Question 552: 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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