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