A monoatomic gas is suddenly compressed to $(1/8)^{th}$ of its innitial 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)

Question

Dr. Abubacker · Accepted Answer

(a) In an adiabatic process,
$pV^{\gamma} = constant$
$\Rightarrow \ \ \frac{p_{1}}{p_{2}} = \left( \frac{V_{2}}{V_{1}} ight)^{\gamma}$
$\Rightarrow \ \ \frac{p_{1}}{p_{2}} = \left( \frac{1}{8} ight)^{5/3}$
$\Rightarrow \ \ \frac{p_{1}}{p_{2}} = \left( \frac{1}{2^{3}} ight)^{5/3} = \frac{1}{32}$
$	herefore\ \frac{p_{2}}{p_{1}} = 32$

Q. A monoatomic gas is suddenly compressed to $(1/8)^{th}$ of its innitial 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)

Explanation

Reviewed by Dr. Abubacker

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