GATE ME 2023 Set 1 — Question 22
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Thermodynamics → Laws & Properties → Second Law Statements
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Question
A heat engine extracts heat () from a thermal reservoir at a temperature of and rejects heat () to a thermal reservoir at a temperature of , while producing work (). Which one of the combinations of [] given is allowed?
Correct answer
(B) Q_H = 2000 J, Q_L = 750 J, W = 1250 J
Solution
For a heat engine to be allowed, it must satisfy both the First and Second Laws of Thermodynamics.
1.First Law of Thermodynamics:
2.Second Law of Thermodynamics (Carnot's Theorem): The efficiency must be less than or equal to the reversible efficiency .
Given and , the maximum possible efficiency is:Checking the options:- (A): . Since , it violates the First Law.
- (B): . First Law is satisfied. Efficiency . Since , the Second Law is also satisfied. This combination is allowed.
- (C): . First Law is satisfied. Efficiency . Since , it violates the Second Law.
- (D): . Since , it violates the First Law.
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