) and volume \( V \), changing variables to temperature and pressure.
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Refer to the diagram below showing graphs of Gibbs free energy \( G \) vs temperature \( T \) for two phases of a substance. At which temperature does phase equilibrium occur?
A · At the temperature where both curves intersect
Phase equilibrium occurs at the temperature where Gibbs free energies of the two phases are equal, i.e., the intersection point.
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Which thermodynamic potential is most useful to determine the spontaneity of a reaction at constant temperature and volume?
C · Helmholtz free energy \( A \)
Helmholtz free energy \( A \) is used to determine spontaneity at constant temperature and volume.
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At constant temperature and pressure, the condition for equilibrium is:
D · \( dG = 0 \)
At constant temperature and pressure, equilibrium occurs when Gibbs free energy \( G \) is at a minimum, so \( dG = 0 \).
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Which thermodynamic potential decreases during a spontaneous isothermal and isobaric process?
D · Gibbs free energy \( G \)
Gibbs free energy \( G \) decreases during a spontaneous process at constant temperature and pressure.
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The differential form of the internal energy \( U(S,V) \) is given by \( dU = TdS - PdV \). Which of the following correctly expresses \( T \) and \( P \) in terms of partial derivatives?
A · \( T = \left( \frac{\partial U}{\partial S} \right)_V, \quad P = -\left( \frac{\partial U}{\partial V} \right)_S \)
Temperature \( T \) and pressure \( P \) can be expressed as \( T = \left( \frac{\partial U}{\partial S} \right)_V \) and \( P = -\left( \frac{\partial U}{\partial V} \right)_S \).
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Which of the following differential expressions correctly represents Gibbs free energy \( G(T,P) \)?
A · \( dG = -SdT + VdP \)
The differential form of Gibbs free energy is \( dG = -SdT + VdP \).
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Refer to the diagram below showing the variation of Helmholtz free energy \( A \) with temperature \( T \) at constant volume. What does the slope of the curve represent?
B · Entropy \( S \)
The slope of \( A \) vs \( T \) at constant volume is \( \left( \frac{\partial A}{\partial T} \right)_V = -S \), the negative entropy.
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Which of the following is the correct Legendre transformation to obtain Helmholtz free energy \( A \) from internal energy \( U \)?
A · \( A = U - TS \)
Helmholtz free energy \( A \) is obtained by Legendre transforming \( U \) with respect to entropy \( S \), replacing \( S \) by \( T \), giving \( A = U - TS \).
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Refer to the phase diagram below. Which thermodynamic potential is most useful to predict phase stability at constant temperature and pressure?
D · Gibbs free energy \( G \)
Gibbs free energy \( G \) is the appropriate potential to determine phase stability at constant temperature and pressure.
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Which thermodynamic potential is minimized at constant entropy and volume?
A · Internal energy \( U \)
Internal energy \( U \) is minimized at constant entropy and volume at equilibrium.
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Refer to the energy level schematic below. Which thermodynamic potential corresponds to the maximum useful work obtainable from a system at constant temperature and volume?
C · Helmholtz free energy \( A \)
Helmholtz free energy \( A \) represents the maximum useful work obtainable from a system at constant temperature and volume.
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Which of the following statements about Legendre transformations is FALSE?
B · They convert extensive variables into intensive variables
Legendre transformations do not convert extensive variables into intensive variables; they change the variables on which the function depends.
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Refer to the thermodynamic cycle schematic below. Which thermodynamic potential is most appropriate to analyze the work output of the cycle operating at constant temperature and volume?
C · Helmholtz free energy \( A \)
Helmholtz free energy \( A \) is used to analyze work output in cycles at constant temperature and volume.
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Which of the following best describes the significance of thermodynamic potentials in analyzing thermodynamic systems?
B · They represent state functions that help determine equilibrium and spontaneous processes
Thermodynamic potentials are state functions that provide valuable information about equilibrium conditions and spontaneity of processes, making them essential in thermodynamic analysis.
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Which thermodynamic potential is defined as the total energy contained within a system, including kinetic and potential energies at the microscopic level?
B · Internal energy (U)
Internal energy (U) is the total energy contained within the system, including microscopic kinetic and potential energies of molecules.
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For a system at constant pressure and temperature, which thermodynamic potential is minimized at equilibrium?
C · Gibbs free energy (G)
At constant pressure and temperature, the Gibbs free energy (G) is minimized at equilibrium, indicating the most stable state.
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Which of the following expressions correctly defines enthalpy (H) in terms of internal energy (U), pressure (P), and volume (V)?
B · \( H = U + PV \)
Enthalpy is defined as \( H = U + PV \), combining internal energy with the product of pressure and volume.
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Refer to the diagram below showing Helmholtz free energy \( A \) as a function of temperature for a system at constant volume. At which temperature does the system reach equilibrium?
