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Internal Energy

The ratio of ...

Question

The ratio of specific heats of a gas is $γ$ . The change in internal energy of one mole of the gas when the volume changes from V to 2V at constant pressure P is

A

\frac{γ - 1}{P V}

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B

PV

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C

\frac{P V}{γ - 1}

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D

V

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Solution

The correct option is B $\frac{P V}{γ - 1}$
The change in the internal energy of a gas is given by,
$U = n C_{v} Δ T$
or
$U = \frac{n R Δ T}{γ - 1} = \frac{P Δ V}{γ - 1}$
or
$U = \frac{P (2 V - V)}{γ - 1} = \frac{P V}{γ - 1}$

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