Q104 / 150 · MHT CET 2022 (10 Aug Shift 2) · Physics

A monoatomic gas $\left(y=\frac{5}{3}\right)$ initially at $27^{\circ} \mathrm{C}$ having volume $V$ is suddenly compressed to one-eight of its original volume $\left(\frac{V}{8}\right)$. After the compression temperature becomes.

A
$1160 \mathrm{~K}$
B
$580 \mathrm{~K}$
Correct answer
C
$1200 \mathrm{~K}$
D
$927 \mathrm{~K}$

Solution

The change in volume is sudden so, we have to consider adiabatic compression: $T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1}$ $T_2=T_1\left(\frac{V_1}{V_2}\right)^{Y-1}=(273 \mathrm{~K}+27 \mathrm{~K})\left(\frac{8 V}{V_2}\right)^{\frac{5}{3}-1}=4 \times 300 \mathrm{~K}=1200 \mathrm{~K}$

Hence, the correct answer is option: 'C'.

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