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Question 13

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in 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:

Option A (Whole Cyclic Process):

Since internal energy is a state function, the net change over any complete cycle is always zero. (Statement A is False)

Option B (Process CA):
$$\Delta U_{CA} = n C_v (T_A - T_C) = 1 \times \frac{5}{2}R \times (400 - 600) = \frac{5}{2}R \times (-200) = -500R$$ (Statement B is False)

Option C (Process AB):
$$\Delta U_{AB} = n C_v (T_B - T_A) = 1 \times \frac{5}{2}R \times (800 - 400) = \frac{5}{2}R \times (400) = 1000R$$ (Statement C is False)

Option D (Process BC):

$$\Delta U_{BC} = n C_v (T_C - T_B) = 1 \times \frac{5}{2}R \times (600 - 800) = \frac{5}{2}R \times (-200) = -500R$$ (Statement D is True)

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