B · At the temperature where \( A \) is minimum
At constant volume and temperature, the Helmholtz free energy \( A \) is minimized at equilibrium, indicating the most stable state.
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Which thermodynamic potential is most appropriate for analyzing chemical reactions occurring at constant temperature and pressure?
C · Gibbs free energy (G)
Gibbs free energy (G) is used to analyze chemical reactions at constant temperature and pressure, as it predicts spontaneity and equilibrium.
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Which of the following Maxwell relations is derived from the Helmholtz free energy \( A = U - TS \)?
A · \( \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V \)
From Helmholtz free energy, one Maxwell relation is \( \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V \).
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Legendre transformations are used in thermodynamics primarily to:
B · Transform one thermodynamic potential into another by changing natural variables
Legendre transformations allow changing the natural variables of a thermodynamic potential, thus defining new potentials like enthalpy or Gibbs free energy.
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At constant entropy and volume, which thermodynamic potential remains constant during a reversible process?
A · Internal energy (U)
At constant entropy and volume, the internal energy (U) remains constant during a reversible process as no heat or work is exchanged.
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Which of the following statements about the stability criteria related to thermodynamic potentials is TRUE?
C · The second derivative of internal energy with respect to entropy at constant volume must be positive for stability
For stability, the second derivative of internal energy with respect to entropy at constant volume must be positive, indicating a convex energy surface.
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Refer to the phase diagram below for a pure substance. At constant temperature and pressure, which thermodynamic potential determines the phase equilibrium?
C · Gibbs free energy (G)
Gibbs free energy (G) is minimized at phase equilibrium under constant temperature and pressure conditions, determining the stable phase.
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Which of the following is a correct Legendre transformation to obtain enthalpy (H) from internal energy (U)?
B · \( H = U + PV \)
Enthalpy is obtained from internal energy by adding the product of pressure and volume, which is a Legendre transformation changing the natural variable from volume to pressure.
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Which thermodynamic potential is most suitable for analyzing processes occurring at constant volume and temperature?
C · Helmholtz free energy (A)
Helmholtz free energy (A) is minimized at constant volume and temperature, making it suitable for analyzing such processes.
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Which of the following relations correctly expresses the differential form of Gibbs free energy \( G \)?
A · \( dG = -SdT + VdP \)
The differential form of Gibbs free energy is \( dG = -SdT + VdP \), showing its natural variables are temperature and pressure.
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Refer to the schematic below of a thermodynamic process at constant pressure. Which potential change corresponds to the heat absorbed by the system?
B · Change in enthalpy (\( \Delta H \))
At constant pressure, the heat absorbed by the system equals the change in enthalpy \( \Delta H \).
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Which of the following statements about Gibbs free energy \( G \) is FALSE?
D · It is minimized at equilibrium under constant volume and temperature
Gibbs free energy is minimized at constant temperature and pressure, not at constant volume and temperature.
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Which thermodynamic potential is most directly related to the maximum useful work obtainable from a system at constant temperature and volume?
C · Helmholtz free energy (A)
Helmholtz free energy (A) represents the maximum useful work obtainable from a system at constant temperature and volume.
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Which of the following is NOT a natural variable of internal energy (U)?
C · Temperature (T)
Internal energy is naturally expressed as a function of entropy and volume, not temperature.
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The Maxwell relation derived from the Gibbs free energy \( G(T,P) \) is:
A · \( \left( \frac{\partial S}{\partial P} \right)_T = -\left( \frac{\partial V}{\partial T} \right)_P \)
From Gibbs free energy, the Maxwell relation is \( \left( \frac{\partial S}{\partial P} \right)_T = -\left( \frac{\partial V}{\partial T} \right)_P \).
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Refer to the diagram below showing Gibbs free energy change \( \Delta G \) vs reaction coordinate for a chemical reaction. At which point is the reaction at equilibrium?
B · At the point where \( \Delta G = 0 \)
The reaction is at equilibrium when \( \Delta G = 0 \), indicating no net driving force for the reaction.
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Which of the following potentials is minimized during an isothermal-isobaric process at equilibrium?
C · Gibbs free energy (G)
Gibbs free energy is minimized during isothermal-isobaric processes at equilibrium.
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The Helmholtz free energy \( A \) is related to internal energy \( U \) by which of the following expressions?
B · \( A = U - TS \)
Helmholtz free energy is defined as \( A = U - TS \).
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Which of the following is a correct statement regarding the use of thermodynamic potentials in stability analysis?
B · Thermodynamic potentials must have a positive definite Hessian matrix for stability
Stability requires the thermodynamic potential to be convex, which mathematically means a positive definite Hessian matrix of second derivatives.
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Which thermodynamic potential is most useful for describing the maximum work obtainable from a system when both temperature and pressure are held constant?
