In an electrical generating station, energy in the form of heat is converted into mechanical energy which is then converted into electrical energy. The conversion from mechanical energy is typically about 90% efficient, with about 10% dissipated in the form of heat. The steam turbine power plant specified in Table 5.1 can generate electrical energy at a rate of 6 million kilowatts. (a) Calculate the rate of deposited of heat into the power plant’s cooling system during the course of normal operation. [Hint: Efficiency can be expressed as useful energy output (work) per heat energy input or alternately as useful power output per rate of heat input.] (b) Calculate the rate of entropy increase in the universe during the normal operation of this power plant.
In an electrical generating station, energy in the form of heat is converted into mechanical energy which is then converted into electrical energy. The conversion from mechanical energy is typically about 90% efficient, with about 10% dissipated in the form of heat. The steam turbine power plant specified in Table 5.1 can generate electrical energy at a rate of 6 million kilowatts. (a) Calculate the rate of deposited of heat into the power plant’s cooling system during the course of normal operation. [Hint: Efficiency can be expressed as useful energy output (work) per heat energy input or alternately as useful power output per rate of heat input.] (b) Calculate the rate of entropy increase in the universe during the normal operation of this power plant.
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
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13) In an electrical generating station, energy in the form of heat is converted into
(a) Calculate the rate of deposited of heat into the power plant’s cooling system during the course of normal operation. [Hint: Efficiency can be expressed as useful energy output (work) per heat energy input or alternately as useful power output per rate of heat input.]
(b) Calculate the rate of entropy increase in the universe during the normal operation of this power plant.
Transcribed Image Text:**Table 5-1: Efficiencies of Some Heat Engines**
| Type of Engine | Hot Reservoir Temperature (Kelvin) | Cold Reservoir Temperature (Kelvin) | Efficiency (percent) |
|----------------------------------------------|-----------------------------------|------------------------------------|----------------------|
| Newcomen engine Watt's engine | 373 | 385 | 1/2 - 3 - 4 |
| **Ideal Carnot** | | | |
| | 1500 | 300 | 80 |
| | 1000 | 300 | 70 |
| | 500 | 300 | 62 |
| Rankine | 811 | 311 | 50 |
| **Actual steam turbine power plant** | 811 | 311 | 40 |
| Binary vapor cycle | 811 | 310 | 57 |
| Gasoline engine with Carnot efficiency | 1944 | 289 | 85 |
| Ideal Otto gasoline engine | 1944 | 289 | 58 |
| **Actual gasoline engine** | | | 30 |
| **Actual diesel engine** | | | 40 |
**Overview:**
- The table showcases various types of heat engines, their respective hot and cold reservoir temperatures in Kelvin, and their efficiencies in percentage.
- Ideal Carnot engines have efficiencies ranging from 62% to 80% depending on the temperature difference between reservoirs.
- Actual steam turbine power plants and actual gasoline engines show lower efficiency compared to their ideal counterparts.
**Highlighted Entries:**
- **Ideal Carnot** engines demonstrate theoretical maximum efficiencies given specific reservoir temperatures.
- **Actual steam turbine power plant** is highlighted with 40% efficiency, lower than the ideal.
- **Actual gasoline engine** and **Actual diesel engine** have efficiencies of 30% and 40% respectively, indicating real-world performance differences from the ideal models.
![## Equations
1. **Average Speed**:
\[
v = \frac{d}{t}
\]
- \(d\): distance, \(t\): time
2. **Distance Under Acceleration**:
\[
d = v_0 t + \frac{1}{2} a t^2
\]
- \(v_0\): initial velocity, \(a\): acceleration
3. **Weight**:
\[
W = mg
\]
- \(m\): mass, \(g\): gravitational acceleration
4. **Acceleration**:
\[
a = \frac{F_{\text{net}}}{m}
\]
- \(F_{\text{net}}\): net force
5. **Gravity Law**:
\[
F = \frac{Gm_1m_2}{r^2}
\]
- \(G\): gravitational constant, \(m_1, m_2\): masses, \(r\): distance between masses
6. **Momentum**:
\[
p = mv
\]
- \(m\): mass, \(v\): velocity
7. **Kinetic Energy**:
\[
KE = \frac{1}{2} mv^2
\]
- \(m\): mass, \(v\): velocity
8. **Potential Energy**:
\[
PE = mgh
\]
- \(m\): mass, \(g\): gravitational acceleration, \(h\): height
9. **Work Done**:
\[
W = F \cdot d
\]
- \(F\): force, \(d\): distance
10. **Heat Energy**:
\[
Q = mc\Delta T
\]
- \(m\): mass, \(c\): specific heat capacity, \(\Delta T\): change in temperature
11. **Latent Heat Energy**:
\[
Q = mL
\]
- \(m\): mass, \(L\): latent heat
12. **Heat Engine Efficiency**:
\[
\text{eff} = \frac{W}{Q_H}
\]
- \(W\): work done, \(Q_H\):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c7a7557-48de-4534-a80a-48391c1bf13e%2Fead15ae0-9779-48d7-baec-395b2bcd0c0f%2Flj1xopq_processed.png&w=3840&q=75)
Transcribed Image Text:## Equations
1. **Average Speed**:
\[
v = \frac{d}{t}
\]
- \(d\): distance, \(t\): time
2. **Distance Under Acceleration**:
\[
d = v_0 t + \frac{1}{2} a t^2
\]
- \(v_0\): initial velocity, \(a\): acceleration
3. **Weight**:
\[
W = mg
\]
- \(m\): mass, \(g\): gravitational acceleration
4. **Acceleration**:
\[
a = \frac{F_{\text{net}}}{m}
\]
- \(F_{\text{net}}\): net force
5. **Gravity Law**:
\[
F = \frac{Gm_1m_2}{r^2}
\]
- \(G\): gravitational constant, \(m_1, m_2\): masses, \(r\): distance between masses
6. **Momentum**:
\[
p = mv
\]
- \(m\): mass, \(v\): velocity
7. **Kinetic Energy**:
\[
KE = \frac{1}{2} mv^2
\]
- \(m\): mass, \(v\): velocity
8. **Potential Energy**:
\[
PE = mgh
\]
- \(m\): mass, \(g\): gravitational acceleration, \(h\): height
9. **Work Done**:
\[
W = F \cdot d
\]
- \(F\): force, \(d\): distance
10. **Heat Energy**:
\[
Q = mc\Delta T
\]
- \(m\): mass, \(c\): specific heat capacity, \(\Delta T\): change in temperature
11. **Latent Heat Energy**:
\[
Q = mL
\]
- \(m\): mass, \(L\): latent heat
12. **Heat Engine Efficiency**:
\[
\text{eff} = \frac{W}{Q_H}
\]
- \(W\): work done, \(Q_H\):
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