A Carnot heat engine absorbs 600 J of heat from a source at a temperature of 127°C and rejects 400 J of heat to a sink in each cycle. The temperature of the sink is
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- \(266.7\,\text{K}\)
- \(166.7\,\text{K}\)
- \(133.3\,\text{K}\)
- \(333.3\,\text{K}\)
The Correct Option is A
Solution and Explanation
Step 1: Use Carnot's relation: \[ \frac{Q_C}{Q_H} = \frac{T_C}{T_H} \] Where: \( Q_C = 400\,\text{J} \), \( Q_H = 600\,\text{J} \), \( T_H = 127^\circ\text{C} = 127 + 273 = 400\,\text{K} \)
Step 2: Plug values into the equation: \[ \frac{400}{600} = \frac{T_C}{400} \Rightarrow \frac{2}{3} = \frac{T_C}{400} \Rightarrow T_C = \frac{2}{3} \times 400 = 266.7\,\text{K} \]
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