JEE Advanced 2021 Full Test 4 Paper 2

Find the network done for the process, then find heat supplied. By this you can find the value x with the help of efficiency formula.
Efficiency =

Total work done

Total heat sup plied

WAB=p(ΔV)=nRΔT (isochoric process)
=2×

25

3

×300=5000J
WBC=nRT‌ln(

Tf

ti

)=nRT‌ln(

pi

pt

) (isothermal process)
=2×R×600‌ln(

2×105

1×105

)
=1200R‌ln(2)
WCA=

nr.ΔT

2−γ

=

−2R×300

1− 1 2

[

pT=k

p2V=K

p×V1∕2=K

]
=–1200R
W=600R+1200R‌ln(2)−1200R
W=600R[2‌ln(2)−1]
Heat supplied,
QAB=nCpΔT =2×

5R

2

×300=1500R
QBC=WBC=1200R‌ln(2)
η=

600R[2‌ln(2)−1]

1500R+1200R‌ln(2)

=

12‌ln(2)−6

15+12‌ln(2)

η=1−

21

15+12‌ln(2)

=1−

3×7

15+12‌ln(2)

∴x=7