A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2$R$, then the ratio of initial to final pressure is nearly equal to

Question

Dr. Abubacker · Accepted Answer

(a) As gas is suddenly expanded so it is an adiabatic process,
ie, $\ \ \ \ \ \ \ \ \ \ \ \ pV^{\gamma} = constant$
$or\ \ \ \ \ {\ \ \ \ \ \ \ \ \ p}_{1}V_{1}^{\gamma} = p_{2}V_{2}^{\gamma}$
Given, $V_{2} = 3V_{1},\ C_{V} = 2R$
$	herefore\ \ \ C_{P} = 2R + R = 3R$
$\Rightarrow \ \ \ \gamma = \frac{C_{P}}{C_{V}} = \frac{3R}{2R} = 1.5$
$	herefore\ \ \frac{P_{1}}{P_{2}} = \left( \frac{V_{2}}{V_{1}} ight)^{\gamma} = (3)^{1.5} = 5.1 \approx 5$

Q. A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2$R$, then the ratio of initial to final pressure is nearly equal to

Explanation

Reviewed by Dr. Abubacker

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