First slide

Different type of processes

Question

The pressure and density of a diatomic gas (γ = 7/5 ) change adiabatically from (P, p) to (P', p'). If P/ P' = 128 then p'/p is equal to

Moderate

A

128
B

32
C

1/125
D

1/32

Solution

${PV}^{γ} = Constant$
$\frac{P}{ρ^{γ}} = Constant$
$ρ \propto P^{\frac{1}{γ}}$
$\frac{ρ}{ρ^{'}} = {(\frac{P}{P^{'}})}^{\frac{1}{r}} = {(\frac{1}{128})}^{\frac{5}{7}} = {(\frac{1}{2^{7}})}^{\frac{5}{7}}$
$= \frac{1}{2^{5}} = \frac{1}{32}$

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