The temperature of the sink of a Carnot engine is 250K. In order to increase the efficiency of the Carnot engine from 25% to 50%, the temperature of the sink should be increased by
Initial temperature of the sink, T2=250K Initial efficiency of carnot engine,η1=25%=0.25 If T1 be the temperature of the sink, then ‌η1=1−‌
T2
T1
‌0.25=1−‌
250
T1
⇒‌
250
T1
=0.75 ‌⇒‌‌T1=‌
1000
3
K When efficiency is increased by 50% i.e ‌‌η2=50%=0.5 Then if T2′ be temperature of sink, then η2=1−‌
T2′
T1
⇒0.5=1−‌
T2′
1000∕3
⇒‌
T2′
1000∕3
=1−0.5=0.5=‌
1
2
. ⇒T2′=‌
1
2
×‌
1000
3
=‌
500
3
K Here we see that to increase the efficiency of carnot engine temperature of the sink should be decreased, but in question, asked about increasing temperature of sink to increase efficiency, which is not possible. Hence, no option is correct.