Given, Initial efficiency of Carnot engine, η1=50%. Temperature of sink,T2=500K. Final efficiency of Carnot engine, η2=80%. T1 and T1f be the initial and final temperature of source. As we know that, η=1−
T2
T1
∴η1=
50
100
=1−
500
T1i
⇒
500
T1i
=1−
1
2
⇒
500
T1i
=
1
2
⇒T1i=1000K Similarly, η2=1−
T2
T1f
⇒
80
100
=1−
500
T1f
⇒
500
T1
=1−
80
100
=
20
100
=
1
5
⇒T1f=2500K ⇒ Change in temperature, ∆T=T1f−T1i =2500−1000=1500K