GATE 2025 CY – Question 64

Physical Chemistry · Equilibrium: Laws of thermodynamics. Standard states. Thermochemistry. Thermodynamic functions and their relationships: Gibbs-Helmholtz and Maxwell relations, Gibbs-Duhem equation, Van’t Hoff equation. Criteria of spontaneity and equilibrium. Absolute entropy. Partial molar quantities. Thermodynamics of mixing. Chemical potential. Fugacity, Activity and Activity coefficient. Chemical equilibria. Dependence of equilibrium constant on temperature and pressure. · 2 marks · Numerical answer

Consider a Carnot engine with a hot source kept at 500 K. From the hot source, 100 J of energy (heat) is withdrawn at 500 K. The cold sink is kept at 300 K. The efficiency of the Carnot engine is _____ (rounded off to one decimal place).

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Correct answer: 0.4 to 0.4

Explanation

The efficiency of a Carnot engine depends only on the temperatures of the hot source and the cold sink:
$$\eta=1-\frac{T_c}{T_h}=1-\frac{300}{500}=1-0.6=\mathbf{0.4}.$$

(The 100 J of heat withdrawn is not needed for the efficiency; it would give a work output of $0.4\times100=40$ J.)

Official GATE 2025 answer key: https://gate2026.iitg.ac.in/doc/download/2025_Key/CY_Keys.pdf