First slide

Different type of processes

Question

When an ideal gas is expanded adiabatically to eight times its initial volume, its temperature is reduced to four times its initial temperature. Then the ratio $\frac{C_{V}}{R}$ for the gas is

Moderate

A

$\frac{5}{2}$
B

$\frac{3}{2}$
C

$3$
D

$\frac{3}{5}$

Solution

For adiabatic process $T V^{1 - δ} = constant$
$∴ {(\frac{V_{2}}{V_{1}})}^{δ - 1} = \frac{T_{1}}{T_{2}} \Rightarrow {(8)}^{δ - 1} = 4 \Rightarrow 2^{3 (δ - 1)} = 2^{2}$
$∴ 3 (δ - 1) = 2 \Rightarrow δ = \frac{5}{3}$
Now $C_{V} = \frac{R}{δ - 1} \Rightarrow \frac{C_{V}}{R} = \frac{1}{(\frac{5}{3} - 1)} = \frac{3}{2}$

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