Chapter 18 Entropy
This chapter will discuss thermal energy and the extraction of useful work from the thermal energy.
Calculate the value of the thermal energy in our classroom (12 m by 8m by 3m).
page 18-2 Introduction
Imagine that a 0.15kg ball is dropped from rest from a height of 3 meters. It’s speed just before it hits the floor would be about 7.67 m/s. Is energy conserved in this process? What is the kinetic energy of the ball just before it hits the floor?
Suppose that a ball resting on the floor is given this amount of thermal energy. Would you expect the ball to rise 3 meters above the floor? Have you ever seen something like this occur in the natural world? Would energy be conserved if the thermal energy became potential energy?
*Can thermal energy be converted into useful work?
page 18-4 Suppose $30 worth of gasoline is required to fill the tank in your car. Let the efficiency of your car be 1/5 (this is probably too high for your car). This means that 1/5 of the available energy in the gasoline tank goes into useful work (moving the car) and 4/5 of the available energy is wasted (and for the most part goes out the exhaust pipe). Calculate the dollar value of the energy that goes out the exhaust pipe for every tank of gas for your car.
*True or False Thermal energy is organized energy.
*Entropy represents _________________________________________________ .
When did the industrial revolution occur?
Why would Carnot want to figure out how to improve the efficiency of steam engines?
A heat engine can be schematically represented by three regions: 1) high temperature region, 2) machinery where work is done, 3) lower temperature region than region 1). In a heat engine a portion of the energy moving from the high temperature region to the low temperature region is converted to useful work.
drawing of a heat engine
Carnot discovered that the theoretical maximum efficiency of a heat engine is proportional to the temperature difference between region 1 and region 3.
First Law of Thermodynamics Energy from region 1 = Work done + Energy into region 3.
This is a statement of conservation of energy.
D U = Q - W is another mathematical version of the First Law. D U is the change in the internal energy of the system. Q is the value of the heat. W is the value of the work. Q is positive if energy enters the system. W is positive if the system does work (for a gas system W is positive if the volume increases).
Second Law of Thermodynamics You cannot convert thermal energy into useful work if region 1 and region 3 have the same temperature.
OR
In any process, the total entropy (disorder) of a system either stays the same or increases.
The First Law of Thermodynamics does not make any statements about the direction energy will "flow" in a situation. Energy would be conserved if 3,000 J left a cold object and entered a hot object. But, we do not observe this process occur without the input of work. Name a device in a home for which energy leaves a cold region and enters a warm region.
The Second Law of Thermodynamics is a statement as to which processes are allowed and which processes are not allowed.
One statement of the Second Law is due to Clausius: Heat flows naturally from a hot object to a cold object; heat will not flow spontaneously from a cold object to a hot object.
Kelvin-Planck Statement of the Second Law: No device is possible whose sole effect is to transform a given amount of heat completely into work.
OR It is impossible for any system to undergo a cyclic process whose sole result is the absorption of heat from a single reservoir at a single temperature and the performance of an equivalent amount of work.
OR 100% efficiency is impossible.
page 18-5 Work Done by and Expanding Gas
Work is equal to force times distance (with force and distance parallel).
W = F*d or W = ( P*Area ) * d = P * ( Area *d )
or W = P* D Volume This is only to be used if pressure is constant
In a gas system we can calculate work by multiplying a constant pressure by the change that has occurred in the volume. W is positive when a system expands.
Suppose the pressure in a system is maintained at 3 atmospheres. Calculate the work done by the system if it expands from 2.5 Liters to 3.2 Liters.
page 18-6 Specific Heats CV and CP We will skip this section.
page 18-8 Isothermal Expansion and PV Diagrams
I want to use a more precise definition for "heat" than the one given in the book.
Heat is the transfer of energy from a hot region to a cold region. Heat does not flow. Heat is not a substance. To accomplish "heat" work is done on the cold region.
Isothermal Process: A process in which the temperature of the system remains constant.
PV Diagram Pressure will be plotted on the vertical axis. Volume will be plotted on the horizontal axis.
