JEE Mains · Physics · STD 11 - Thermodynamics
- JEE Mains 2025
- Medium
- MCQ
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)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) 300 K
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \mathrm{V}_1=800 \mathrm{~cm}^3 \quad \mathrm{~V}_2=200 \mathrm{~cm}^3 \\
& \mathrm{~T}_1=300 \mathrm{~K}
\end{aligned}\)
for adiabatic
\(\begin{aligned}
& \mathrm{TV}^{\gamma-1}=\text { const. } \\
& (300)(800)^{1.5-1}=\mathrm{T}_2(200)^{1.5-1} \\
& \mathrm{~T}_2=300\left[\frac{800}{200}\right]^{0.5}=300 \times\left(2^2\right)^{1 / 2} \\
& \mathrm{~T}_2=600 \mathrm{~K} \\
& \Delta \mathrm{~T}=600-300=300 \mathrm{~K}
\end{aligned}\)
& \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
\(\begin{aligned}
& \mathrm{TV}^{\gamma-1}=\text { const. } \\
& (300)(800)^{1.5-1}=\mathrm{T}_2(200)^{1.5-1} \\
& \mathrm{~T}_2=300\left[\frac{800}{200}\right]^{0.5}=300 \times\left(2^2\right)^{1 / 2} \\
& \mathrm{~T}_2=600 \mathrm{~K} \\
& \Delta \mathrm{~T}=600-300=300 \mathrm{~K}
\end{aligned}\)
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