Class 11 NEET Physics Thermodynamics and Kinetic Theory

Efficiency of an engine, η=1−

T2

T1

where T1 is the temperature of the source and T2 is the temperature of the sink.
∴

1

6

=1−

T2

T1

or,

T2

T1

=

5

6

...(i)
When the temperature of the sink is decreased by 62°C (or 62K ), efficiency becomes double. since, the temperature of the source remains unchanged
∴2×

1

6

=1−

(T2−62)

T1

or,

1

3

=1−

(T2−62)

T1

or,

2

3

=

T2−62

T1

or, 2T1=3T2−186
or, 2T1=3[

5

6

]T1−186 [using (i)]
∴[

5

2

−2]T1=186 or,

T1

2

=186
or, T1=372K=99°C