This fixed mass system contains 1.07185388 kgs of water (m) and undergoes a reversible, polytropic process from state 1 to state 2. P₁ is 2000 kPa, P₂ is 1400 kPa, T₁ is 773.15 K and T₂ is 673.15 K. Find the work (₁W₂) in KJoules, the 1Q₂ in KJoules and then apply the 2nd Law to the process to determine if the process is possible or impossible.
This fixed mass system contains 1.07185388 kgs of water (m) and undergoes a reversible, polytropic process from state 1 to state 2. P₁ is 2000 kPa, P₂ is 1400 kPa, T₁ is 773.15 K and T₂ is 673.15 K. Find the work (₁W₂) in KJoules, the 1Q₂ in KJoules and then apply the 2nd Law to the process to determine if the process is possible or impossible.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![### Thermodynamic Analysis of a Polytropic Process
#### Problem Statement
This fixed mass system contains 1.07185388 kg of water (m) and undergoes a reversible, polytropic process from state 1 to state 2. The given conditions are:
- Initial pressure \( P_1 = 2000 \) kPa
- Final pressure \( P_2 = 1400 \) kPa
- Initial temperature \( T_1 = 773.15 \) K
- Final temperature \( T_2 = 673.15 \) K
#### Tasks
1. **Work Calculation ( \(W_{1 \rightarrow 2}\) )**
Determine the work done, \(W_{1 \rightarrow 2}\), in kilojoules.
2. **Heat Calculation ( \(Q_{1 \rightarrow 2}\) )**
Calculate the heat transferred, \(Q_{1 \rightarrow 2}\), in kilojoules.
3. **Second Law Analysis**
Apply the Second Law of Thermodynamics to verify if the process is possible or impossible.
---
#### Detailed Solution
1. **Work Calculation**
The work done in a polytropic process can be calculated using the following formula:
\[
W = \frac{P_2 V_2 - P_1 V_1}{1 - n}
\]
where \(n\) is the polytropic index. For this specific case, you will need to determine the exact values of \(V_1\) and \(V_2\) and the index \(n\) which fits the given conditions.
2. **Heat Calculation**
The heat transferred in a polytropic process can be determined by the first law of thermodynamics:
\[
Q = \Delta U + W
\]
where \( \Delta U \) is the change in internal energy.
3. **Second Law Analysis**
To verify the process:
- Calculate the entropy change \( \Delta S \).
- Check if the entropy change complies with the second law of thermodynamics.
#### Graphical Representation
A detailed graph typically includes:
- An isobaric process curve showing the pressure change from 2000 kPa to 1400 kPa.
- An isothermal curve representing temperature drop from 773.15 K to 673.15 K.
- Volume changes corresponding to the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3acf6a6-30f5-4bc7-ac16-270edca78ecc%2F3af7c6b1-3e48-49e1-8991-94dc9fb162b2%2Fbtxzm5w_processed.png&w=3840&q=75)
Transcribed Image Text:### Thermodynamic Analysis of a Polytropic Process
#### Problem Statement
This fixed mass system contains 1.07185388 kg of water (m) and undergoes a reversible, polytropic process from state 1 to state 2. The given conditions are:
- Initial pressure \( P_1 = 2000 \) kPa
- Final pressure \( P_2 = 1400 \) kPa
- Initial temperature \( T_1 = 773.15 \) K
- Final temperature \( T_2 = 673.15 \) K
#### Tasks
1. **Work Calculation ( \(W_{1 \rightarrow 2}\) )**
Determine the work done, \(W_{1 \rightarrow 2}\), in kilojoules.
2. **Heat Calculation ( \(Q_{1 \rightarrow 2}\) )**
Calculate the heat transferred, \(Q_{1 \rightarrow 2}\), in kilojoules.
3. **Second Law Analysis**
Apply the Second Law of Thermodynamics to verify if the process is possible or impossible.
---
#### Detailed Solution
1. **Work Calculation**
The work done in a polytropic process can be calculated using the following formula:
\[
W = \frac{P_2 V_2 - P_1 V_1}{1 - n}
\]
where \(n\) is the polytropic index. For this specific case, you will need to determine the exact values of \(V_1\) and \(V_2\) and the index \(n\) which fits the given conditions.
2. **Heat Calculation**
The heat transferred in a polytropic process can be determined by the first law of thermodynamics:
\[
Q = \Delta U + W
\]
where \( \Delta U \) is the change in internal energy.
3. **Second Law Analysis**
To verify the process:
- Calculate the entropy change \( \Delta S \).
- Check if the entropy change complies with the second law of thermodynamics.
#### Graphical Representation
A detailed graph typically includes:
- An isobaric process curve showing the pressure change from 2000 kPa to 1400 kPa.
- An isothermal curve representing temperature drop from 773.15 K to 673.15 K.
- Volume changes corresponding to the
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