Question

A steam engine operating between \( 100^\circ C \) and \( 40^\circ C \) has an efficiency of \( 25% \). The heat absorbed by the engine is:

• A. \( 1.0 \times 10^6 \, \text{J} \)
• B. \( 2.0 \times 10^6 \, \text{J} \)
• C. \( 4.0 \times 10^6 \, \text{J} \)
• D. \( 3.0 \times 10^6 \, \text{J} \)

Hint:

For heat engines, efficiency is the ratio of work done to the heat absorbed.

Answer 1

The Correct Option is C

Step 1: Use the formula for efficiency.
The efficiency of a heat engine is given by: \[ \eta = \frac{W}{Q_H} \] where \( W \) is the work done, and \( Q_H \) is the heat absorbed.

Step 2: Apply the efficiency.
Given that the efficiency \( \eta = 25% = 0.25 \), and the work done \( W = Q_H - Q_C \), where \( Q_C \) is the heat rejected. The efficiency can be used to find the heat absorbed.