A heat engine operates between a cold reservoir at temperature 300 K and a hot reservoir at temperature $T_1$. It takes 200 J of heat from the hot reservoir and delivers 120 J of heat to the cold reservoir in a cycle. The minimum temperature $T_1$ of the hot reservoir is:

Question

A Carnot engine operates between temperatures of $ 600 \, \text{K} $ and $ 300 \, \text{K} $. If it absorbs $ 900 \, \text{J} $ of heat from the source, how much work does it perform?

Answer 1

Step 1: Engine work output.
W = Q_H - Q_C = 200 - 120 = 80 J.

Step 2: Thermal efficiency.
η = W/Q_H = 80/200 = 0.4.

Step 3: Carnot efficiency bound.
For maximum efficiency (minimum T₁), η = 1 - T_C/T_H → 0.4 = 1 - 300/T₁.

Step 4: Solving for T₁.
300/T₁ = 0.6 → T₁ = 500 K.

Step 5: Conclusion.
The minimum hot reservoir temperature is 500 K.

A heat engine operates between a cold reservoir at temperature 300 K and a hot reservoir at temperature \(T_1\). It takes 200 J of heat from the hot reservoir and delivers 120 J of heat to the cold reservoir in a cycle. The minimum temperature \(T_1\) of the hot reservoir is:

Show Hint

The Correct Option is C

Solution and Explanation

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