In an adiabatic change, pressure and temperature of a monoatomic gas are related as P pro

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11.Thermodynamics

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In an adiabatic change, the pressure and temperature of a monoatomic gas are related as $P \propto T^C$, where $C$ equals

A

$\frac{2}{5}$

B

$\frac{5}{2}$

C

$\frac{3}{5}$

D

$\frac{5}{3}$

Solution

In adiabatic process, $\mathrm{P}^{\gamma-1} \propto \mathrm{T}^{\gamma}$ where $\gamma=\frac{5}{3}$

for monoatomic gas $\therefore \mathrm{P} \propto \mathrm{T}^{\gamma /(\gamma-1)}$

$\therefore \mathrm{C}=\frac{\gamma}{\gamma-1}=\frac{5 / 3}{5 / 3-1}=\frac{5 / 3}{2 / 3}=\frac{5}{2}$

Standard 11

Physics

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