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Steam is one of the most widely used working fluids in engineering applications, especially in power generation, heating, and industrial processes. Understanding steam's thermodynamic properties is essential for designing and analyzing systems like steam turbines, boilers, and condensers. However, steam does not behave like an ideal gas in many practical situations, especially near the phase change region where water and steam coexist. Therefore, accurate data on steam properties such as pressure, temperature, volume, enthalpy, and entropy are crucial.
Steam tables and Mollier diagrams are indispensable tools that provide this data in an organized and accessible form. Steam tables list numerical values of steam properties at various pressures and temperatures, while Mollier diagrams graphically represent these properties, enabling quick visualization and analysis of thermodynamic processes. Mastery of these tools is vital for solving engineering problems efficiently, particularly in competitive exams where time and accuracy are critical.
To understand steam tables and Mollier diagrams, we first need to grasp the fundamental properties of steam and how they relate to each other.
A thermodynamic state of steam is described by properties such as:
Steam exists in different phases depending on pressure and temperature:
The relationship between pressure, specific volume, and temperature for steam can be visualized as a three-dimensional surface called the p-v-T surface. This surface distinctly shows the regions of saturated liquid, saturated vapor, wet steam, and superheated steam.
Figure: Simplified schematic of the p-v-T surface showing saturated liquid and vapor lines, wet steam region, and superheated steam area.
Understanding this surface helps identify the phase of steam for given pressure and temperature, which is essential before selecting the correct steam table or diagram for property evaluation.
Steam tables are tabulated data sets that provide thermodynamic properties of steam at various pressures and temperatures. They are divided mainly into two categories:
These tables list properties of saturated liquid and saturated vapor at different pressures or temperatures. They include values for:
These tables provide properties of steam at pressures above saturation pressure and temperatures higher than saturation temperature. They include:
To find steam properties:
| Pressure (MPa) | \(T_{sat}\) (°C) | \(v_f\) (m³/kg) | \(v_g\) (m³/kg) | \(h_f\) (kJ/kg) | \(h_g\) (kJ/kg) | \(s_f\) (kJ/kg·K) | \(s_g\) (kJ/kg·K) |
|---|---|---|---|---|---|---|---|
| 0.1 | 99.61 | 0.00104 | 1.6720 | 419.04 | 2675.5 | 1.3036 | 7.3549 |
| 0.5 | 151.83 | 0.00109 | 0.3749 | 640.09 | 2748.7 | 1.8718 | 6.5926 |
| 1.0 | 179.91 | 0.00109 | 0.1944 | 762.81 | 2776.2 | 2.1384 | 6.4469 |
| Temperature (°C) | Specific Volume \(v\) (m³/kg) | Enthalpy \(h\) (kJ/kg) | Entropy \(s\) (kJ/kg·K) |
|---|---|---|---|
| 200 | 0.25798 | 2796.5 | 6.5967 |
| 300 | 0.31998 | 3051.5 | 6.9590 |
| 400 | 0.38642 | 3306.7 | 7.2693 |
The Mollier diagram is a graphical representation of steam properties, plotting enthalpy (\(h\)) against entropy (\(s\)). It is a powerful tool for visualizing thermodynamic processes and quickly estimating property changes without extensive table lookups.
Figure: Mollier diagram showing saturated liquid and vapor lines, superheated region, and an example isentropic expansion path.
Key features of the Mollier diagram:
By plotting initial and final states on this chart, engineers can quickly estimate enthalpy changes, work done, and efficiency of steam processes such as expansion in turbines or compression in pumps.
Step 1: Locate the pressure 0.5 MPa in the saturated steam table.
Step 2: Read the corresponding saturation temperature \(T_{sat}\), which is 151.83 °C.
Step 3: Read the specific volume of saturated vapor \(v_g = 0.3749 \, m^3/kg\).
Step 4: Read the enthalpy of saturated vapor \(h_g = 2748.7 \, kJ/kg\).
Step 5: Read the entropy of saturated vapor \(s_g = 6.5926 \, kJ/kg·K\).
Answer: At 0.5 MPa, \(T_{sat} = 151.83^\circ C\), \(v_g = 0.3749 \, m^3/kg\), \(h_g = 2748.7 \, kJ/kg\), \(s_g = 6.5926 \, kJ/kg·K\).
