 # The Second Law of Thermodynamics Physics 102 Professor Lee Carkner Lecture 7.

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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) = 1246.5 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 149200 joules per second to the drive train and burns fuel at a rate of 746000 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: 15.7-15.11  Homework: Ch 15, P 26, 31, 35, 37  I will also post some practice problems  Won’t count for grade

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