What is the shape of the P,V points for a system undergoing an Isothermal Process? Let the system be an ideal gas such that PV=nRT applies. With this equation in mind, now describe the shape of the graph.
Since the pressure is not zero and the volume is not changing the system is doing work as the volume increases. How is it possible for the system to expend energy and do work and yet have a constant temperature?
You can use a PV diagram to calculate the value of the work. Work is equal to the area under the curve on the PV diagram. We will do some examples with calculating work on a PV diagram.
Isothermal Compression
*How is it possible for the temperature to remain constant as the gas is compressed?
page 18-9 Adiabatic Expansion
Q = 0 during an adiabatic process. In an expansion with pressure not equal to zero, work is done. What is the source of the energy that became useful work?
*Describe the change in the temperature of the system during an adiabatic expansion.
Which process leads to a faster drop in pressure: isothermal expansion or adiabatic expansion ?
Why?
page 18-11 The Carnot Cycle
Heat Engine: a device that converts thermal energy into work
Cycle: a process that returns the system to its initial state at the end of the cycle
i.e. same pressure, volume, temperature
So far the text has discussed expansions. What must take place in order to create a cycle?
*Write the steps of the Carnot cycle in order, starting with the system at its highest pressure. Use Figure 11 to follow the cycle.
1. 2.
3. 4.
Which has the greater magnitude for a heat engine:
a) the energy value of the expansion b) the energy value of the compression?
The difference a) – b) is the work value for the engine.
*Why does it take less work to compress the gas than the work done by the gas when it expands?
page 18-12 The net work is shown on a PV diagram as the area bounded by the paths of the cycle.
It is a common goal of heat engines to produce as much work as possible.
How could the area bounded by the paths of the cycle be made larger?
Thermal Efficiency of the Carnot Cycle
What questions do you have on the discussion of QH and QL?
Do you agree with the text that W = QH - QL?
It turns out that for the Carnot Cycle: QH / QL = TH / TL
page 18-13 Reversible Engines
The Carnot Engine is a theoretical concept. This engine can be run in reverse. Compare Figures 14 and 13. A heat engine run in reverse is called a refrigerator. Does a refrigerator do useful work or must work be done on a refrigerator as it goes through one cycle?
page 18-15 Energy Flow Diagrams
The reservoirs have the characteristic that they maintain a constant temperature during the operation of the heat engine (or refrigerator).
QH and QL are the values of the energy moving into or out of each reservoir during the cycle.
For both the heat engine and the refrigerator which is larger: QH or QL ?
Maximally Efficient Engines
*What is the colloquial statement of the First Law of Thermodynamics?
*What is the colloquial statement of the Second Law of Thermodynamics?
Do you think both statements capture the key concept of each law?
The conclusion of the discussion in the book is: A Carnot Engine has the maxium possible efficiency of any heat engine.
page 18-17 Applications of the Second Law
Describe some of the motivations for using energy efficiently.
What questions do you have on equations 15, 16 and 17?
efficiency = W / QH for any heat engine efficiency = ( TH – TL ) / TH for a Carnot engine
Calculate the Carnot efficiency for the case TH = 200 degrees Celsius TL = 100 degrees Celsius
Why are power plants often located along rivers?
What is the approximate maximum efficiency for a power plant that is not located along a river?
Why don’t power plants have an efficiency equal to the Carnot Efficiency value?
page 18-19 Electric Cars
Which is less harmful: pollution caused by cars operating on gasoline or pollution from power plants?
How do hybrid cars achieve such high miles/gallon values?
The Heat Pump
TRUE or FALSE The outside air on a cold January day contains thermal energy.
A heat pump a heat engine run in reverse. Work is put in and energy is moved to the hot reservoir. The coefficient of performance, CP, is
CP = QH / W or CP = QH / (QH – QL )
with a maximum CP of TH / ( TH – TL )
Suppose the Work done in a heat pump has a value of $3. Suppose CP = 4. What is the dollar value of QH ?
