Question 75 of 190
A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of and temperature . The change in temperature when the gas is adiabatically compressed to is :
(Take is the ratio of specific heats at constant pressure and at constant volume)
Show answer and solution
Answer: (D) 300 K
\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}