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11.Thermodynamics
normal
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
