First slide

Different type of processes

Question

During an adiabatic process the pressure of a gas is found to be proportional to the cube of the absolute temperature. The ratio of the specific heats of the gas is

Moderate

A

2
B

$\frac{3}{2}$
C

$\frac{5}{3}$
D

$\frac{4}{3}$

Solution

$P^{1 - γ} T^{γ} = constant$
or $\frac{T^{γ}}{P^{γ - 1}} = constant$
or $P^{γ - 1} = \frac{T^{γ}}{constant}$
or $P \propto T^{\frac{γ}{γ - 1}}$
But $P \propto T^{a}$
Hence, $\frac{γ}{γ - 1} = 3 or γ = \frac{3}{2}$

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