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Chapter 12

Chapter 12. The Laws of Thermodynamics. Principles of Thermodynamics. Energy is conserved FIRST LAW OF THERMODYNAMICS Examples: Engines (Internal -> Mechanical) Friction (Mechanical -> Internal) All processes must increase entropy SECOND LAW OF THERMODYNAMICS

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Chapter 12

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  1. Chapter 12 The Laws of Thermodynamics

  2. Principles of Thermodynamics • Energy is conserved • FIRST LAW OF THERMODYNAMICS • Examples: Engines (Internal -> Mechanical) Friction (Mechanical -> Internal) • All processes must increase entropy • SECOND LAW OF THERMODYNAMICS • Entropy is measure of disorder • Engines can not be 100% efficient

  3. Work done by expansion Converting Internal Energy to Mechanical

  4. Example 12.1 A cylinder of radius 5 cm is kept at pressure with a piston of mass 75 kg. a) What is the pressure inside the cylinder? b) If the gas expands such that the cylinder rises 12.0 cm, what work was done by the gas? c) What amount of the work went into changing the gravitational PE of the piston? d) Where did the rest of the work go? 1.950x105 Pa 183.8 J 88.3 J Compressing the outside air

  5. Example 12.2 A massive copper piston traps an ideal gas as shown to the right. The piston is allowed to freely slide up and down and equilibrate with the outside air. Choose T or F. A. The pressure is higher inside the cylinder than outside. B. The temperature inside the cylinder is higher than outside the cylinder. C. If the gas is heated by applying a flame to cylinder, and the piston comes to a new equilibrium, the inside pressure will have increased. T F F

  6. V V V V Some Vocabulary P • Isobaric • P = constant • Isovolumetric • V = constant • Isothermal • T = constant • Adiabatic • Q = 0 P P P

  7. Outside Air: Room T, Atm. P Example 12.3 A massive piston traps an amount of Helium gas as shown. The piston freely slides up and down. The system initially equilibrates at room temperature (a) Weight is slowly added to the piston, isothermally compressing the gas to half its original volume (b) A. Pb ( > < = ) Pa B. Tb ( > < = ) Ta C. Wab ( > < = ) 0 D. Ub ( > < = ) Ua E. Qab ( > < = ) 0 Vocabulary: Wab is work done by gas between a and b Qab is heat added to gas between a and b

  8. Outside Air: Room T, Atm. P Example 12.4 A massive piston traps an amount of Helium gas as shown. The piston freely slides up and down. The system initially equilibrates at room temperature (a) Weight is slowly added to the piston, adiabatically compressing the gas to half its original volume (b) A. Pb ( > < = ) Pa B. Wab ( > < = ) 0 C. Qab ( > < = ) 0 D. Ub ( > < = ) Ua E. Tb ( > < = ) Ta Vocabulary: Wab is work done by gas between a and b Qab is heat added to gas between a and b

  9. Outside Air: Room T, Atm. P Example 12.5 A massive piston traps an amount of Helium gas as shown. The piston freely slides up and down. The system initially equilibrates at room temperature (a) The gas is cooled, isobarically compressing the gas to half its original volume (b) A. Pb ( > < = ) Pa B. Wab ( > < = ) 0 C. Tb ( > < = ) Ta D. Ub ( > < = ) Ua E. Qab ( > < = ) 0 Vocabulary: Wab is work done by gas between a and b Qab is heat added to gas between a and b

  10. WA->B -WB->A Work from closed cycles Consider cycle A -> B -> A

  11. Work from closed cycles Consider cycle A -> B -> A WA->B->A= Area

  12. -WB->A WA->B Work from closed cycles Reverse the cycle, make it counter clockwise

  13. a) What amount of work is performed by the gas in the cycle IAFI? b) How much heat was inserted into the gas in the cycle IAFI? c) What amount of work is performed by the gas in the cycle IBFI? Example 12.6 W=3.04x105 J Q = 3.04x105 J V (m3) W = -3.04x105 J

  14. Consider a monotonic ideal gas. a) What work was done by the gas from A to B? b) What heat was added to the gas between A and B? c) What work was done by the gas from B to C? d) What heat was added to the gas beween B and C? e) What work was done by the gas from C to A? f) What heat was added to the gas from C to A? Example 12.7 P (kPa) A 75 20,000 J 50 20,000 B 25 -10,000 J C V (m3) -25,000 J 0.2 0.4 0.6 0 15,000 J

  15. Example Continued Take solutions from last problem and find: a) Net work done by gas in the cycle b) Amount of heat added to gas WAB + WBC + WCA = 10,000 J QAB + QBC + QCA = 10,000 J This does NOT mean that the engine is 100% efficient!

  16. Entropy • Measure of Disorder of the system(randomness, ignorance) • S = kBlog(N) N = # of possible arrangements for fixed E and Q py px

  17. Entropy • Total Entropy always rises! (2nd Law of Thermodynamics) • Adding heat raises entropy Defines temperature in Kelvin!

  18. Why does Q flow from hot to cold? • Consider two systems, one with TA and one with TB • Allow Q > 0 to flow from TA to TB • Entropy changed by:DS = Q/TB - Q/TA • If TA > TB, then DS > 0 • System will achieve more randomness by exchanging heat until TB = TA

  19. Qhot engine W Qcold Efficiencies of Engines • Consider a cycle described by:W, work done by engineQhot, heat that flows into engine from source at ThotQcold, heat exhausted from engine at lower temperature, Tcold • Efficiency is defined: Since ,

  20. Carnot Engines • Idealized engine • Most efficient possible

  21. Carnot Cycle

  22. Example 12.8 An ideal engine (Carnot) is rated at 50% efficiency when it is able to exhaust heat at a temperature of 20 ºC. If the exhaust temperature is lowered to -30 ºC, what is the new efficiency. e = 0.585

  23. Qhot engine W Qcold Refrigerators Given: Refrigerated region is at Tcold Heat exhausted to region with Thot Find: Efficiency Since , Note: Highest efficiency for small T differences

  24. Qhot engine W Qcold Heat Pumps Given: Inside is at Thot Outside is at Tcold Find: Efficiency Since , Like Refrigerator: Highest efficiency for small DT

  25. Example 12.9 A modern gas furnace can work at practically 100% efficiency, i.e., 100% of the heat from burning the gas is converted into heat for the home. Assume that a heat pump works at 50% of the efficiency of an ideal heat pump. If electricity costs 3 times as much per kw-hr as gas, for what range of outside temperatures is it advantageous to use a heat pump?Assume Tinside = 295 ºK.

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