First slide

Different type of processes

Question

A mono atomic ideal gas at temperature T is expanded adiabatically to eight times its initial volume. Then final temperature of the gas is

Moderate

A

$\frac{T}{4}$
B

$\frac{T}{32}$
C

$\frac{T}{8}$
D

$\frac{T}{2}$

Solution

$δ = \frac{f + 2}{f} = \frac{3 + 2}{3} = \frac{5}{3}$
Now $\frac{T_{2}}{T_{1}} = {(\frac{V_{1}}{V_{2}})}^{δ - 1} \Rightarrow \frac{T_{2}}{T} = {(\frac{V_{1}}{8 V_{1}})}^{\frac{5}{3} - 1} = \frac{1}{{(2^{3})}^{\frac{2}{3}}} = \frac{1}{4}$
$\Rightarrow T_{2} = \frac{T}{4}$

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