1. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 1 Equation of State for Gases EQUATIONS OF STATE FOR GASES

2. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 2 Equation of State for Gases Real gases... Compressibility Factor

3. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 3 Equation of State for Gases Real Gases P 1 Z T1T1 T2T2 T3T3 T 1 < T 2 < T 3 Ideal Gas

4. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-13 FIGURE 2-51 Comparison of Z factors for various gases. Z = v actual /v ideal

5. Reduced pressure and temperature Generalized Compressibility Chart T r1 T r2 Z PrPr P r = P/P critical T r = T/T critical (14.6) Figures A30abc page 867 v R = v actual /(RT cr /P cr )

6. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 6 Equation of State for Gases Real gases... Van der Waals Equation 2 gas-specific constants a and b calculated from critical values Found in Table A-1

7. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 7 Equation of State for Gases Real gases... Beattie-Bridgeman Equation 5 gas-specific constants Found in Table 2-4 for ρ ≤.8ρ cr

8. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 8 Equation of State for Gases Real gases... Benedict-Webb-Rubin Equation 8 gas-specific constants Found in Table 2-4 for ρ ≤ 2.5ρ cr

9. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-14 FIGURE 2-60 Percentage of error involved in various equations of state for nitrogen.

10. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 10 Equation of State for Gases Real gases... Stonebridge Equation 16 gas-specific constants

11. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 11 Equation of State for Gases Real gases... Virial Equation Variable number of constants

12. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 12 Equation of State for Gases Specific Heats or Specific Energy

13. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 13 Equation of State for Gases Specific heat at constant volume

14. Instructor’s Visual Aids Heat Work and Energy. A First Course in Thermodynamics © 2001, F. A. Kulacki Chapter 2 Module 3 Slide 14 Equation of State for Gases Specific heat at constant pressure Always larger than c v because work is done by expanding substance. Are properties, and depend on the state, so can vary with temp.