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  4. An ideal gas at 27° C is compressed adiabatically to (8/27) of its original volume. If γ=(5/3), then rise in temperature is

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Q. An ideal gas at $27^{\circ} C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $\gamma=\frac{5}{3}$, then rise in temperature is

Solution:

$(300) V^{\frac{5}{3}-1}=T_{2}\left(\frac{8 V}{27}\right)^{\frac{5}{3}-1}$
$\Rightarrow T_{2}=300\left(\frac{9}{4}\right)=675\, K$
Rise in temperature $=675-300 $
$=375\, K$