The volume of an ideal gas increases 8 times and temperature becomes of the initial temperature during a reversible change. [2026]

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Solution

Q.
The volume of an ideal gas increases 8 times and temperature becomes ${(\frac{1}{4})}^{th}$ of the initial temperature during a reversible change. If there is no exchange of heat in this process $(Δ Q = 0)$ , then identify the gas from the following options (assuming gases given in the options are ideal gases): [2026]

1 ${CO}_{2}$

2 ${NH}_{3}$

3 $O_{2}$

4 $He$

Ans.
(4)

$P V^{γ} = constant$

$T V^{γ - 1} = constant$

$T V^{γ - 1} = (\frac{T}{4}) {(8 V)}^{(γ - 1)}$

$4 = 8^{(γ - 1)}$

$2^{2} = 2^{3 γ - 3}$

$2 = 3 (γ - 1)$

$γ = \frac{5}{3}$

Gas is a monoatomic gas.

Answer is He.

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