U 1
U 2
¼
γ À 1
ð
Þþ γ þ 1
ð
Þ p 2 =p 1
ð
Þ
γ þ 1
ð
Þþ γ À 1
ð
Þ p 2 =p 1
ð
Þ
ð3:18Þ
and from the equation of state we obtain
T 2
T 1
¼
p 2
p 1
γ þ 1
ð
Þþ γ À 1
ð
Þ p 2 =p 1
ð
Þ
γ À 1
ð
Þþ γ þ 1
ð
Þ p 2 =p 1
ð
Þ
:
ð3:19Þ
3.7 Entropy Change of the Gas on Its Passage Through
a Shock
By returning again to the conservation equations;
ρ 1 U 1 ¼ρ 2 U 2
ρ 1 U
2
1 þ p 1 ¼ρ 2 U
2
2 þ p 2
1
2
U
2
1 þ c P T 1 ¼
1
2
U
2
2 þ c P T 2
Fig. 3.2 Pressure ratio versus specific volume ratio across the shock (solid line) is shown. The
isentropic relation, pυ
γ ¼ constant, is also shown (broken line), (see text)
3.7 Entropy Change of the Gas on Its Passage Through a Shock
99