Question 492: Thermodynamics & KTG

Question

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

Accepted Answer

$P \propto {T^3} \Rightarrow P{T^{ - 3}} = $ constant ....$(i)$
But for an adiabatic process, the pressure temperature relationship is given by
${P^{1 - \gamma }}\,\,{T^\gamma } = $ constant $ \Rightarrow P{T^{{\gamma  \over {1 - \gamma }}}} = $ constant. ....$(ii)$
From $(i)$ and $(ii)$ ${\gamma  \over {1 - \gamma }} =  - 3 \Rightarrow \gamma  =  - 3 + 3\gamma  \Rightarrow \gamma  = {3 \over 2}$

Answer

${4 \over 3}$

Answer

$2$

Answer

${5 \over 3}$

Answer

${3 \over 2}$

Thermodynamics & KTG

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio {C_p}/{C_V} for the gas is

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