Question

A Carnot engine works between \(600\,\text{K}\) and \(300\,\text{K}\). Find its efficiency.

• A. \(25\%\)
• B. \(40\%\)
• C. \(50\%\)
• D. \(60\%\)

Hint:

Carnot efficiency depends only on temperatures of reservoirs: \[ \eta = 1-\frac{T_C}{T_H} \] Temperatures must always be in Kelvin.

Answer 1

The Correct Option is C

Concept: The efficiency of a Carnot engine operating between two reservoirs is \[ \eta = 1-\frac{T_C}{T_H} \] where
• \(T_H\) = temperature of hot reservoir
• \(T_C\) = temperature of cold reservoir

Step 1: Substitute the given temperatures. \[ T_H = 600\,K, \quad T_C = 300\,K \] \[ \eta = 1-\frac{300}{600} \]

Step 2: Simplify the expression. \[ \eta = 1-0.5 \] \[ \eta = 0.5 \]

Step 3: Convert to percentage. \[ \eta = 50\% \] \[ \boxed{50\%} \]