When does a heat pump have a large value for CP?
page 18-21 The Internal Combustion Engine
Examine Figure 21. What is the main difference between this cycle and the Carnot cycle?
*What part of the cycle represents the burning of the gasoline?
a) 1 to 2 b) 2 to 3 c) 3 to 4 d) 4 to 1
In order to maximize the work out of the engine, the range of volumes, V1 to V4, is made relatively large. Why can too large of a change in volume lead to "knocking" in a gasoline engine?
page 18-22 Entropy, S
D S = Q/T is a measure of the change in entropy for a system.
State the conditions that lead to a small value for the change in the entropy.
What questions do you have about the illustration of the tool shop and entropy?
We will not do numerical calculations with entropy.
For all natural processes D S is either 0 or a positive number. A portion of a system may have a negative D S but the remaining portion of the system will have a D S that has a positive magnitude greater than the magnitude of the negative D S. D S is 0 for an adiabatic process. Why?
Entropy provides another statement of the Second Law: The total entropy of any system plus that of its environment increases as a result of any natural process.
OR The entropy of an isolated system increases in every natural process, and only those processes are possible for which the entropy of the system increases or remains a constant.
page 18-25 The Direction of Time
We may look at some video clips related to the direction of time.
Another statement of the Second Law of Thermodynamics: Natural Processes tend to move toward a state of greater disorder
OR
An isolated system in a state of relative order will always pass to a state of relative disorder until it reaches the state of maximum disorder, which is thermal equilibrium.
Unavailability of Energy; Heat Death
Theoretically, the universe is moving toward maximum disorder. When (if) it reaches this state, all objects will have the same temperature.
Can work be done with a heat engine in such a universe?
Our textbook is an organized and information-packed book. It was made in a factory from raw materials that were disorganized at one point (vat of ink, wood pulp, etc.) An outside agent acted on the raw materials to create the book. The D S for the book is negative but the D S for the factory and environment is positive such that D S for the universe is positive as the book is made.
We are an organized set of molecules. If you would accumulate the chemical ingredients that match your body composition and put them in a container, shake, and then open the container you would not have a copy of yourself. If evolution is defined as the creation of life from raw materials by random chance arrangement of the molecules and a progression of the arrangement of molecules to form the plants, animals and people we observe today, then I don’t believe in evolution. I believe that an outside agent, God, created life as outlined in Genesis. In my opinion, only an outside agent can bring the order and information into the world that we see today. In my opinion, God created the laws of physics (& chemistry, biology, DNA, etc.) and gave order and life to the universe. Since this paragraph represents my opinion, it will not be used as the basis of a test question. Feel free to visit more with me about this in my office.
Energy Resources: Thermal Pollution
Is an automobile engine a heat engine? (yes) Do heat engines use all of the energy available from the high temperature reservoir? (no) The unwanted release of thermal energy into the environment is known as thermal pollution. What are some examples of thermal pollution?
The total energy released as thermal pollution from human activity about 6 x 10-6 of the energy received by the earth from the sun but it is still a concern in small environments (e.g. temperature increase in a small body of water). How can thermal pollution be reduced?
Why should you be concerned about thermal pollution and the use of energy by our society?
In the winter which nights are the coldest: nights with no clouds or nights with cloud cover present? All other factors being equal, the coldest nights are the nights without cloud cover. Water vapor absorbs some infrared radiation. Clouds occur when there is more water vapor in the atmosphere compared to when skies are clear. As the earth radiates infrared energy towards space, the clouds absorb some of the infrared radiation and radiate a portion back to the earth. This prevents the earth surface from cooling as much as would occur if clouds were not present.
The text briefly discusses the topic of air pollution. The burning of fossil fuels releases gases into our atmosphere that absorb infrared radiation. As the earth radiates energy towards space these extra gases absorb the infrared energy and radiate a portion back towards the earth. There are predictions that the earth’s surface temperature will increase by a few oC over the next 100 years due to this "greenhouse" effect of infrared absorption. Why should this concern you?
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