Welcome to Lesson 3!

Alright, we are into lesson 3. Lesson 3 basically deals with energy efficiency. Upon completing this lesson, you will really get a quantitative feel for what energy efficiency is and also how to calculate energy efficiency with a conversion device. A conversion device can be anything – an automobile or a power plant or any device that converts one form of energy to another form.

And we will also understand the concept of entropy. Entropy is disorder. Because of entropy, our efficiencies are lower than what we normally expect. And we will look at the operating principle of a heat engine. A heat engine is a device that converts heat to work. Particularly, automobiles are all heat engines, and they are notoriously inefficient. We will see 2 examples and calculations of why these automobiles are notoriously inefficient.

We can also calculate the efficiency of a whole process from the step efficiencies. For example, if it involves 2 or 3 steps like in a relay race. You know you have 3 or 4 players taking the baton and one lap by each of the athletes. So, what is the overall or team efficiency if we know the efficiency of each of those steps or the efficiency of each of those players? That is a very important concept in this chapter.

While doing this, we will also learn about temperature scales; Kelvin scale, Fahrenheit, and also Celsius. So there will be a lot of numerical problems in this lesson.

Alright! Good luck!

Lesson 3 Objectives

Upon completing this lesson, you should be able to:

• define and calculate efficiency of an energy conversion device;
• articulate the concept of entropy;
• explain operating principles of a heat engine; and
• calculate overall efficiency from step efficiencies.

See the calendar in Canvas for due dates/times.

Questions?

If you have any questions, please post them to the General Course Questions forum in located in the Discussions tab in Canvas. I will check that discussion forum daily to respond. While you are visiting the discussion board, feel free to post your own responses to questions posted by others - this way, you might help a classmate!

In the first lesson, we saw that energy can be transformed from one form to another, and during this conversion, all the energy that we put into a device comes out. However, all the energy that we put in may not come out in the desired form.

For example, we put electrical energy into a bulb and the bulb produces light (which is the desired form of output from a bulb), but we also get heat from the bulb (undesired form of energy from an electric bulb).

Electrical energy conversion to light and heat.

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Therefore, energy flow into and out of any energy conversion device can be summarized in the diagram below:

Energy Flow Diagram for an Energy Conversion Device

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When all forms of energy coming out of an energy conversion device are added up, it will be equal to the energy that is put into a device. Energy output must be equal to the input. This means that energy can not be destroyed or created. It can only change its form.

In the case of an electric bulb, the electrical energy is converted to light and heat.

Self Check

Instructions: Identify the useful energy output(s) and undesirable energy output(s) in the energy conversion devices below. Enter your answers in the fields provided, and click the "Check" button to check your work.

Efficiency is the useful output of energy. To calculate efficiency, the following formula can be used:

$$Efficiency=\frac{UsefulEnergyOutput}{TotalEnergyOutput}$$

The previous example about an electrical motor is very simple because both mechanical and electrical power is given in Watts. Units of both the input and the output have to match; if they do not, you must convert them to similar units.

Practice 2

The United States' power plants consumed 39.5 quadrillion Btus of energy and produced 3.675 trillion kWh of electricity. What is the average efficiency of the power plants in the U.S.?

Energy Efficiencies

Energy efficiencies are not 100%, and sometimes they are pretty low. The table below shows typical efficiencies of some of the devices that are used in day to day life:

From our discussion on national and global energy usage patterns in Lesson 2, we have seen that:

• about 40% of the US energy is used in power generation;
• about 27% of the US energy is used for transportation.

Yet the energy efficiency of a power plant is about 35%, and the efficiency of automobiles is about 25%. Thus, over 62% of the total primary energy in the U.S. is used in relatively inefficient conversion processes.

Why are power plant and automobile design engineers allowing this? Can they do better?

There are some natural limitations when converting energy from heat to work.

Thermal energy is energy associated with random motion of molecules. It is indicated by temperature, which is the measure of the relative warmth or coolness of an object.

A temperature scale is determined by choosing two reference temperatures and dividing the temperature difference between these two points into a certain number of degrees.

The two reference temperatures used for most common scales are the melting point of ice and the boiling point of water.

• On the Celsius temperature scale, or centigrade scale, the melting point is taken as 0°C and the boiling point as 100°C, with the difference between them being equal to 100 degrees.
• On the Fahrenheit temperature scale, the melting point is taken as 32°F and the boiling point as 212°F, with the difference between them being equal to 180 degrees.

It is important to realize, however, that the temperature of a substance is not a measure of its heat content, but rather, the average kinetic energy of its molecules resulting from their motions.

When water molecules freeze at 0°C, the molecules still have some energy compared to ice at -50°C. In both cases, the molecules are not moving, so there is no heat energy.

