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

The change in internal energy is given by Δ U=nC_VΔ T [ C_V=Rγ 1] ⇒Δ U=nR(γ 1)Δ T nbsp; Using ideal gas equation, PV=nRT For constant pressure PΔ V=nRΔ T ...

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Standard XII

Chemistry

Internal Energy

If the ratio ...

Question

If the ratio of specific heat of an ideal gas at constant pressure to that at constant volume is $γ$ , the change in internal energy of the given 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
$\frac{P V}{(γ - 1)}$

The change in internal energy is given by
$Δ U = n C_{V} Δ T$

$[C_{V} = \frac{R}{γ - 1}]$

$\Rightarrow Δ U = n \frac{R}{(γ - 1)} Δ T$

Using ideal gas equation, $P V = n R T$
For constant pressure $P Δ V = n R Δ T$

$\Rightarrow Δ U = \frac{P Δ V}{γ - 1} = \frac{P (2 V - V)}{(γ - 1)}$

$Δ U = \frac{P V}{(γ - 1)}$

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

The correct option is C PV(γ−1) The change in internal energy is given by ΔU=nCVΔT [CV=Rγ−1] ⇒ΔU=nR(γ−1)ΔT Using ideal gas equation, PV=nRT For constant pressure PΔV=nRΔT ⇒ΔU=PΔVγ−1=P(2V−V)(γ−1) ΔU=PV(γ−1)

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