GATE 2020 CH – Question 32

Thermodynamics · Laws of thermodynamics, open and closed systems, entropy and chemical potential · 1 mark · Numerical answer

Two Carnot engines operate in series between reservoirs R1→R2 and R2→R3 as shown. Their efficiencies are 0.40 and 0.35 respectively. If R1 is at 800 K, find R3 temperature in K, rounded to the nearest integer.

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Correct answer: 311 to 313

Explanation

For a Carnot engine, $\eta=1-T_c/T_h$. The first engine therefore gives $T_2=800(1-0.40)=480$ K. The second gives $T_3=480(1-0.35)=312$ K. Multiplying the two temperature ratios is valid because R2 is the common reservoir. Thus R3 is at 312 K.

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