So what is the temperature at which all the molecules have absolutely zero energy? A temperature scale can be defined theoretically, for which zero degree corresponds to zero average kinetic energy. Such a point is called absolute zero, and such a scale is known as an absolute temperature scale. At absolute zero, the molecules do not have any energy.

The Kelvin temperature scale is an absolute scale having degrees the same size as those of the Celsius temperature scale. Therefore, all the temperature measurements related to energy measurements must be made on Kelvin scale.

Energy conversions occurring in an automobile are illustrated below:

Energy Conversions in an Automobile

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Any device that converts thermal energy into mechanical energy—such as an automobile or a power plant—is called a heat engine. In these devices, high temperature heat (thermal energy) produced by burning a fuel is partly converted to mechanical energy to do work and the rest is rejected into the atmosphere, typically as a low temperature exhaust.

Heat Engine

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A general expression for the efficiency of a heat engine can be written as:

$$\text{Efficiency =}\frac{\text{Work}}{{\text{HeatEnergy}}_{Hot}}$$

We know that all the energy that is put into the engine has to come out either as work or waste heat. So work is equal to Heat at High temperature minus Heat rejected at Low temperature. Therefore, this expression becomes:

$$\text{Efficiency=}\frac{{\text{Q}}_{\text{Hot}}{\text{-Q}}_{\text{Cold}}}{{\text{Q}}_{\text{Hot}}}$$

Where, Q_Hot = Heat input at high temperature and Q_Cold= Heat rejected at low temperature. The symbol (Greek letter eta) is often used for efficiency this expression can be rewritten as:

$${\eta }^{\prime }\left(\%\right)=1-\frac{Q_{Cold}}{Q_{Hot}}\times 100$$

The above equation is multiplied by 100 to express the efficiency as percent.

French Engineer Sadi Carnot showed that the ratio of Q_HighT to Q_LowT must be the same as the ratio of temperatures of high temperature heat and the rejected low temperature heat. So this equation, also called Carnot Efficiency, can be simplified as:

The Carnot Efficiency is the theoretical maximum efficiency one can get when the heat engine is operating between two temperatures:

• The temperature at which the high temperature reservoir operates ( T_Hot ).
• The temperature at which the low temperature reservoir operates ( T_Cold ).

In the case of an automobile, the two temperatures are:

• The temperature of the combustion gases inside the engine ( T_Hot ).
• The temperature at which the gases are exhausted from the engine ( T_Cold ).

It's like taxes. The more money you earn (heat), the more money is taxed (cold), leaving you with less money to take home (efficiency). However, if you could earn more money (heat) and find a way to have less taxes taken out (better engine material), you would have more money to take home (efficiency).

Below is a table showing two temperature scales. The scale labeled "HOT," shows the range of temperatures for the combustion of gases in a car engine. The scale labeled "COLD," shows the range of temperatures at which gases are exhausted from the car engine.

Car Engine Temperatures: red indicates combustion temperatures and blue indicates exhausted temperatures.

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Instructions: Look carefully at the efficiency numbers in the body of the table. How do the Hot and Cold temperatures' effect on the efficiency.

Answer the following questions based on the information in the Car Engine Efficiency table above.

Let’s look at an example of how temperature differences are used to generate power. Power plants convert chemical energy into electrical power. Here is a video overviewing the operation of a geothermal energy system, a classic thermal power generation plant.

Below are two temperature scales. The scale labeled "HOT," shows the range of temperatures for the combustion of gases in a power plant. The scale, "COLD," shows the range of temperatures at which gases are exhausted from the power plant.

Power Plant Temperatures: red indicates power plant combustion temperatures and blue indicates exhausted gas temperatures.

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Instructions: Look carefully at the efficiency numbers in the body of the table. How do the Hot and Cold temperatures' effect on the efficiency.

Answer the following questions based on the information in the Power Plant Efficiency table above.

Calculating Overall Efficiency

Using the energy efficiency concept, we can calculate the component and overall efficiency:

$$OverallEfficiency=\frac{Electrica\mathrm{l }Energ\mathrm{y }Output}{Chemica\mathrm{l }Energ\mathrm{y }Input}$$

Here the electrical energy is given in Wh and Chemical Energy in Btus. So Wh can be converted to Btus knowing that there are 3.412 Wh in a Btu.

