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  4. A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be 5/3)

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Q. A monoatomic gas is suddenly compressed to $(1/8)^{th}$ of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be $5/3$)

KCETKCET 2006Thermodynamics

Solution:

In an adiabatic process,
$P V^{\gamma}$ constant
$\Rightarrow \frac{P_{1}}{P_{2}}=\left(\frac{V_{2}}{V_{1}}\right)^{\gamma}$
$\Rightarrow \frac{P_{1}}{P_{2}}=\left(\frac{1}{8}\right)^{5 / 3}$
$\Rightarrow \frac{P_{1}}{P_{2}}=\left(\frac{1}{2^{3}}\right)^{5 / 3}$
$=\frac{1}{32}$
$\frac{P_{2}}{P_{1}}=32$