Question

An engine has an efficiency of \( \frac{1}{3} \). The amount of work this engine can perform per kcal of heat input is :

• A. 1400 cal
• B. 700 cal
• C. 700 J
• D. 1400 J

Hint:

Always convert kcal to Joules when options involve SI units.

Answer 1

The Correct Option is D

Concept: Efficiency: \[ \eta = \frac{W}{Q} \]

Step 1: Given values.
\[ \eta = \frac{1}{3}, \quad Q = 1 \, \text{kcal} = 1000 \, \text{cal} \]

Step 2: Work done.
\[ W = \eta Q = \frac{1}{3} \times 1000 = 333.3 \, \text{cal} \]

Step 3: Convert to joules.
\[ 1 \, \text{cal} = 4.2 \, \text{J} \] \[ W = 333.3 \times 4.2 = 1400 \, \text{J} \]