The Second Law of Thermodynamics Physics 102 Professor Lee Carkner Lecture 7
PAL #6 First Law 1 mole of gas at 300 K and 2 m 3 compressed to 1 m 3, constant pressure P = nRT/V = (1)(8.31)(300)/(2) = Pa W = P V = (P) (V f -V i ) Sign of work? Volume decreased
Engines General engine properties: An input of heat An output of heat
Heat and Work Over the Cycle Four parts of the cycle: compression output of heat Q C Over the course of one cycle positive work is done and heat is transferred Since the engine is a cycle, the change in internal energy is zero U=(Q H -Q C )-W =0 W = Q H - Q C
Efficiency In order for the engine to work we need a source of heat for Q H e = W/Q H An efficient engine converts as much of the input heat as possible into work
Today’s PAL If an automobile engine outputs joules per second to the drive train and burns fuel at a rate of joules per second, what is the efficiency? If gas is $2.00 per gallon, how much money per gallon are you wasting?
Efficiency and Heat e = 1 - (Q C /Q H ) The efficiency depends on how much of Q H is transformed into W and how much is lost in Q C : Reducing the output heat means improving the efficiency
The Second Law of Thermodynamics This is one way of stating the second law: It is impossible to build an engine that converts heat completely into work Engines get hot, they produce waste heat (Q C )
Carnot Engine In 1824 Sadi Carnot related the maximum efficiency to the temperature of the reservoirs: e C = 1 - (T C / T H ) A hot input reservoir and a cold output reservoir make it “easier” to move heat in and out e < e C Another way to state the second law is: There is a limit as to how efficient you can make your engine
The First and Second Laws The first law of thermodynamics says: The second law of thermodynamics says: The two laws imply: W < Q H W Q H
Dealing With Engines Most engine problems can be solved by knowing how to express the efficiency and relate the work and heats: W = Q H - Q C e = W/Q H = (Q H - Q C )/Q H = 1 - (Q C /Q H ) e C = 1 - (T C /T H ) For individual parts of the cycle you can often use the ideal gas law: PV = nRT
P-V Diagram for Engine The total work output per cycle Positive work is clockwise
Refrigerators A refrigerator is a device that uses work to move heat from low to high temperature The refrigerator is the device on the back of the box Your kitchen is the hot reservoir Heat Q C is input from the cold reservoir, W is input power, Q H is output to the hot reservoir
How a Refrigerator Works The fluid is pumped into the hot chamber (coils on the back) and compressed, adding work W Need special fluid that can evaporate and condense in the right place
Refrigerator Cycle Liquid Gas Compressor (work =W) Expansion Valve Heat removed from fridge by evaporation Heat added to room by condensation High Pressure Low Pressure QCQC QHQH
Refrigerator Performance Input equals output: The equivalent of efficiency for a refrigerator is the coefficient of performance COP: COP = Q C / W Unlike efficiency, COP can be greater than 1
Today’s PAL Lets say you wanted to cool your house on a hot day so you buy a refrigerator, plug it in and open the door. Does the temperature of the house, increase, decrease or stay the same? Why? (assume insulated house)
Heat Pumps It removes Q C from your house and exhausts Q H to the outside It removes Q C from the outside and adds Q H to your house Heat pump COP = Q H / W Want the most heat output for the work
Refrigerators and Temperature We can relate the coefficient of performance to the temperature: COP = T C /(T H -T C ) This is the maximum COP for a fridge operating between these two temperatures
Refrigerators and the Second Law You cannot move heat from low to high temperature without the addition of work COP cannot be infinite Heat doesn’t flow “uphill” by itself, although this would not violate the first law
Statements of the Second Law It is impossible for any device which operates in a cycle to convert heat completely to work For refrigerators:
Next Time Read: Homework: Ch 15, P 26, 31, 35, 37 I will also post some practice problems Won’t count for grade