costs Tom and Jerry are each trying to sell you a heat engine. Both engines work between high and low temperature reservoirs of 975 K and 375 K, respectively. Tom's engine sells for $500 and he claims that with an input of 375 kJ into the engine, the engine will produce 225 kJ. Jerry's engine $350 and he claims that with an input of 375 kJ, the heat engine between the same two thermal reservoirs. Which heat engine justify your answer. will produce you 250 kJ of work purchase? You must should
costs Tom and Jerry are each trying to sell you a heat engine. Both engines work between high and low temperature reservoirs of 975 K and 375 K, respectively. Tom's engine sells for $500 and he claims that with an input of 375 kJ into the engine, the engine will produce 225 kJ. Jerry's engine $350 and he claims that with an input of 375 kJ, the heat engine between the same two thermal reservoirs. Which heat engine justify your answer. will produce you 250 kJ of work purchase? You must should
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Thermo
![**Comparison of Heat Engines**
**Scenario:**
Tom and Jerry are each trying to sell you a heat engine. Both engines work between high and low temperature reservoirs of 975 K and 375 K, respectively.
**Tom's Engine:**
- **Price:** $500
- **Input Energy:** 375 kJ
- **Work Output:** 225 kJ
**Jerry's Engine:**
- **Price:** $350
- **Input Energy:** 375 kJ
- **Work Output:** 250 kJ
**Question:**
Which heat engine should you purchase? You must justify your answer.
**Analysis:**
1. **Efficiency of Engines:**
The efficiency \( \eta \) of a heat engine is given by:
\[
\eta = \frac{W}{Q_{in}} \times 100\%
\]
Where \( W \) is the work output and \( Q_{in} \) is the input energy.
- **Tom's Engine Efficiency:**
\[
\eta_{Tom} = \frac{225 \text{ kJ}}{375 \text{ kJ}} \times 100\% = 60\%
\]
- **Jerry's Engine Efficiency:**
\[
\eta_{Jerry} = \frac{250 \text{ kJ}}{375 \text{ kJ}} \times 100\% = 66.67\%
\]
2. **Cost per Unit Work:**
To compare the cost-effectiveness, we calculate the cost per unit work (dollars per kJ).
- **Tom's Engine:**
\[
\text{Cost per kJ} = \frac{\$500}{225 \text{ kJ}} \approx \$2.22 \text{ per kJ}
\]
- **Jerry's Engine:**
\[
\text{Cost per kJ} = \frac{\$350}{250 \text{ kJ}} = \$1.40 \text{ per kJ}
\]
**Conclusion:**
Based on efficiency and cost per unit work analysis:
- **Efficiency:** Jerry's engine is more efficient (66.67%) compared to Tom's engine (60%).
- **Cost-effectiveness:** Jerry's engine provides a better cost per unit](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf82ec8f-02f7-492b-b62b-f53ab94e90b9%2F31bb0453-c31c-472b-9962-2130c8a7b1fa%2Fa3sdu1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Comparison of Heat Engines**
**Scenario:**
Tom and Jerry are each trying to sell you a heat engine. Both engines work between high and low temperature reservoirs of 975 K and 375 K, respectively.
**Tom's Engine:**
- **Price:** $500
- **Input Energy:** 375 kJ
- **Work Output:** 225 kJ
**Jerry's Engine:**
- **Price:** $350
- **Input Energy:** 375 kJ
- **Work Output:** 250 kJ
**Question:**
Which heat engine should you purchase? You must justify your answer.
**Analysis:**
1. **Efficiency of Engines:**
The efficiency \( \eta \) of a heat engine is given by:
\[
\eta = \frac{W}{Q_{in}} \times 100\%
\]
Where \( W \) is the work output and \( Q_{in} \) is the input energy.
- **Tom's Engine Efficiency:**
\[
\eta_{Tom} = \frac{225 \text{ kJ}}{375 \text{ kJ}} \times 100\% = 60\%
\]
- **Jerry's Engine Efficiency:**
\[
\eta_{Jerry} = \frac{250 \text{ kJ}}{375 \text{ kJ}} \times 100\% = 66.67\%
\]
2. **Cost per Unit Work:**
To compare the cost-effectiveness, we calculate the cost per unit work (dollars per kJ).
- **Tom's Engine:**
\[
\text{Cost per kJ} = \frac{\$500}{225 \text{ kJ}} \approx \$2.22 \text{ per kJ}
\]
- **Jerry's Engine:**
\[
\text{Cost per kJ} = \frac{\$350}{250 \text{ kJ}} = \$1.40 \text{ per kJ}
\]
**Conclusion:**
Based on efficiency and cost per unit work analysis:
- **Efficiency:** Jerry's engine is more efficient (66.67%) compared to Tom's engine (60%).
- **Cost-effectiveness:** Jerry's engine provides a better cost per unit
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