One mole of a 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: (a) The change in internal energy in whole cyclic process is 250 R. (b) The change in internal energy in the process CA is 700 R. (c) The change in internal energy in the process AB is - 350 R. (d) The change in internal energy in the process BC is - 500 R.

Answer: (d). For 1 mol of diatomic gas, Δ U = CvΔ T = 5/2R Δ T AB: Δ U = 5/2R(800 - 400) = 1000R BC: Δ U = 5/2R(600 - 800) = -500R CA: Δ U = 5/2R(400 - 600) = -500R; whole cycle: Δ U = 0 So the answer is (d) Δ UBC = -500R.

One mole of a diatomic ideal gas undergoes a cyclic process ABC as… | JEE Main 2014

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P-V Diagrams & Cyclic Processes

One mole of a 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 $400\text{ K},\ 800\text{ K}$ and $600\text{ K}$ respectively. Choose the correct statement:

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Answer: (d)

For 1 mol of diatomic gas, $\Delta U = C_v\Delta T = \frac{5}{2}R\,\Delta T$
$AB$ : $\Delta U = \frac{5}{2}R(800 - 400) = 1000R$
$BC$ : $\Delta U = \frac{5}{2}R(600 - 800) = -500R$
$CA$ : $\Delta U = \frac{5}{2}R(400 - 600) = -500R$ ; whole cycle: $\Delta U = 0$
So the answer is (d) $\Delta U_{BC} = -500R$ .

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