Modern Engineering Thermodynamics

16.4 The Mach Number 659
Since for ideal gases c p − c v = R and k = c p /c v ,wecanwritec p = R + c v = kR/ðk−1Þ: Also, from Eq. (16.10), we
find that R = c 2 /ðkg c TÞ: Then, the equations for the isentropic stagnation temperature, pressure, and density
(Eqs. (16.2), (16.3), and (16.4)) for an ideal gas become
T os
T = 1 + V2 /ð2g c c p TÞ = 1 + k − 1
2 M2 (16.12)
and
p
os
p = 1 + k − 1 k/ðk−1Þ
2 M2
(16.13)
ρ
os
ρ = 1 + k − 1 1/ðk−1Þ
2 M2
(16.14)
Table C.18 in Thermodynamic Tables to accompany Modern Engineering Thermodynamics contains tabulated values of
T/T os , p/p os ,andρ/ρ os for air ðk = 1:40Þ for various values of M. These tabulations were made using Eqs.
(16.12), (16.13), and (16.14) and may be used in place of these equations when convenient. Table 16.2 lists
various values of k = c p /c v and Figure 16.6 shows k at various pressures.
Table 16.2 Typical Values of the Specific Heat Ratio k
Gas
k = c p /c v
Monatomic
Argon, helium, neon, xenon, etc. 1.67
Diatomic
Air 1.40
Nitrogen 1.40
Oxygen 1.39
Carbon monoxide 1.40
Hydrogen 1.40
Triatomic
Carbon dioxide 1.29
Sulfur dioxide 1.25
Isentropic exponent, k
1.33
1.32
1.31
1.30
1.29
1.28
1.27
1.26
1.25
1.24
1.23
1.22
400°F
600°F
800°F
1000°F
1200°F
1400°F
1600°F
1800°F
2000°F
1.21
1.20
1 10 100 1000
Pressure, psia
FIGURE 16.6
The variation in the isentropic exponent k = c p /c v of steam with pressure and temperature.