College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Please show all calculations and type them out since I have bad eyesight and it is very difficult for me to read handwriting
![**Problem Statement:**
A heat engine receives 7000 J of heat and loses 3000 J in each cycle. What is the efficiency of this engine?
**Options:**
A) 43%
B) 30%
C) 57%
D) 70%
**Explanation:**
To determine the efficiency of a heat engine, you can use the formula:
\[ \text{Efficiency} (\eta) = \frac{\text{Work Output}}{\text{Heat Input}} \times 100 \]
From the problem statement:
- Heat received by the engine (Heat Input) \( Q_{in} = 7000 \) J
- Heat lost by the engine (Heat Output or Heat Rejected \( Q_{out}) = 3000 \) J
First, calculate the Work Output:
\[ \text{Work Output} = Q_{in} - Q_{out} = 7000 \text{ J} - 3000 \text{ J} = 4000 \text{ J} \]
Then, substitute the values into the efficiency formula:
\[ \eta = \frac{4000 \text{ J}}{7000 \text{ J}} \times 100 \]
\[ \eta = \frac{4000}{7000} \times 100 \]
\[ \eta = 0.5714 \times 100 \]
\[ \eta = 57.14\% \]
Thus, considering the given options, the closest value is:
**Correct Option:**
C) 57%](https://content.bartleby.com/qna-images/question/93bd9d77-dcfb-4bce-a8b6-6527873699f2/752fc2ce-aec4-45e3-9126-d04984ee6f3a/8camtvk_processed.png)
Transcribed Image Text:**Problem Statement:**
A heat engine receives 7000 J of heat and loses 3000 J in each cycle. What is the efficiency of this engine?
**Options:**
A) 43%
B) 30%
C) 57%
D) 70%
**Explanation:**
To determine the efficiency of a heat engine, you can use the formula:
\[ \text{Efficiency} (\eta) = \frac{\text{Work Output}}{\text{Heat Input}} \times 100 \]
From the problem statement:
- Heat received by the engine (Heat Input) \( Q_{in} = 7000 \) J
- Heat lost by the engine (Heat Output or Heat Rejected \( Q_{out}) = 3000 \) J
First, calculate the Work Output:
\[ \text{Work Output} = Q_{in} - Q_{out} = 7000 \text{ J} - 3000 \text{ J} = 4000 \text{ J} \]
Then, substitute the values into the efficiency formula:
\[ \eta = \frac{4000 \text{ J}}{7000 \text{ J}} \times 100 \]
\[ \eta = \frac{4000}{7000} \times 100 \]
\[ \eta = 0.5714 \times 100 \]
\[ \eta = 57.14\% \]
Thus, considering the given options, the closest value is:
**Correct Option:**
C) 57%
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