1. Entropy Physics 102 Professor Lee Carkner Lecture 8 “Entropy isn’t what it used to be.” --Anonymous physicist

2. Auto Engine  If an automobile engine outputs 149200 W to the drive shaft and outputs 596800 W to the radiator, what is the efficiency?  W = 149200 W  Q C = 596800 W  W = Q H – Q C, Q H = W + Q C  Q H = 149200 + 596800 = 746000  e = W/Q H = 149200/746000 = 0.2  Note: can write as 20%  If gas is $2.50 per gallon, how much money per gallon are you wasting?  Only use 20%, so you waste 80%  (2.50) X (0.8) = 2  You waste $2.00 per gallon

3. Which of the following engines would be useful and possible to build? A)One with work equal to zero B)One with work greater than input heat C)One with input heat equal to zero D)One with input heat greater than work E)All are impossible

4. Which of the following engines would be possible to build? A)One with work equal to input heat B)One with efficiency equal to 1 C)One that operates between two regions at the same temperature D)One with output heat greater than zero E)All are impossible

5. Lets say you wanted to cool your house on a hot day so you buy a refrigerator, plug it in and open the door. Assume your house is insulated. What happens to the temperature of the house? A)It increases B)It decreases C)It stays the same D)It depends on the COP of the refrigerator E)You cannot tell from the information given

6. The Second Law -- A Look Back  How can you express the second law?   Can’t move heat from cold to hot without doing work   These formulations suggest there is a preferred direction processes want to move in

7. Reversibility  Carnot engines are maximally efficient because they are reversible    e.g. When you add heat to a gas to raise a piston and produce work, can you put the work back in and compress the gas to get your heat back out?  No, because you lost some energy in friction   Can get close to reversible by reducing friction, doing process slowly, etc.

8. Heat, Temperature and Entropy  Equate the efficiencies of a Carnot engine:  We can them write Q C /T C = Q H /T H  Q/T is known as the change in entropy (  S)    No real process is truly reversible (due to friction, turbulence etc.), so we can say:   This is the second law of thermodynamics: Entropy always increases

9. Determining Entropy  For any process:  S = Q/T   Technically this equation only holds when the entire process happens at constant T   we can use the average T for small temperature changes   Losing heat decreases entropy (-Q means -  S), gaining heat increases it (+Q means +  S)

10. Randomness  What is entropy?   A universe with objects sorted by temperature is ordered   A universe at a uniform temperature is disordered   As heat flows from hot to cold, the disorder increases  Note that the overall entropy of the universe always increases, even if in some small area it decreases

11. Entropy and Reversibility  The second law explains why some processes are not reversible  Examples:    These processes only happen in one direction because:    Work into heat creates more disorder  Heat is a less ordered form of energy

12. Statistical Mechanics   We will use statistical mechanics to explore the reason why gas diffuses throughout a container   The box contains 4 indistinguishable molecules

13. Molecules in a Box  There are 16 ways that the molecules can be distributed in the box   Since the molecules are indistinguishable there are only 5 configurations   If all microstates are equally probable, the configuration with equal distribution is the most probable

14. Distributions Configuration I Probability = (1/16) Configuration II Probability = (4/16)

15. Probability  There are more microstates for the configurations with roughly equal distributions   Gas diffuses throughout a room because the probability of a configuration where all of the molecules bunch up is low 

16. Arrows of Time  Three arrows of time:  Thermodynamic   Psychological   Cosmological 

17. Fate of the Universe  If the universe has enough mass, its expansion will reverse   Cosmological arrow will go backwards   Universe seems to be open   Entropy keeps increasing   Universe becomes completely random radiation field 

18. Next Time  Exam #1 Friday  Covers all of Ch 13-15  Lectures 1-8  About 10 multiple choice (~25%)  3-4 problems (~75%)  Equation and constant sheet given  Must bring calculator and pencil  Review questions posted on WebAssign  Won’t be graded