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(C) For an ideal gas,the change in internal energy is given by $\Delta U = n C_v \Delta T$.For a diatomic gas,the molar specific heat at constant volu

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The change in internal energy in the process $BC$ is $-500 \ R$.

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(C) For an ideal gas,the change in internal energy is given by $\Delta U = n C_v \Delta T$.For a diatomic gas,the molar specific heat at constant volume is $C_v = \frac{5}{2} R$.Given $n = 1 	ext{ mole}$.For process $AB$: $\Delta U_{AB} = n C_v (T_B - T_A) = 1 	imes \frac{5}{2} R 	imes (800 - 400) = \frac{5}{2} R 	imes 400 = 1000 \ R$.For process $BC$: $\Delta U_{BC} = n C_v (T_C - T_B) = 1 	imes \frac{5}{2} R 	imes (600 - 800) = \frac{5}{2} R 	imes (-200) = -500 \ R$.For process $CA$: $\Delta U_{CA} = n C_v (T_A - T_C) = 1 	imes \frac{5}{2} R 	imes (400 - 600) = \frac{5}{2} R 	imes (-200) = -500 \ R$.In a cyclic process,the total change in internal energy is zero.Comparing the calculated values with the options,option $C$ is correct.

One mole of a diatomic ideal gas undergoes a cyclic process $ABC$ as shown in the figure. The process $BC$ is adiabatic. The temperatures at $A, B$ and $C$ are $400 \ K, 800 \ K$ and $600 \ K$ respectively. Choose the correct statement.

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