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The pressure and density of a diatomic g...

The pressure and density of a diatomic gas `(gamma = (7)/(5))` change adiabatically form `(P,d) to (P', d')`. If `(d')/(d) = 32`, then find the value of `(P')/(P)`?

A

`(1/32)^(1.33)`

B

`(1/32)^(1/1.33)`

C

`(32)^(1/1.33)`

D

`(32)^(1/1.4)`

Text Solution

Verified by Experts

The correct Answer is:
C
`PV^(1) = "constant" rArr PV^(y) = P^(1)(V^(1))^(Y) rArr P/P^(1) = (V^(1)V)^(y) = (32 xx P^(1))/P^(1) = (d/d^(1))^(y)`
(As `V propto 1/d`)
`rArr 32 = (d/d^(1))^(y) rArr d/d^(1) = (32)^(1/y) = (32)^(1/1.33)`
Hence, ( c) is the correct option.
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