Entropy Physics 102 Professor Lee Carkner Lecture 7
Auto Engine If an automobile engine outputs W to the drive shaft and outputs W to the radiator, what is the efficiency? W = W Q C = W W = Q H – Q C, Q H = W + Q C Q H = = e = W/Q H = / = 0.2 Note: can write as 20% If gas is $2.00 per gallon, how much money per gallon are you wasting? Only use 20%, so you waste 80% (2.00) X (0.8) = 1.60 You waste $1.60 per gallon Minimum temperature The Carnot efficiency must be greater than the actual efficiency 0.2 = 1 –(T L /T H ) = (T L /T H ) 0.8T H = T L T H = T L /0.8 = 273/0.8 = 341 K = 68 C Temp of engine must be greater than 68 C so that e ideal is greater than e
Reversibility Any process in the engine can be run backwards with no loss of energy 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.
Heat, Temperature and Entropy Equate the efficiencies of a Carnot engine: We can them write Q L /T L = Q H /T H Q/T is known as the change in entropy ( S) S=0 only for reversible processes (like Carnot engines) S>0 This is the second law of thermodynamics: Entropy always increases
Determining Entropy For any process: S = Q/T Technically, this equation only holds when the entire process happens at constant T sometimes we use a heat reservoir (a body so large it hardly changes temperature) Note that we have to add up the entropy from all processes Any individual process can have an increase or decrease on entropy, only the net entropy has to increase
Solving Entropy Problems Can always use S = Q/T Need to find heat Sign of S is sign of Q (positive in and negative out) T constant for phase change or heat reservoir For total entropy, must consider all sources and sinks of heat
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
Entropy and Reversibility The second law explains why some processes are not reversible Examples: These processes only happen in one direction because: They become more random Heat is a less ordered form of energy
Probability There are lots of ways to mix the molecules up, only one way to put them all together Gas diffuses throughout a room because the probability of a configuration where all of the molecules bunch up is low There are a lot of ways to fill up the room, only one way to get bunched in a corner 1 way to arrange 4 ways to arrange
Arrows of Time Three arrows of time: Thermodynamic Psychological Cosmological Direction of increasing expansion of the universe
Fate of the Universe If the universe has enough mass, its expansion will reverse Cosmological arrow will go backwards Universe seems to be open Expand forever Entropy keeps increasing Universe becomes completely random radiation field
Next Time Exam #1 Friday Covers Ch Lectures 1-7 About 10 multiple choice (~20%) About 4 problems (~80%) Equation and constant sheet given Must bring calculator and pencil Review questions posted on WebAssign Won’t be graded
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)One with output heat equal to zero
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