One mole of an ideal gas expands adiabatically at constant pressure such that its temperature T ∝ 1/√(V). The value of γ for the gas is ( γ = (Cp)/(Cv), V = Volume of the gas) (a) 1.8 (b) 1.5 (c) 1.3 (d) 1.4

Answer: (b). For an adiabatic process TVγ-1 = const, i.e. T ∝ V-(γ-1). Given T ∝ V-1/2, so γ - 1 = 1/2. So the answer is (b) γ = 1.5.

One mole of an ideal gas expands adiabatically at constant pressure… | MHT CET 2021 (20 Sep, Shift 1)

Q189MHT CET 2021 · 20 SEP · SHIFT 1Medium

Thermodynamic Processes

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$ . The value of $\gamma$ for the gas is ( $\gamma = \frac{C_p}{C_v}\ , V =$ Volume of the gas)

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Answer: (b)

For an adiabatic process $TV^{\gamma-1} = \text{const}$ , i.e. $T \propto V^{-(\gamma-1)}$ .
Given $T \propto V^{-1/2}$ , so $\gamma - 1 = \frac{1}{2}$ .
So the answer is (b) $\gamma = 1.5$ .

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