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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 up C P,m for 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 up C P,m for N 2 , O 2 , and CO at 298.15 K in Appendix A. Compare each value with
7R/2.
If the approximations in Eq. (2.5-13) are not adequate, C P,m can be represented by
the polynomial
C P,m a + bT + cT
−2
(2.5-13d)
Table A.6 in Appendix A gives the values of the constant parameters a, b, and c for
several gases.
Exercise 2.22
Evaluate C P,m for 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 by γ:
γ
C P
C V
(definition of γ)
(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
and C P,m and C V,m are 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 of γ as follows:
T 2
T 1
V 1
V 2
γ−1
(2.5-16a)
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 up C P,m for 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 up C P,m for N 2 , O 2 , and CO at 298.15 K in Appendix A. Compare each value with
7R/2.
If the approximations in Eq. (2.5-13) are not adequate, C P,m can be represented by
the polynomial
C P,m a + bT + cT
−2
(2.5-13d)
Table A.6 in Appendix A gives the values of the constant parameters a, b, and c for
several gases.
Exercise 2.22
Evaluate C P,m for 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 by γ:
γ
C P
C V
(definition of γ)
(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
and C P,m and C V,m are 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 of γ as follows:
T 2
T 1
V 1
V 2
γ−1
(2.5-16a)