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Question: The pressure and density of a diatomic gas \(\frac { P ^ { \prime } } { P }\) should be...

The pressure and density of a diatomic gas P′P\frac { P ^ { \prime } } { P } should be

A

1/128

B

32

C

128

D

None of the above

Answer

128

Explanation

Solution

Volume of the gas PVγP V ^ { \gamma }= constant

We get P′P=(VV′)γ=(d′d)γ=(32)7/5=128\frac { P ^ { \prime } } { P } = \left( \frac { V } { V ^ { \prime } } \right) ^ { \gamma } = \left( \frac { d ^ { \prime } } { d } \right) ^ { \gamma } = ( 32 ) ^ { 7 / 5 } = 128