Question

Carnot engine operates between temperatures, 600 K and 300 K. If it absorbs 1200 J of heat from source, the work done by the engine is

• A. 6000 J
• B. 3600 J
• C. 2400 J
• D. 1200 J
• E. 600 J

Hint:

For a Carnot engine: \[ \eta=1-\frac{T_2}{T_1} \] Always use temperature in Kelvin.

Answer 1

Answer: (E)

Efficiency of Carnot engine is: \[ \eta=1-\frac{T_2}{T_1} \] Here, \[ T_1=600\text{ K},\qquad T_2=300\text{ K} \] So, \[ \eta=1-\frac{300}{600}=1-\frac12=\frac12 \] Also, \[ \eta=\frac{W}{Q_1} \] Given: \[ Q_1=1200\text{ J} \] Thus, \[ W=\eta Q_1=\frac12 \times 1200 = 600\text{ J} \]
Hence, the correct answer is: \[ \boxed{(E)\ 600\text{ J}} \]