Nitrogen turbine. Nitrogen expands from 30 bar, 600°C to 12 bar in a turbine operating at steady-state. Assume nitrogen to be an ideal gas (C₂=29 J/mol-K). a. Calculate the amount of work and the final temperature if expansion is reversible. b. Repeat the calculation if the efficiency of the turbine is 82% and report the lost work.
Nitrogen turbine. Nitrogen expands from 30 bar, 600°C to 12 bar in a turbine operating at steady-state. Assume nitrogen to be an ideal gas (C₂=29 J/mol-K). a. Calculate the amount of work and the final temperature if expansion is reversible. b. Repeat the calculation if the efficiency of the turbine is 82% and report the lost work.
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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![### Nitrogen Turbine Analysis
In this example, we examine the behavior of nitrogen gas expanding in a turbine under specified conditions. The expansion of nitrogen occurs from an initial pressure and temperature, leading to a specific final pressure. The conditions are as follows:
- **Initial Pressure (P1)**: 30 bar
- **Initial Temperature (T1)**: 600°C
- **Final Pressure (P2)**: 12 bar
We assume that nitrogen behaves as an ideal gas with a constant specific heat capacity at constant pressure (\(C_p\)) provided as:
- \(C_p = 29 \, \text{J/(mol·K)}\)
The problem is divided into two parts:
#### Part (a): Reversible Expansion
1. **Objective**: Calculate the work done and the final temperature when the expansion is reversible.
2. **Approach**: Utilize the principles of thermodynamics for a reversible process.
#### Part (b): Real Expansion with Efficiency Consideration
1. **Objective**: Recalculate the work done considering the turbine operates with 82% efficiency, and report the lost work.
2. **Approach**: Apply the efficiency factor to the work calculated in (a), and determine the corresponding loss.
#### Understanding Principles and Formulas
- **Reversible Process**: A process that can be reversed without leaving any change in both the system and the surroundings.
- **Efficiency of Turbine (\(\eta\))**: The ratio of actual work output to the ideal (reversible) work output.
\[ \eta = \frac{\text{Actual Work}}{\text{Reversible Work}} \]
\[ \text{Loss of Work} = \text{Reversible Work} - \text{Actual Work} \]
### Steps for Calculation
1. **For Part (a)**:
- Use the ideal gas law and isentropic relations for a reversible adiabatic process to find work output and final temperature.
- **Isentropic Process Formulae**:
\[ \left( \frac{T_2}{T_1} \right) = \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} \]
\[ W = C_p(T_1 - T_2) \]
- Where \(\gamma\) is the heat capacity ratio \(\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd903732-8d16-4d51-97da-0f4385778344%2Fe94cb812-e699-4e83-9208-044797b217d9%2F81fhl9m_processed.png&w=3840&q=75)
Transcribed Image Text:### Nitrogen Turbine Analysis
In this example, we examine the behavior of nitrogen gas expanding in a turbine under specified conditions. The expansion of nitrogen occurs from an initial pressure and temperature, leading to a specific final pressure. The conditions are as follows:
- **Initial Pressure (P1)**: 30 bar
- **Initial Temperature (T1)**: 600°C
- **Final Pressure (P2)**: 12 bar
We assume that nitrogen behaves as an ideal gas with a constant specific heat capacity at constant pressure (\(C_p\)) provided as:
- \(C_p = 29 \, \text{J/(mol·K)}\)
The problem is divided into two parts:
#### Part (a): Reversible Expansion
1. **Objective**: Calculate the work done and the final temperature when the expansion is reversible.
2. **Approach**: Utilize the principles of thermodynamics for a reversible process.
#### Part (b): Real Expansion with Efficiency Consideration
1. **Objective**: Recalculate the work done considering the turbine operates with 82% efficiency, and report the lost work.
2. **Approach**: Apply the efficiency factor to the work calculated in (a), and determine the corresponding loss.
#### Understanding Principles and Formulas
- **Reversible Process**: A process that can be reversed without leaving any change in both the system and the surroundings.
- **Efficiency of Turbine (\(\eta\))**: The ratio of actual work output to the ideal (reversible) work output.
\[ \eta = \frac{\text{Actual Work}}{\text{Reversible Work}} \]
\[ \text{Loss of Work} = \text{Reversible Work} - \text{Actual Work} \]
### Steps for Calculation
1. **For Part (a)**:
- Use the ideal gas law and isentropic relations for a reversible adiabatic process to find work output and final temperature.
- **Isentropic Process Formulae**:
\[ \left( \frac{T_2}{T_1} \right) = \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} \]
\[ W = C_p(T_1 - T_2) \]
- Where \(\gamma\) is the heat capacity ratio \(\
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