C · Gibbs free energy (G)
Gibbs free energy (G) represents the maximum non-expansion work obtainable from a system at constant temperature and pressure.
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Refer to the diagram below showing the variation of Gibbs free energy \( G \) with pressure at constant temperature. Which pressure corresponds to phase equilibrium?
C · Where the Gibbs free energies of two phases intersect
Phase equilibrium occurs where the Gibbs free energies of two phases are equal, i.e., their curves intersect.
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Which of the following is NOT a thermodynamic potential?
C · Entropy (S)
Entropy (S) is a state function but not a thermodynamic potential; potentials are energy-related functions.
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Which thermodynamic potential is most appropriate for describing spontaneous processes at constant volume and temperature?
C · Helmholtz free energy (A)
At constant volume and temperature, spontaneous processes occur with a decrease in Helmholtz free energy (A).
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Which of the following expressions correctly relates Gibbs free energy \( G \) to Helmholtz free energy \( A \)?
A · \( G = A + PV \)
Gibbs free energy is related to Helmholtz free energy by \( G = A + PV \).
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In a chemical reaction at constant temperature and pressure, the reaction is spontaneous if:
B · \( \Delta G < 0 \)
A reaction is spontaneous at constant temperature and pressure if the Gibbs free energy change \( \Delta G < 0 \).
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Which of the following is a correct expression for the Helmholtz free energy differential \( dA \)?
A · \( dA = -SdT - PdV \)
The differential form of Helmholtz free energy is \( dA = -SdT - PdV \).
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Which of the following describes the role of Legendre transformations in thermodynamics?
B · They allow changing the natural variables of thermodynamic potentials
Legendre transformations are mathematical operations that change the natural variables of thermodynamic potentials, enabling new potentials to be defined.
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Refer to the diagram below showing the variation of Helmholtz free energy \( A \) with volume at constant temperature. What does the minimum point indicate?
B · Mechanical equilibrium
The minimum of Helmholtz free energy at constant temperature with respect to volume indicates mechanical equilibrium.
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Which of the following is a correct stability criterion for a system described by Gibbs free energy \( G \)?
A · \( \left( \frac{\partial^2 G}{\partial T^2} \right)_P > 0 \)
For stability, the Gibbs free energy must be convex, so the second derivative with respect to temperature at constant pressure must be positive.
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Which thermodynamic potential is most appropriate to analyze a process occurring at constant entropy and pressure?
B · Enthalpy (H)
Enthalpy (H) is the natural potential for processes at constant entropy and pressure.
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Which of the following expressions correctly represents the Legendre transformation from internal energy \( U(S,V) \) to Helmholtz free energy \( A(T,V) \)?
B · \( A = U - TS \)
Helmholtz free energy is obtained by Legendre transforming internal energy with respect to entropy, \( A = U - TS \).
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In a system undergoing a reversible isothermal expansion at constant temperature, the change in Helmholtz free energy \( \Delta A \) is equal to:
A · Maximum work done by the system
During a reversible isothermal process, the change in Helmholtz free energy equals the maximum work obtainable from the system.
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Which of the following statements about enthalpy (H) is TRUE?
C · It is useful for analyzing processes at constant pressure
Enthalpy is useful for analyzing processes at constant pressure and is defined as \( H = U + PV \).
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Refer to the diagram below showing the variation of Gibbs free energy with temperature at constant pressure. What does the intersection point of two curves represent?
B · Phase transition temperature
The intersection of Gibbs free energy curves for two phases at constant pressure indicates the phase transition temperature.
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Which thermodynamic potential is minimized during an adiabatic and isochoric (constant volume) process?
A · Internal energy (U)
During an adiabatic and constant volume process, internal energy (U) is minimized.
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Which of the following is a correct Maxwell relation derived from the enthalpy \( H(S,P) \)?
A · \( \left( \frac{\partial T}{\partial P} \right)_S = \left( \frac{\partial V}{\partial S} \right)_P \)
From enthalpy, the Maxwell relation is \( \left( \frac{\partial T}{\partial P} \right)_S = \left( \frac{\partial V}{\partial S} \right)_P \).
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Which thermodynamic potential is most suitable for analyzing the maximum work output of a system undergoing an isothermal expansion at constant volume?
B · Helmholtz free energy (A)
Helmholtz free energy (A) is used to analyze maximum work output at constant temperature and volume.
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Which of the following is TRUE regarding the use of Gibbs free energy in chemical reactions?
B · It predicts the direction of spontaneous reactions at constant T and P
Gibbs free energy predicts spontaneity and equilibrium direction for reactions at constant temperature and pressure.
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Which of the following correctly describes the natural variables of enthalpy (H)?
C · Entropy (S) and Pressure (P)
Enthalpy is naturally expressed as a function of entropy and pressure, \( H(S,P) \).
