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An ideal diatomic gas undergoes a process such that, $p \propto V$ . At the end of process, rms speed of gas molecules is found double of its initial value. Initially gas is at pressure $p$ and have volume $V_{1}$ . Choose the correct options.

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Molar specific heat for the process is $\frac{5}{2} k$

Heat added to the gas during the process is $9 p_{1} V_{1}$

Heat added to the gas during the process is $\frac{15}{2} P_{1} V_{1}$

Molar specific heat for the process is $3 n$

answer is B, C.

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Detailed Solution

$p \propto y \Rightarrow p V^{- 1} =$ constant, process is polytropic with $x = - 1$ and $C =$ specific heat for the process

$= \frac{R}{γ - 1} + \frac{R}{1 - x}$

$= C_{γ} + \frac{R}{1 - x}$

$= \frac{5}{2} R + \frac{R}{2} = 3 R$

$Δ Q = n C Δ T$

$= n C (T_{f} - T_{i})$

$= n C (4 T_{i} - T_{i})$

$= 3 n C T_{i}$

$= 9 n R T_{i} = 9 p_{1} V_{1}$

As, vims $\infty \sqrt{T}$ , rms speed is doubled.

$∴$ Temperature becomes four times.

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