During an adiabatic process pressure of gas is found to be proportional to cube of absolute temperat

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11.Thermodynamics

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During an adiabatic process the pressure of the gas is found to be proportional to the cube of the absolute temperature. The ratio $C_P/C_V = \gamma $ for the gas is

A

$3/2$

B

$2$

C

$4/3$

D

$5/3$

Solution

$\mathrm{P} \propto \mathrm{T}^{3}$

$\Rightarrow P=\mathrm{k}\left(\frac{\mathrm{PV}}{\mathrm{nR}}\right)^{3}$

$\Rightarrow \mathrm{P}^{2} \mathrm{V}^{3}=\mathrm{const.}$

$\therefore \mathrm{PV}^{3 / 2}=$ const. $\therefore \mathrm{Y}=3 / 2$

Standard 11

Physics

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