JEE Advanced 2020 Full Test 3 Paper 2

One mole of a monatomic gas undergoes the cycle shown in the diagram: The pressure, volume and temperature at A are P0,V0 and T0 respectively; the pressure at B is 2P0 and the volume at D is 2V0. The processes AB and CD are isochoric. During BC DA, the gas undergoes the processes such that during an infinitesimal contraction or expansion, the heat absorbed dQ, the change in internal energy dU and dW, the work done satisfy the relation:
dQ=‌

1

2

dU+‌

2

3

dW For the process BC,DA, we can write
dQ=‌

1

2

dU+‌

2

3

dW=dU+dW
or, +‌

1

2

dU=−‌

1

3

dW‌‌;‌‌ or ,‌

1

2

⋅‌

3

2

R∣dT=−‌

1

3

dW
pdV+Vdp⇒RdT‌‌;‌‌ or ,‌

13

9

pdV+Vdp=0
or, pV‌

13

9

= constant