AP EAMCET · PHYSICS · Thermodynamics

A Carnot engine whose heat sink is at $27 ° C$ has an efficieny of $40 %$ . By how much should its source temperature be changed so as to increase its efficiency to $60 %$ ?

A $250 K$
B $100 K$
C $500 K$
D $350 K$

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Answer & Solution

Correct Answer

(A) $250 K$

Step-by-step Solution

Detailed explanation

Efficiency of the engine, η=1-TsinkTsource Given, Sink temperature, Tsink=27° C=300 K ⇒0.4=1-300Tsource ⇒300Tsource=0.6 ⇒Tsource=500 K For η=60%, ⇒0.6=1-300Tsource ⇒300Tsource=0.4 ⇒Tsource=750 K Change in…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A Carnot engine whose heat sink is at 27°C has an efficieny of 40%. By how much should its source temperature be changed so as to increase its efficiency to 60%?

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A Carnot engine whose heat sink is at $27 ° C$ has an efficieny of $40 %$ . By how much should its source temperature be changed so as to increase its efficiency to $60 %$ ?