Steam at 400°C and 40.0 bar enters an adiabatic turbine. The turbine generates 300 kW of work, and the effluent saturated steam leaves at 2.60 bar. Assume changes in kinetic and potential energy are negligible. Determine the mass flow rate of steam in the turbine (kg/h)
Steam at 400°C and 40.0 bar enters an adiabatic turbine. The turbine generates 300 kW of work, and the effluent saturated steam leaves at 2.60 bar. Assume changes in kinetic and potential energy are negligible. Determine the mass flow rate of steam in the turbine (kg/h)
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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![### Thermodynamics Problem: Determining Mass Flow Rate of Steam
**Problem Statement:**
Steam at 400°C and 40.0 bar enters an adiabatic turbine. The turbine generates 300 kW of work, and the effluent saturated steam leaves at 2.60 bar. Assume changes in kinetic and potential energy are negligible.
**Task:**
Determine the mass flow rate of steam in the turbine (kg/h).
---
**Explanation:**
In this problem, we are given certain conditions for steam entering and exiting an adiabatic turbine, along with the work output. Our goal is to determine the mass flow rate of the steam passing through the turbine.
1. **Initial Conditions:**
- Inlet steam temperature: 400°C
- Inlet steam pressure: 40.0 bar
2. **Final Conditions:**
- Outlet steam is saturated at: 2.60 bar
3. **Work Output:**
- Turbine generates: 300 kW of work
4. **Assumptions:**
- Adiabatic process (no heat exchange with surroundings)
- Negligible changes in kinetic and potential energy
**Steps to Solve:**
1. Use steam tables to find the specific enthalpies:
- \( h_1 \) for steam at 400°C and 40.0 bar.
- \( h_2 \) for saturated steam at 2.6 bar (use the enthalpy of vaporization at this pressure).
2. Apply the first law of thermodynamics for an adiabatic turbine:
\[
W_{turb} = \dot{m} (h_1 - h_2)
\]
where \( W_{turb} \) is the work done by the turbine, \( \dot{m} \) is the mass flow rate, and \( h_1 - h_2 \) is the change in specific enthalpy.
3. Rearrange to solve for \( \dot{m} \):
\[
\dot{m} = \frac{W_{turb}}{h_1 - h_2}
\]
4. Convert the mass flow rate to the desired units (kg/h).
By following these steps, you should be able to determine the mass flow rate of steam passing through the turbine based on the provided conditions. This exercise provides practical experience in applying](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10115ea5-5f0e-4fb5-b400-8bf897ed7680%2F8b2412c7-df6c-4e74-a2fd-5c75d4d106d3%2Fbd5c797_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Thermodynamics Problem: Determining Mass Flow Rate of Steam
**Problem Statement:**
Steam at 400°C and 40.0 bar enters an adiabatic turbine. The turbine generates 300 kW of work, and the effluent saturated steam leaves at 2.60 bar. Assume changes in kinetic and potential energy are negligible.
**Task:**
Determine the mass flow rate of steam in the turbine (kg/h).
---
**Explanation:**
In this problem, we are given certain conditions for steam entering and exiting an adiabatic turbine, along with the work output. Our goal is to determine the mass flow rate of the steam passing through the turbine.
1. **Initial Conditions:**
- Inlet steam temperature: 400°C
- Inlet steam pressure: 40.0 bar
2. **Final Conditions:**
- Outlet steam is saturated at: 2.60 bar
3. **Work Output:**
- Turbine generates: 300 kW of work
4. **Assumptions:**
- Adiabatic process (no heat exchange with surroundings)
- Negligible changes in kinetic and potential energy
**Steps to Solve:**
1. Use steam tables to find the specific enthalpies:
- \( h_1 \) for steam at 400°C and 40.0 bar.
- \( h_2 \) for saturated steam at 2.6 bar (use the enthalpy of vaporization at this pressure).
2. Apply the first law of thermodynamics for an adiabatic turbine:
\[
W_{turb} = \dot{m} (h_1 - h_2)
\]
where \( W_{turb} \) is the work done by the turbine, \( \dot{m} \) is the mass flow rate, and \( h_1 - h_2 \) is the change in specific enthalpy.
3. Rearrange to solve for \( \dot{m} \):
\[
\dot{m} = \frac{W_{turb}}{h_1 - h_2}
\]
4. Convert the mass flow rate to the desired units (kg/h).
By following these steps, you should be able to determine the mass flow rate of steam passing through the turbine based on the provided conditions. This exercise provides practical experience in applying
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