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$P \propto {T^3};\,\,\,\,\,\,P{T^{ - 3}}=constant$             $...(i)$

For an adiabatic process; $P{T^{\fr

Vedclass · Accepted Answer

$1.5$

Vedclass · Answer

$P \propto {T^3};\,\,\,\,\,\,P{T^{ - 3}}=constant$             $...(i)$

For an adiabatic process; $P{T^{\frac{\gamma }{{1 - \gamma }}}}=constant$             $...(ii)$

Comparing $(i)$ and $(ii)$, we get

$\frac{\gamma }{{1 - \gamma }} =  - 3\,\,;\,\,\gamma  =  - 3 + 3\gamma $

$ - 2\gamma  =  - 3\,\,or\,\,\gamma  = \frac{3}{2}$

$As\,\,\,\gamma  = \frac{{{C_p}}}{{{C_v}}}\,\,\,	herefore \,\,\,\frac{{{C_p}}}{{{C_v}}} = \frac{3}{2}$

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{{{C_P}}}{{{C_V}}}$ for the gas is

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