Step 1: Identify initial state on Mollier diagram at 3 MPa and 400 °C. From superheated region, note initial enthalpy \(h_1\) (approx. 3200 kJ/kg) and entropy \(s_1\).
Step 2: Since expansion is isentropic, entropy remains constant: \(s_2 = s_1\).
Step 3: Move vertically downward on the Mollier diagram to pressure 0.1 MPa along the constant entropy line to find final enthalpy \(h_2\) (approx. 2700 kJ/kg).
Step 4: Calculate work done by turbine per kg steam:
\[ W = h_1 - h_2 = 3200 - 2700 = 500 \, kJ/kg \]
Answer: The enthalpy at final state is approximately 2700 kJ/kg, and the turbine work output is 500 kJ/kg.
Step 1: Find initial enthalpy \(h_1\) and entropy \(s_1\) at 3 MPa and 350 °C from superheated steam tables.
From tables: \(h_1 = 3115.5 \, kJ/kg\), \(s_1 = 6.7 \, kJ/kg·K\).
Step 2: At turbine exit pressure 10 kPa, find enthalpy \(h_2\) for isentropic expansion (constant entropy \(s_2 = s_1 = 6.7\)).
At 10 kPa, saturation temperature is 45.8 °C. Since \(s_1 > s_g\) at 10 kPa, steam is wet.
From saturated steam tables at 10 kPa:
Calculate quality \(x\):
\[ x = \frac{s_2 - s_f}{s_g - s_f} = \frac{6.7 - 0.6492}{8.1489 - 0.6492} = \frac{6.0508}{7.4997} \approx 0.807 \]
Calculate enthalpy at turbine exit:
\[ h_2 = h_f + x h_{fg} = 191.81 + 0.807 \times 2392.8 = 191.81 + 1930.9 = 2122.7 \, kJ/kg \]
Step 3: Calculate turbine work output:
\[ W_{turbine} = h_1 - h_2 = 3115.5 - 2122.7 = 992.8 \, kJ/kg \]
Step 4: Calculate heat added in boiler:
Assuming feedwater enters boiler as saturated liquid at 10 kPa, \(h_f = 191.81 \, kJ/kg\).
\[ Q_{in} = h_1 - h_f = 3115.5 - 191.81 = 2923.7 \, kJ/kg \]
Answer: Turbine work output is 992.8 kJ/kg and heat added in boiler is 2923.7 kJ/kg.
Step 1: Locate pressure 2 MPa in superheated steam tables.
Step 2: Find the row corresponding to 400 °C.
Step 3: Read the specific volume \(v = 0.127 \, m^3/kg\), enthalpy \(h = 3215.5 \, kJ/kg\), and entropy \(s = 6.85 \, kJ/kg·K\).
Answer: At 2 MPa and 400 °C, \(v = 0.127 \, m^3/kg\), \(h = 3215.5 \, kJ/kg\), \(s = 6.85 \, kJ/kg·K\).
Step 1: From Mollier diagram or tables, find initial enthalpy \(h_1\) and entropy \(s_1\) at 4 MPa and 450 °C.
Approximate values: \(h_1 = 3300 \, kJ/kg\), \(s_1 = 7.0 \, kJ/kg·K\).
Step 2: For isentropic expansion to 0.1 MPa, find enthalpy \(h_{2s}\) at \(s = s_1 = 7.0\) and \(p = 0.1\) MPa from Mollier diagram or tables.
Approximate \(h_{2s} = 2600 \, kJ/kg\).
Step 3: Given actual enthalpy at exit \(h_2 = 2700 \, kJ/kg\).
Step 4: Calculate turbine isentropic efficiency \(\eta_t\):
\[ \eta_t = \frac{h_1 - h_2}{h_1 - h_{2s}} = \frac{3300 - 2700}{3300 - 2600} = \frac{600}{700} = 0.857 \, (85.7\%) \]
Answer: The turbine isentropic efficiency is approximately 85.7%.
When to use: When given pressure and temperature, to decide whether to use saturated or superheated steam tables.
When to use: When steam is in the two-phase region and properties are not directly given.
When to use: To quickly estimate steam state without referring to tables during exams.
When to use: When analyzing turbines, compressors, or expansion processes to save time on calculations.
When to use: During exam preparation to reduce time spent on property lookup.
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