Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
expand_more
expand_more
format_list_bulleted
Related questions
Question
![### Problem Statement
A Carnot engine rejects 50% of the heat absorbed from a source to a sink at 27°C. What is the source temperature?
### Explanation
The problem describes a scenario involving a Carnot engine, which is a theoretical model of a thermodynamic engine used to explain the principles of thermodynamic cycles. The Carnot engine operates between a heat source and a heat sink, rejecting a certain percentage of heat absorbed from the source to the sink. In this problem, the heat sink is at 27°C.
To solve this, we need to employ the Carnot efficiency formula and the relationship between the temperatures of the source and the sink.
### Key Concepts
1. **Carnot Efficiency**: The efficiency \(\eta\) of a Carnot engine is given by:
\[ \eta = 1 - \frac{T_\text{sink}}{T_\text{source}} \]
2. **Percentage of Heat Rejection**: If 50% of the heat is rejected, then \(\eta = 0.50\).
3. **Temperature Conversion**: Temperatures must be converted to an absolute scale (Kelvin, K) for calculations:
\[ T(K) = T(°C) + 273.15 \]
### Steps to Solve:
1. Convert the sink temperature to Kelvin:
\[ T_\text{sink} = 27 + 273.15 = 300.15\,K \]
2. Use the efficiency formula:
\[ \eta = 1 - \frac{T_\text{sink}}{T_\text{source}} \]
Since the Carnot engine rejects 50% of the heat, the efficiency \(\eta = 0.50\):
\[ 0.50 = 1 - \frac{300.15}{T_\text{source}} \]
3. Solve for \(T_\text{source}\):
\[ \frac{300.15}{T_\text{source}} = 0.50 \]
\[ T_\text{source} = \frac{300.15}{0.50} \]
\[ T_\text{source} = 600.30\,K \]
4. Convert back to Celsius if required:
\[ T_\text{source}(°C) = T_\text{source}(K) - 273.15 \]
\[](https://content.bartleby.com/qna-images/question/8b0c6ab4-d33d-4950-8248-4c194605f8ab/8e6401bf-0542-4102-b511-d7d65d5e193f/yzlghe_processed.jpeg)
Transcribed Image Text:### Problem Statement
A Carnot engine rejects 50% of the heat absorbed from a source to a sink at 27°C. What is the source temperature?
### Explanation
The problem describes a scenario involving a Carnot engine, which is a theoretical model of a thermodynamic engine used to explain the principles of thermodynamic cycles. The Carnot engine operates between a heat source and a heat sink, rejecting a certain percentage of heat absorbed from the source to the sink. In this problem, the heat sink is at 27°C.
To solve this, we need to employ the Carnot efficiency formula and the relationship between the temperatures of the source and the sink.
### Key Concepts
1. **Carnot Efficiency**: The efficiency \(\eta\) of a Carnot engine is given by:
\[ \eta = 1 - \frac{T_\text{sink}}{T_\text{source}} \]
2. **Percentage of Heat Rejection**: If 50% of the heat is rejected, then \(\eta = 0.50\).
3. **Temperature Conversion**: Temperatures must be converted to an absolute scale (Kelvin, K) for calculations:
\[ T(K) = T(°C) + 273.15 \]
### Steps to Solve:
1. Convert the sink temperature to Kelvin:
\[ T_\text{sink} = 27 + 273.15 = 300.15\,K \]
2. Use the efficiency formula:
\[ \eta = 1 - \frac{T_\text{sink}}{T_\text{source}} \]
Since the Carnot engine rejects 50% of the heat, the efficiency \(\eta = 0.50\):
\[ 0.50 = 1 - \frac{300.15}{T_\text{source}} \]
3. Solve for \(T_\text{source}\):
\[ \frac{300.15}{T_\text{source}} = 0.50 \]
\[ T_\text{source} = \frac{300.15}{0.50} \]
\[ T_\text{source} = 600.30\,K \]
4. Convert back to Celsius if required:
\[ T_\text{source}(°C) = T_\text{source}(K) - 273.15 \]
\[
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education 
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY