A piston-cylinder device contains 2.2 kg of nitrogen initial nitrogen is now compressed slowly in a polytropic process constant until the volume is reduced by one-half Determin
A piston-cylinder device contains 2.2 kg of nitrogen initial nitrogen is now compressed slowly in a polytropic process constant until the volume is reduced by one-half Determin
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
Related questions
Question
![### Problem Statement
A piston–cylinder device contains 2.2 kg of nitrogen initially at 100 kPa and 25°C. The nitrogen is now compressed slowly in a polytropic process during which \( PV^{1.3} = \) constant until the volume is reduced by one-half. Determine the work done and the heat transfer for this process, in kJ. Use \( R = 0.2968 \, \text{kJ/kg.K} \) and \( C_v = 0.744 \, \text{kJ/kg.K} \).
### Explanation and Calculations
1. **Initial Conditions:**
- Mass (\( m \)): 2.2 kg
- Initial Pressure (\( P_1 \)): 100 kPa
- Initial Temperature (\( T_1 \)): 25°C (or 298 K)
2. **Process Description:**
- Polytropic process with \( PV^{1.3} = \) constant.
- Volume is reduced by half.
3. **Process Equations:**
- Use the ideal gas law for initial state:
\[ P_1V_1 = mRT_1 \]
- For polytropic processes:
\[ W = \frac{P_2V_2 - P_1V_1}{1-n} \]
- Use the given \( n = 1.3 \).
4. **Finding Final State and Calculations:**
- Use the relationship \( V_2 = \frac{V_1}{2} \).
- Substitute \( n \) into the polytropic formula for further calculations.
5. **Heat Transfer:**
- Employ the first law of thermodynamics:
\[ Q = \Delta U + W \]
- Calculate change in internal energy using:
\[ \Delta U = mC_v(T_2 - T_1) \]
Conduct these calculations step-by-step to find the work done and heat transfer in kJ for the given compression process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa437b1f1-94c0-462c-9640-81b3f97959f1%2F02bb6245-fe57-4d89-a489-b9a8fe1838c4%2F0ayyz5_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A piston–cylinder device contains 2.2 kg of nitrogen initially at 100 kPa and 25°C. The nitrogen is now compressed slowly in a polytropic process during which \( PV^{1.3} = \) constant until the volume is reduced by one-half. Determine the work done and the heat transfer for this process, in kJ. Use \( R = 0.2968 \, \text{kJ/kg.K} \) and \( C_v = 0.744 \, \text{kJ/kg.K} \).
### Explanation and Calculations
1. **Initial Conditions:**
- Mass (\( m \)): 2.2 kg
- Initial Pressure (\( P_1 \)): 100 kPa
- Initial Temperature (\( T_1 \)): 25°C (or 298 K)
2. **Process Description:**
- Polytropic process with \( PV^{1.3} = \) constant.
- Volume is reduced by half.
3. **Process Equations:**
- Use the ideal gas law for initial state:
\[ P_1V_1 = mRT_1 \]
- For polytropic processes:
\[ W = \frac{P_2V_2 - P_1V_1}{1-n} \]
- Use the given \( n = 1.3 \).
4. **Finding Final State and Calculations:**
- Use the relationship \( V_2 = \frac{V_1}{2} \).
- Substitute \( n \) into the polytropic formula for further calculations.
5. **Heat Transfer:**
- Employ the first law of thermodynamics:
\[ Q = \Delta U + W \]
- Calculate change in internal energy using:
\[ \Delta U = mC_v(T_2 - T_1) \]
Conduct these calculations step-by-step to find the work done and heat transfer in kJ for the given compression process.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
Recommended textbooks for you
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
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