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Q.

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $γ$ is the ratio of specific heats):

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a

$\frac{d V}{V}$

b

$- \frac{1}{γ} \frac{d V}{V}$

c

$- γ \frac{d V}{V}$

d

$- γ \frac{V}{d V}$

answer is D.

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Detailed Solution

Equation of adiabatic process is $P V^{γ} =$ constant
$P γ V^{γ - 1} d V + V^{γ} d P = 0$ Or

$\frac{d P}{P} = \frac{- γ d V}{V}$ is the fractional change in pressure.

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