AP EAMCET Engineering 21 Sep 2020 Shift 1 Paper

For ideal heat engine, efficiency is given as
η=‌

W

Q4

=‌

Q1−Q2

Q1

⇒‌‌η=1−‌

Q2

Q1

=1−‌

T2

T1

⇒‌‌‌

T2

T1

=1−η
⇒‌‌‌

T1

T2

=‌

1

1−η

...(i)
When heat engine operated in backward direction, then coefficient of performance is given as
β=‌

Q2

W

=‌

Q2

Q1−Q2

=‌

T2

T1−T2

⇒‌‌β=‌

1

T1 T2 −1

=‌

1

1 1−η −1

[from Eq. (i)]
=‌

1−η

1−1+η

=‌

1−η

η

=‌

1

η

−1