Q. A monoatomic gas at $27^{\circ} C$ is suddenly compressed to one eighth of its original volume. The temperature of the gas sample is :

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A

$27^{\circ} C$

9%

B

$300^{\circ} C$

64%

C

$327^{\circ} C$

15%

D

None of the above

12%

Solution:

Since the process is adiabatic (sudden) we use
$T V^{\gamma-1}=$ constant
$\Rightarrow (273+27) V^{\frac{5}{3}-1} =T\left(\frac{V}{8}\right)^{\frac{5}{3}-1}$
$\Rightarrow 300 =T\left(\frac{1}{8}\right)^{2 / 3}$
$\Rightarrow T =300 \times 4=1200 K =927^{\circ} C$

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