First slide

Different type of processes

Question

A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be 0.75 of its initial pressure. The ratio of the specific heats of the gas is approximately:

Easy

A

1.20
B

1.41
C

1.67
D

1.83

Solution

$A \to B : PV = 2 {PV}_{1} \Rightarrow V_{1} = \frac{V}{2} B \to C : 2 {PV}_{1}^{γ} = 0.75 {PV}^{γ} \Rightarrow \frac{8}{3} {(\frac{V}{2})}^{γ} = V^{γ} \Rightarrow 2^{γ} = 2.67 \Rightarrow γ = 1.41$

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