During an adiabatic process, volume of gas is found to be inversely proportional to cube of its

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11.Thermodynamics

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During an adiabatic process, the volume of gas is found to be inversely proportional to the cube of its temperature. The ratio of $\frac{{{C_p}}}{{{C_v}}}$ for the gas is

A

$1.5$

B

$1.33$

C

$2$

D

$1.67$

Solution

$V \propto \frac{1}{T^{3}}$

$\mathrm{VT}^{3}=\mathrm{const}$

$\mathrm{V}^{1 / 3} \mathrm{T}=\mathrm{const} \ldots \ldots(\mathrm{i})$

$\mathrm{V}^{\gamma-1} \mathrm{T}=\mathrm{const.} \ldots(\mathrm{ii})$

comparing equation $( i )$ $\&$ (ii)

$\gamma-1=1 / 3$

$\gamma=4 / 3$

Standard 11

Physics

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