Question 1 : A carnot engine whose sink is at 300K has an efficiency of 40%. By how much should the Temperature of source be increased to as to increase its efficiency by 60% of original efficiency ?
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Temperature of sink T
L
=300 K
Original efficiency η=40 % =0.4
Let the Initial temperature of the source be T
H
Using η=1−
T
H
T
L
∴ 0.4=1−
T
H
300
⟹T
H
=500 K
Now the efficiency of the engine is increased by 50 % of original efficiency,
∴ New efficiency η
′
=40 % +20 % =60 %
∴ η
′
=1−
T
H
′
T
L
OR 0.6=1−
T
H
′
300
OR
T
H
′
300
=0.4 ⟹T
H
′
=750 K
Increase in source temperature ΔT
H
=T
H
′
−T
H
=750−500=250 K
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