Question:
A Carnot engine operating between temperatures \(600\,K\) and \(300\,K\), absorbs \(800\,J\) of heat from the source. The mechanical work done per cycle is
A Carnot engine operating between temperatures \(600\,K\) and \(300\,K\), absorbs \(800\,J\) of heat from the source. The mechanical work done per cycle is
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For a Carnot engine, efficiency depends only on the temperatures of the hot and cold reservoirs:
\[
\eta = 1-\frac{T_C}{T_H}
\]
Then use \(W=\eta Q_H\) to find the work done.
Updated On: Jun 24, 2026
- \(400\,J\)
- \(650\,J\)
- \(750\,J\)
- \(600\,J\)
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The Correct Option is A
Solution and Explanation
Step 1: Write the efficiency formula of a Carnot engine.
For a Carnot engine, \[ \eta = 1-\frac{T_C}{T_H} \] where \(T_H\) is the temperature of the hot reservoir and \(T_C\) is the temperature of the cold reservoir.
Here, \[ T_H=600\,K \] and \[ T_C=300\,K \]
Step 2: Calculate the efficiency.
Substituting the values, \[ \eta = 1-\frac{300}{600} \] \[ \eta = 1-\frac{1}{2} \] \[ \eta = \frac{1}{2} \] So, \[ \eta = 0.5 \]
Step 3: Use the relation between efficiency and work done.
Efficiency is given by \[ \eta = \frac{W}{Q_H} \] where \(W\) is the work done and \(Q_H\) is the heat absorbed from the source.
Given, \[ Q_H=800\,J \] Therefore, \[ W=\eta Q_H \] \[ W=0.5 \times 800 \] \[ W=400\,J \]
Step 4: Final conclusion.
Hence, the mechanical work done per cycle is \[ \boxed{400\,J} \]
For a Carnot engine, \[ \eta = 1-\frac{T_C}{T_H} \] where \(T_H\) is the temperature of the hot reservoir and \(T_C\) is the temperature of the cold reservoir.
Here, \[ T_H=600\,K \] and \[ T_C=300\,K \]
Step 2: Calculate the efficiency.
Substituting the values, \[ \eta = 1-\frac{300}{600} \] \[ \eta = 1-\frac{1}{2} \] \[ \eta = \frac{1}{2} \] So, \[ \eta = 0.5 \]
Step 3: Use the relation between efficiency and work done.
Efficiency is given by \[ \eta = \frac{W}{Q_H} \] where \(W\) is the work done and \(Q_H\) is the heat absorbed from the source.
Given, \[ Q_H=800\,J \] Therefore, \[ W=\eta Q_H \] \[ W=0.5 \times 800 \] \[ W=400\,J \]
Step 4: Final conclusion.
Hence, the mechanical work done per cycle is \[ \boxed{400\,J} \]
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