How to Use Steam Tables on the FE Exam
Steam tables are one of the most important reference tools for thermodynamics problems on the FE exam. They provide the thermodynamic properties of water and steam at various pressures and temperatures. Knowing how to navigate these tables quickly and correctly is a critical exam skill.
What Steam Tables Contain
The NCEES Reference Handbook contains steam tables organized in several sections:
- Saturated water tables (by temperature): Properties of water and steam at saturation conditions, organized by temperature.
- Saturated water tables (by pressure): The same information organized by pressure instead of temperature.
- Superheated steam tables: Properties of steam at temperatures above the saturation temperature for a given pressure.
- Compressed liquid tables: Properties of water at pressures above the saturation pressure for a given temperature.
Key Properties in the Tables
- T: Temperature
- P: Pressure
- v_f, v_g: Specific volume of saturated liquid (f) and saturated vapor (g)
- h_f, h_fg, h_g: Specific enthalpy of saturated liquid, enthalpy of vaporization, and saturated vapor
- s_f, s_fg, s_g: Specific entropy of saturated liquid, entropy of vaporization, and saturated vapor
- u_f, u_g: Specific internal energy of saturated liquid and saturated vapor
Step 1: Determine the State of the Water
Before looking up properties, you must determine what state the water is in:
- Compressed liquid: Temperature is below the saturation temperature at the given pressure (or pressure is above the saturation pressure at the given temperature).
- Saturated liquid-vapor mixture: Temperature and pressure correspond to saturation conditions, and the substance is partly liquid and partly vapor.
- Superheated vapor: Temperature is above the saturation temperature at the given pressure.
To determine the state:
- If given T and P: Look up the saturation temperature at the given P. If T is less than T_sat, the water is compressed liquid. If T equals T_sat, it is at saturation. If T is greater than T_sat, it is superheated.
- If given T and quality (x): The substance is a saturated mixture by definition.
Step 2: Find Properties for Each State
Compressed Liquid
For compressed liquids, the properties are approximately equal to the saturated liquid properties at the given temperature:
h approximately equals h_f at T, v approximately equals v_f at T, etc.
For more precision, use the compressed liquid tables if available, but the saturated liquid approximation is usually sufficient for the FE exam.
Saturated Mixture
For a saturated liquid-vapor mixture with quality x (where x = mass of vapor / total mass):
- v = v_f + x * v_fg, where v_fg = v_g - v_f
- h = h_f + x * h_fg
- s = s_f + x * s_fg
- u = u_f + x * u_fg
If you know the specific volume, enthalpy, or entropy and need to find quality:
x = (v - v_f) / v_fg = (h - h_f) / h_fg = (s - s_f) / s_fg
Quality must be between 0 and 1. If x is less than 0, the substance is compressed liquid. If x is greater than 1, it is superheated vapor.
Superheated Vapor
For superheated steam, use the superheated steam tables. Find the section corresponding to the given pressure, then look up properties at the given temperature. You may need to interpolate between table entries if the exact temperature is not listed.
Linear Interpolation
When the exact temperature or pressure is not in the table, use linear interpolation:
h = h_1 + (h_2 - h_1) * (T - T_1) / (T_2 - T_1)
Where T_1 and T_2 are the table temperatures bracketing your value, and h_1 and h_2 are the corresponding enthalpy values.
Common Problem Types
Rankine Cycle Analysis
Find enthalpy at each state point of the cycle using steam tables:
- State 1 (pump inlet): Saturated liquid at condenser pressure. h_1 = h_f at P_condenser.
- State 2 (pump outlet): Compressed liquid at boiler pressure. h_2 approximately equals h_1 + v_f * (P_boiler - P_condenser).
- State 3 (turbine inlet): Superheated steam at boiler pressure and temperature. Look up in superheated tables.
- State 4 (turbine outlet): Typically a saturated mixture at condenser pressure. Use isentropic expansion: s_4 = s_3, then find quality and enthalpy.
Isentropic Expansion
For an ideal (isentropic) expansion in a turbine, entropy remains constant: s_2 = s_1. Use this to determine the state at the turbine exit:
- Find s_1 from the superheated tables at the turbine inlet conditions.
- At the exit pressure, compare s_1 to s_f and s_g to determine the exit state.
- If s_f is less than s_1 which is less than s_g: it is a saturated mixture. Find x = (s_1 - s_f) / s_fg and then h_2 = h_f + x * h_fg.
- If s_1 is greater than s_g: it is superheated. Interpolate in the superheated tables.
Tips for Using Steam Tables on the FE Exam
- Know the table layout. Spend time during your study sessions becoming familiar with how the handbook's steam tables are organized.
- Always determine the state first. This tells you which table to use.
- Practice interpolation. Many problems require values between table entries.
- Watch your units. Make sure you are using consistent units for pressure (kPa vs MPa, psi vs atm) and temperature (C vs K, F vs R).
- Mark reference pages. During the exam, note which pages of the handbook contain the steam tables so you can find them quickly when needed.
Steam tables are a tool that becomes intuitive with practice. Work through at least 10 to 15 thermodynamics problems using the actual reference handbook tables, and you will develop the speed and confidence needed for the exam.