This overall efficiency can also be expressed in steps as follows:$$OverallEfficiency=\underset{Efficienc\mathrm{y }oftheBoiler}{\underbrace{\left[\frac{Therma\mathrm{l }Energy}{ChemicalEnergy}\right]}}\times \underset{Efficienc\mathrm{y }o\mathrm{f\; }th\mathrm{e }Turbine}{\underbrace{\left[\frac{Mechanica\mathrm{l }Energy}{ThermalEnergy}\right]}}\times \underset{EfficiencyoftheGenerator}{\underbrace{\left[\frac{ElectricalEnergy}{MechanicalEnergy}\right]}}$$

$$OverallEfficiency=Boile\mathrm{r, }\eta \times Turbin\mathrm{e, }\eta \times Generato\mathrm{r, }\eta$$

Applying this method to the above power plant example:

$$\begin{array}{l}OverallEfficiency=\left[\frac{88Btus}{100Btus}\right]\times \left[\frac{36Btus}{88Btus}\right]\times \left[\frac{35Btus}{36Btus}\right]\\ \\ =0.88\times 0.41\times 0.97\\ \\ =\mathrm{0.35 }o\mathrm{r }35\%\end{array}$$

It can be seen that the overall efficiency of a system is equal to the product of efficiencies of the individual subsystems or processes. What is the implication of this?

Steps of Overall Efficiency

We have been looking at the efficiencies of an automobile or a power plant individually. But when the entire chain of energy transformations is considered—from the moment the coal is brought out to the surface to the moment the electricity turns into its final form—true overall efficiency of the energy utilization will be revealed. The final form at home could be light from a bulb or sound from a stereo. The series of steps as shown in the figure below are: 1) Production of coal (Mining), 2) Transportation to power plant, 3) Electricity generation, 4) Transmission of electricity, and 5) Conversion of electricity into light (Use).

We know what the cumulative efficiency is actually. We looked at that in the previous diagram. We talked about it. On this diagram, we are looking at cumulative or overall efficiency for a qualified power plant. Basically, in the ground, we have coal, right? We have to bring the coal out to the surface. That step is called mining. Obviously, we need to spend some energy to bring the coal from the ground to the surface. So mining by itself has some kind of, let's say, about 95% efficient. Or that step is 95% efficient. In other words, if we have 100 units in the ground, and by the time this energy comes out to the surface, we will be left with only 95 units. Because five units, we will be spending in operating the equipment and in bringing the coal from the ground to the surface.

Now, this 95 obviously is not readily available, because we need to take these 95 BTUs to a power plant. So the trucks have to use some energy to take these 95 BTUs all the way up to the power plant. So when it reaches the power plant, these 95 units may turn out to be 90 units. In other words, we will be spending about five units in the transportation. So once we put in 90 units into a power plant, which is roughly about by now 33% efficient or 35% efficient, what this tells us is when we put in 90 units into the power plant, the output from the power plant in the form of electricity is only 30 units.

So now, at this point, we have only 30 units left over when we started our business with 100 units. Now, these 30 units are transported through these high voltage lines to a user. By the time you get to the user, we're talking about a unit or two lost. All right? And now, when we have about, let's say for simplicity purposes we will still have about 29 units or 30 units. And as you all know, the efficiency of a light bulb is notoriously low. It's about 5% efficient. Which means that out of these 29 units or 30 units that we will get into the home, only 5% of that, or 1.5 units are converted, really, to the light.

So we started off with 100, and we ended up with 1.5 units of light. So that means the overall efficiency is 1.5 divided by 100. Both are BTUs here. So the overall efficiency is only 1.5%. That is pathetically low. Which means to use 1.5 units of light, we are taking from Mother Earth 100 units. And along the way, we are dumping about 98.5 units of energy during various steps of conversion processes, and we're using 1.5 BTUs and 1.5%. That is the message.

Efficiency of a Light Bulb

If the efficiency of each step is known, we can calculate the overall efficiency of production of light from coal in the ground. The table below illustrates the calculation of overall efficiency of a light bulb.

Efficiency of an Automobile

A similar analysis on automobile efficiency is shown in the Figure below.

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Overall Automobile Efficiency

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The table below shows that only about 10% of the energy in the crude oil in the ground is in fact turned into mechanical energy moving people.

Review

Please watch the 5:30 Lesson 3 Review below:

Test Yourself

The questions below are your chance to test and practice your understanding of the content covered in this lesson. In other words, you should be able to answer the following questions if you know the material that was just covered! If you have problems with any of the items, feel free to post your question on the unit message board so your classmates, and/or your instructor, can help you out!

1. A heat engine has Carnot efficiency of 30%. Useful output from the engine is 1000J. How much heat is wasted?
2. How can we improve the Carnot efficiency of a heat engine by changing the hot and cold reservoir temperatures?
3. Most of the energy conversion devices that we use in our day-to-day life can be classified as Heat Engines. Give two examples.

Extra Resources

For more information on topics discussed in Lesson 3, see these selected References:

1. Hinrichs, R. A., “Energy,” Saunders College Publishers, Philadelphia, PA, 1992.
2. Aubrecht, G. L., “Energy,” Prentice Hall, Inc., Englewood Cliffs, NJ, 1995.
3. Fay, J.A. and Golomb, D. S., “Energy and the Environment,” Oxford University Press, New York, NY, 2002.
4. Christensen, J. W., “Global Science: Energy Resources Environment."