An ideal gas at $27^{\circ} \mathrm{C}$ is compressed adiabatically to (8/27) of its original volume. If…
An ideal gas at $27^{\circ} \mathrm{C}$ is compressed adiabatically to (8/27) of its original volume. If ratio of specific heats, $\gamma=5 / 3$ then the rise in temperature of the gas is
$500 \mathrm{~K}$
$125 \mathrm{~K}$
$250 \mathrm{~K}$
$375 \mathrm{~K}$
Solution
For an adiabatic process $\mathrm{TV}^{\gamma-1}=$ constant
$\begin{aligned}
& \therefore \frac{\mathrm{T}_2}{\mathrm{~T}_1}=\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right)^{\gamma-1}=\left(\frac{27}{8}\right)^{\frac{5}{3}-1}=\left(\frac{27}{8}\right)^{\frac{2}{3}}=\frac{9}{4} \\
& \therefore \mathrm{T}_2=\frac{9}{4} \cdot \mathrm{T}_1=\frac{9}{4} \times 300=675 \mathrm{~K} \\
& \therefore \mathrm{T}_2-\mathrm{T}_1=675-300=375 \mathrm{~K}
\end{aligned}$
.