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Q. An ideal gas is expanded adiabatically at an initial temperature of $300\, K$. So, that its volume is doubled. The final temperature of the hydrogen gas is $(\gamma=1.40)$

Chhattisgarh PMTChhattisgarh PMT 2011

Solution:

For an adiabatic process $T_{1} V_{1}^{\gamma-1}=T_{2} V_{2}^{\gamma-1}$
$\left(\frac{T_{1}}{T_{2}}\right)=\left(\frac{V_{2}}{V_{1}}\right)^{\gamma-1}$
$\Rightarrow \frac{T_{1}}{T_{2}}=\left(\frac{V_{2}}{V_{1}}\right)^{\gamma-1}$
$\frac{300}{T_{2}}=(2)^{\gamma-1}$
$\frac{300}{T_{2}}=(2)^{1.4-1}$
$T_{2}=227.36\, K$