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The Second Law of Thermodynamics

Physics 102 Professor Lee Carkner Lecture 7. The Second Law of Thermodynamics. 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 D V = (P) (V f -V i ) Sign of work? Volume decreased. Engines.

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The Second Law of Thermodynamics

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

  2. PAL #6 First Law • 1 mole of gas at 300 K and 2 m3 compressed to 1 m3, constant pressure • P = nRT/V = (1)(8.31)(300)/(2) = 1246.5 Pa • W = PDV = (P) (Vf-Vi) • Sign of work? • Volume decreased

  3. Engines • General engine properties: • An input of heat • An output of heat

  4. Heat and Work Over the Cycle • Four parts of the cycle: • compression • output of heat QC • 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 DU=(QH-QC)-W =0 W = QH - QC

  5. Efficiency • In order for the engine to work we need a source of heat for QH e = W/QH • An efficient engine converts as much of the input heat as possible into work

  6. 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?

  7. Efficiency and Heat e = 1 - (QC /QH) • The efficiency depends on how much of QH is transformed into W and how much is lost in QC: • Reducing the output heat means improving the efficiency

  8. 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 (QC)

  9. Carnot Engine • In 1824 Sadi Carnot related the maximum efficiency to the temperature of the reservoirs: eC = 1 - (TC / TH) • A hot input reservoir and a cold output reservoir make it “easier” to move heat in and out e < eC • Another way to state the second law is: There is a limit as to how efficient you can make your engine

  10. The First and Second Laws • The first law of thermodynamics says: • The second law of thermodynamics says: • The two laws imply: • W < QH • W  QH

  11. Dealing With Engines • Most engine problems can be solved by knowing how to express the efficiency and relate the work and heats: W = QH - QC e = W/QH = (QH - QC)/QH = 1 - (QC/QH) eC = 1 - (TC/TH) • For individual parts of the cycle you can often use the ideal gas law: PV = nRT

  12. P-V Diagram for Engine • The total work output per cycle • Positive work is clockwise

  13. 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 QC is input from the cold reservoir, W is input power, QH is output to the hot reservoir

  14. 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

  15. Refrigerator Cycle Compressor (work =W) Gas QC QH Low Pressure High Pressure Heat removed from fridge by evaporation Heat added to room by condensation Liquid Expansion Valve

  16. Refrigerator Performance • Input equals output: • The equivalent of efficiency for a refrigerator is the coefficient of performance COP: COP = QC / W • Unlike efficiency, COP can be greater than 1

  17. 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)

  18. Heat Pumps • It removes QC from your house and exhausts QH to the outside • It removes QC from the outside and adds QH to your house • Heat pump COP = QH / W • Want the most heat output for the work

  19. Refrigerators and Temperature • We can relate the coefficient of performance to the temperature: COP = TC /(TH-TC) • This is the maximum COP for a fridge operating between these two temperatures

  20. 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

  21. Statements of the Second Law • It is impossible for any device which operates in a cycle to convert heat completely to work • For refrigerators:

  22. 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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