If the ratio of specific heat of a gas at constant pressure to that at constant volume is - the change in internal energy of a mass of gas- when the volume changes from V to 2V at constant pressure P- is -

Let Δ U be the chane in internal energy and n be the number of moles. From formula, nbsp; Δ U = n C_v Δ T =n (Rγ 1 ) Δ T ⇒Δ U = nR Δ Tγ 1 = P(2 V V)γ 1 ...

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Standard XII

Physics

Equipartition Theorem

If the ratio ...

Question

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $γ$ , the change in internal energy of a mass of gas, when the volume changes from $V$ to $2 V$ at constant pressure $P$ , is :-

\frac{R}{(γ - 1)}

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P V

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\frac{P V}{(γ - 1)}

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\frac{γ P V}{(γ - 1)}

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Solution

The correct option is C $\frac{P V}{(γ - 1)}$
Let $Δ U$ be the chane in internal energy and $n$ be the number of moles.
From formula,
$Δ U = n C_{v} Δ T = n (\frac{R}{γ - 1}) Δ T$
$\Rightarrow Δ U = \frac{n R Δ T}{γ - 1} = \frac{P (2 V - V)}{γ - 1}$
$\Rightarrow Δ U = \frac{P V}{γ - 1}$
Hence, option $(c)$ is the correct answer.

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If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ, the change in internal energy of a mass of gas, when the volume changes from V to 2V at constant pressure P, is :-

The correct option is C PV(γ−1)Let ΔU be the chane in internal energy and n be the number of moles. From formula, ΔU=nCvΔT=n(Rγ−1)ΔT ⇒ΔU=nRΔTγ−1=P(2V−V)γ−1 ⇒ΔU=PVγ−1 Hence, option (c) is the correct answer.

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $γ$ , the change in internal energy of a mass of gas, when the volume changes from $V$ to $2 V$ at constant pressure $P$ , is :-