Physical Chemistry Third Edition

76 2 Work, Heat, and Energy: The First Law of Thermodynamics

Equation (2.5-13a) is a good approximation. The other two equations are fairly good

approximations near room temperature.

Exercise 2.21

a.Look upCP, mfor helium, neon, and argon at 298.15 K in Appendix A. Compare each value

with 5R/2. Your results will test our assertion in Eq. (2.5-13a).

b.Look upCP, mfor N 2 ,O 2 , and CO at 298.15 K in Appendix A. Compare each value with

7 R/2.

If the approximations in Eq. (2.5-13) are not adequate,CP, mcan be represented by

the polynomial

CP, ma+bT+cT−^2 (2.5-13d)

Table A.6 in Appendix A gives the values of the constant parametersa,b, andcfor

several gases.

Exercise 2.22

EvaluateCP, mfor CO 2 at 298.15 K, 500 K, and 1000 K using the formula of Eq. (2.5-13d) and

compare your result with the values in Table A.8.

The ratio of the constant-pressure heat capacity to the constant-volume heat capacity

is denoted byγ:

γ

CP

CV

(definition ofγ) (2.5-14)

The values in Eq. (2.5-13) give the following approximations:

γ≈ 5 /3 (dilute monatomic gas) (2.5-15a)

γ≈ 7 /5 (dilute diatomic or linear polyatomic gases) (2.5-15b)

γ≈ 4 /3 (dilute nonlinear polyatomic gases) (2.5-15c)

For many liquids and solids near room temperature, heat capacities are nearly constant

andCP, mandCV, mare nearly equal to each other, so that

γ≈ 1 (many liquids and solids) (2.5-15d)

Equations (2.4-21), (2.4-27), and (2.4-28) can be written in terms ofγas follows:

T 2

T 1



(

V 1

V 2

)γ− 1

(2.5-16a)