A diatomic ideal gas is compressed adiabatically to frac{1}{32} of its initial volume. If initial te

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11.Thermodynamics

hard

A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_1$ (in Kelvin) and the final temperature is $a T_1$, the value of $a$ is

A

$1$

B

$3$

C

$4$

D

$5$

(IIT-2010)

Solution

$ \mathrm{TV}^{\gamma-1}=\text { constant } $

$ \mathrm{TV}^{7 / 5-1}=\mathrm{aT}\left(\frac{\mathrm{v}}{32}\right)^{7 / 5-1} $

$ \therefore \mathrm{a}=4 .$

Standard 11

Physics

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(NEET-2020)