(I) A heat engine exhausts 8200 J of heat while performing 2600 J of useful work. What is the efficiency of this engine?

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter18: Heat Engines, Entropy, And The Second Law Of Thermodynamics
Section: Chapter Questions
Problem 8P
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Please type out and or diagram Your solution in a way that is easy to read I have bad eyesight 

**Question 18: (I)**

A heat engine exhausts 8200 J of heat while performing 2600 J of useful work. What is the efficiency of this engine?

**Solution:**

To find the efficiency of a heat engine, you can use the formula:

\[ \text{Efficiency} (\eta) = \frac{\text{Useful Work Output}}{\text{Total Heat Input}} \times 100\% \]

In this case:
- The useful work output \( W = 2600 \text{ J} \)
- The total heat input \( Q = W + \text{Heat Exhausted} \)
  
So, 

\[ Q = 2600 \text{ J} + 8200 \text{ J} = 10800 \text{ J} \]

Then the efficiency (\(\eta\)) is:

\[ \eta = \frac{2600 \text{ J}}{10800 \text{ J}} \times 100\% \]

\[ \eta = \frac{2600}{10800} \times 100\% \]

\[ \eta \approx 24.07\% \]

Therefore, the efficiency of this engine is approximately 24.07%.
Transcribed Image Text:**Question 18: (I)** A heat engine exhausts 8200 J of heat while performing 2600 J of useful work. What is the efficiency of this engine? **Solution:** To find the efficiency of a heat engine, you can use the formula: \[ \text{Efficiency} (\eta) = \frac{\text{Useful Work Output}}{\text{Total Heat Input}} \times 100\% \] In this case: - The useful work output \( W = 2600 \text{ J} \) - The total heat input \( Q = W + \text{Heat Exhausted} \) So, \[ Q = 2600 \text{ J} + 8200 \text{ J} = 10800 \text{ J} \] Then the efficiency (\(\eta\)) is: \[ \eta = \frac{2600 \text{ J}}{10800 \text{ J}} \times 100\% \] \[ \eta = \frac{2600}{10800} \times 100\% \] \[ \eta \approx 24.07\% \] Therefore, the efficiency of this engine is approximately 24.07%.
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