THE IDEAL-

• Equation of state: Any equation that relates the , , and specific of a substance. • The simplest : ideal-gas equation of state. This equation predicts the P-v-T behavior of a gas quite accurately within some properly selected region. equation of state

Note , P is absolute pressure T is absolute temperature

R: M: (kg/kmol) Different substances have different Ru: universal gas constant gas constants. 1 Mass = Molar mass  number

Real behave as an ideal Different forms of equation of state gas at low (i.e., low Pv= RT pressure, high PV=mRT temperature).

PV= NRuT

Ideal gas equation at two states for a fixed mass

P1V1=mRT1 P2V2=mRT2 The ideal-gas relation often is not applicable to real gases; thus, care should be exercised when using it.

2 When the Ideal gas equation is applicable

• The pressure is small compared to the critical pressure

P< Pcr

• The temperature is twice the critical temperature and pressure is less than 10 times of the critical pressure.

T=2Tcr and P<10Pcr

3 Is Water Vapor an Ideal Gas?

• YES: at below 10 kPa. • NO: in actual application (higher pressure environment) such as Steam Power Plant

4 4-7 FACTOR—A MEASURE OF DEVIATION FROM IDEAL-GAS BEHAVIOR Compressibility factor Z Z bigger than unity, the more the gas deviates A factor that accounts for from ideal-gas behavior. the deviation of real gases Gases behave as an ideal gas at low densities from ideal-gas behavior at (i.e., low pressure, high temperature). a given temperature and pressure. Pvreal =ZRT Pvideal =RT vreal/videal = Z

% error= [(videal-vreal)/vreal]*100

5 Generalized compressibility chart. We can determine compressibility factor Z for normalized pressure and temperature from Generalized Compressibility Chart

Here PR is called the reduced pressure and TR the reduced temperature. We can find Pcr and Tcr from Table A1. Z values for PR and TR from Generalized Compressibility Chart A-28 like below:

FIGURE A–28 Nelson–Obert generalized compressibility chart. 6 1. of State Van der Waals includes two effects not considered in the ideal-gas Eq. a/v2 is intermolecular forces, and b is volume occupied by the gas molecules. The constants a and b can be determined for any substance from the critical point data alone (Table A–1).

2. Beattie-Bridgeman Equation of State

The Beattie-Bridgeman equation of state based on five experimentally determined constants.

The values of the constants appearing in this equation are given in Table 3–4.

7 3. Benedict-Webb-Rubin Equation of State Benedict, Webb, and Rubin extended the Beattie-Bridgeman equation by raising the number of constants to eight.

The values of the constants appearing in this equation are given in Table 3–4.

8 • 3–84 Determine the specific volume of superheated water • vapor at 15 MPa and 350°C, using (a) the ideal-gas equation, • (b) the generalized compressibility chart, and (c) the steam • tables. Also determine the error involved in the first two cases.

9 • 3–84 Determine the specific volume of superheated water • vapor at 15 MPa and 350°C, using (a) the ideal-gas equation, • (b) the generalized compressibility chart, and (c) the steam • tables. Also determine the error involved in the first two cases.

15 0.68 623 0.96

% error= [(videal-vreal)/vreal]*100 10