AP EAPCET 04-Jul-2022 Shift 2 Paper

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.