A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is :
(Take $\gamma=1.5: \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

Question

Aicharya · Accepted Answer

$\begin{aligned}
& \mathrm{V}_1=800 \mathrm{~cm}^3 \quad \mathrm{~V}_2=200 \mathrm{~cm}^3 \\ & \mathrm{~T}_1=300 \mathrm{~K}
\end{aligned}$
for adiabatic
$\begin{aligned}
& \mathrm{TV}^{\gamma-1}=\text { const. } \\ & (300)(800)^{1.5-1}=\mathrm{T}_2(200)^{1.5-1} \\ & \mathrm{~T}_2=300\left[\frac{800}{200}\right]^{0.5}=300 \times\left(2^2\right)^{1 / 2} \\ & \mathrm{~T}_2=600 \mathrm{~K} \\ & \Delta \mathrm{~T}=600-300=300 \mathrm{~K}
\end{aligned}$

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume…

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