First slide

Thermodynamic processes

Question

In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is :

Moderate

A

32
B

$\frac{1}{32}$
C

326
D

128

Solution

If density of certain amount of gas becoming 32 times $\Rightarrow V_{2} = V_{1} / 32$ and it is given that diatomic gas undergoes adiabatic process
$P V^{γ} = c o n s \tan t$
$P {(\frac{m}{ρ})}^{γ} = c o n s \tan t$
$\frac{P}{ρ^{γ}} = c o n s \tan t (∵ ρ = \frac{m}{V}, m i s c o n s \tan t)$
$P \propto ρ^{γ}$
$\frac{P_{2}}{P_{1}} = {(\frac{ρ_{2}}{ρ_{1}})}^{γ}$
$\frac{n P_{1}}{P_{1}} = {(\frac{32 ρ_{1}}{ρ_{1}})}^{\frac{7}{5}}$
$n = {(32)}^{\frac{7}{5}} = {(2^{5})}^{\frac{7}{5}} = 2^{7} = 128$

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