One mole of an ideal monoatomic gas is taken through a cyclic process as shown. Choose the correct option(s)

Work done in process CA is

R T_{o} {ln}_{3}

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Heat given to the gas in process CA is

R T_{o} {ln}_{3}

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The magnitude of change in internal energy in process AB and BC be same

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The change in internal energy in process AB is negative

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Solution

The correct options are
A Work done in process CA is $R T_{o} {ln}_{3}$
B Heat given to the gas in process CA is $R T_{o} {ln}_{3}$
C The magnitude of change in internal energy in process AB and BC be same
Work done $W = R T ln \frac{V_{f}}{V_{i}} = R T_{o} ln \frac{(\frac{R T_{o}}{P_{o}})}{(\frac{R T_{o}}{3 P_{o}})} = R T_{o} ln 3$

As the process is isothermal $Δ U = 0$ therfore heat given $Δ Q = Δ W = R T_{o} ln 3$

Change in internal energy for both AB and BC $Δ U = n C_{v} T_{o}$

Change in internal energy for AB is positive as its a isochoric process and temperature is going up.

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