JEE Advanced 2021 Paper 1

From P - V diagram,
Process 1:
P= constant, Volume (V) increases and temperature (T) also increases.
Work done W=∫PdV= positive,
∆U=‌

f

2

nR∆T= positive
Therefore heat is absorbed by the gas.
∵∆Q=∆U+W
Process -2:
Volume (V)= Constant, Pressure (P) decreases.
∴ Temperature (T) decreases.
∵P∝T
∴‌‌W=∫PdV=0
∆T is negative and
∆U=‌

f

2

nR∆T
∆Q=∆U+W= Negative
Heat is rejected by the gas.
Process 3:
P= Constant, Volume (V) decreases.
∴ Temperature (T) also decreases.
W=P∆V= Negative
∆U=‌

f

2

nR∆T= negative
∴∆Q=W+∆U= negative
∴ Heat is rejected by the gas.
Process 4:
V= constant, Pressure (P) increases.
∴‌‌W=∫PdV=0
PV=nRT⇒ Temperature increases
∴‌‌∆U=‌

f

2

nR∆T is positive
∴∆Q=∆U+W= positive
Therefore heat is absorbed by the gas.