First slide

Thermodynamic processes

Question

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):

Moderate

A

$\frac{d V}{V}$
B

$- \frac{1}{γ} \frac{d V}{V}$
C

$- γ \frac{V}{d V}$
D

$- γ \frac{d V}{V}$

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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