Question

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

• A. \(266.7\,\text{K}\)
• B. \(166.7\,\text{K}\)
• C. \(133.3\,\text{K}\)
• D. \(333.3\,\text{K}\)

Hint:

In Carnot engines, the ratio of heat exchanged equals the ratio of absolute temperatures: \( \frac{Q_C}{Q_H} = \frac{T_C}{T_H} \).

Answer 1

The Correct Option is A

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: \[ \frac{400}{600} = \frac{T_C}{400} \Rightarrow \frac{2}{3} = \frac{T_C}{400} \Rightarrow T_C = \frac{2}{3} \times 400 = 266.7\,\text{K} \]