Question:
A Carnot engine operates between a heat source at $T_1 = 600\text{ K}$ and a sink at $T_2 = 300\text{ K}$. If the engine absorbs $1000\text{ J}$ of heat from the source per cycle, the work done per cycle is:
A Carnot engine operates between a heat source at $T_1 = 600\text{ K}$ and a sink at $T_2 = 300\text{ K}$. If the engine absorbs $1000\text{ J}$ of heat from the source per cycle, the work done per cycle is:
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The temperature of the sink is exactly half of the source temperature, giving an efficiency of exactly $50\%$. Thus, half of the absorbed heat ($500\text{ J}$) is converted into useful work.
Updated On: Jun 3, 2026
- $500\text{ J}$
- $1000\text{ J}$
- $250\text{ J}$
- $750\text{ J}$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$. Also, efficiency is defined as the ratio of work done ($W$) to the heat absorbed from the source ($Q_1$): $\eta = \frac{W}{Q_1}$.
Step 2: Meaning
We first calculate the Carnot efficiency using the absolute temperatures of the reservoir and then use it to find the work output.
Step 3: Analysis
Calculate the efficiency: \[ \eta = 1 - \frac{300}{600} = 1 - \frac{1}{2} = \frac{1}{2} = 0.5 \quad (50\%) \] Now find the work done: \[ W = \eta \cdot Q_1 = 0.5 \times 1000\text{ J} = 500\text{ J} \]
Step 4: Conclusion
The work done per cycle by the Carnot engine is $500\text{ J}$.
Final Answer: (A)
The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$. Also, efficiency is defined as the ratio of work done ($W$) to the heat absorbed from the source ($Q_1$): $\eta = \frac{W}{Q_1}$.
Step 2: Meaning
We first calculate the Carnot efficiency using the absolute temperatures of the reservoir and then use it to find the work output.
Step 3: Analysis
Calculate the efficiency: \[ \eta = 1 - \frac{300}{600} = 1 - \frac{1}{2} = \frac{1}{2} = 0.5 \quad (50\%) \] Now find the work done: \[ W = \eta \cdot Q_1 = 0.5 \times 1000\text{ J} = 500\text{ J} \]
Step 4: Conclusion
The work done per cycle by the Carnot engine is $500\text{ J}$.
Final Answer: (A)
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