Chapter 12. The Laws of Thermodynamics W = P!V. Principles of Thermodynamics. Example Converting Internal Energy to Mechanical !U = Q " P!
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1 rinciples of Thermodynamics hapter 2 The Laws of Thermodynamics Energy is conserved FIRST LW OF THERMODYNMIS Examples: Engines (Internal -> Mechanical) Friction (Mechanical -> Internal) ll processes must increase entropy SEOND LW OF THERMODYNMIS Entropy is measure of disorder Engines can not be 00% efficient 2 onverting Internal Energy to Mechanical Work done by expansion W = F!x, F =,!x =! / Example 2. cylinder of radius 5 cm is kept at pressure with a piston of mass 75 kg. a) What is the pressure inside the cylinder?.950x0 5 a b) If the gas expands such that the cylinder rises 2.0 cm, what work was done by the gas? 83.8 J c) What amount of the work went into changing the gravitational E of the piston? 88.3 J d) Where did the rest of the work go? ompressing the outside air 3 4 Example 2.2a 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. The pressure inside the cylinder is the pressure outside. Example 2.2b 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. The temperature inside the cylinder is the temperature outside. 5 6
2 Example 2.2c 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. If the gas is heated by a steady flame, and the piston rises to a new equilibrium position, the new pressure will be than the previous pressure. Some ocabulary Isobaric = constant Isovolumetric = constant Isothermal T = constant diabatic Q = Example 2.3a Example 2.3b b is a T b is T a 9 0 Example 2.3c Example 2.3d W ab is 0 ocabulary: W ab is work done by gas between a and b U b is U a 2
3 Example 2.3e Example 2.4a Q ab is 0 ocabulary: Q ab is heat added to gas between a and b b is a 3 4 Example 2.4b Example 2.4c W ab is 0 Q ab is Example 2.4d Example 2.4e U b is U a T b is T a 7 8
4 Example 2.5a Example 2.5b b is a = nrt W ab is 0 = nrt 9 20 Example 2.5c Example 2.5d T b is T a U b is U a = nrt = nrt 2 22 Example 2.5e Q ab is 0 = nrt 23 Work from closed cycles onsider cycle -> -> W -> -W -> 24
5 Work from closed cycles onsider cycle -> -> Work from closed cycles Reverse the cycle, make it counter clockwise W ->-> = rea -W -> W -> Example 2.6 (m 3 ) a) What amount of work is performed by the gas in the cycle IFI? W=3.04x0 5 J b) How much heat was inserted into the gas in the cycle IFI? Q = 3.04x0 5 J c) What amount of work is performed by the gas in the cycle IFI? W = -3.04x0 5 J 27 onsider a monotonic ideal gas. a) What work was done by the gas from to? 75 20,000 J b) What heat was added to the gas between and? 50 20,000 c) What work was done by the gas from to? 25-0,000 J d) What heat was added to the gas beween and? -25,000 J e) What work was done by the gas from to? 0 f) What heat was added to the gas from to? 5,000 J Example 2.7 (ka) (m 3 ) Example ontinued Example 2.8a Take solutions from last problem and find: a) Net work done by gas in the cycle b) mount of heat added to gas W + W + W = 0,000 J Q + Q + Q = 0,000 J This does NOT mean that the engine is 00% efficient! onsider an ideal gas undergoing the trajectory through the diagram. In going from to to, the work done Y the gas is
6 Example 2.8b Example 2.8c In going from to to, the change of the internal energy of the gas is 0. In going from to to, the amount of heat added to the gas is 0. D 3 32 Example 2.8d Example 2.8e In going from to to to D to, the work done Y the gas is 0. D In going from to to to D to, the change of the internal energy of the gas is 0. D In going from to to to D to, the heat added to the gas is 0. Example 2.8f D Entropy Measure of Disorder of the system (randomness, ignorance) S = k log(n) p y N = # of possible arrangements for fixed E and Q p x 35 36
7 Entropy Total Entropy always rises! (2nd Law of Thermodynamics) dding heat raises entropy!s = Q / T Why does Q flow from hot to cold? onsider two systems, one with T and one with T llow Q > 0 to flow from T to T Entropy changed by: Defines temperature in Kelvin!!S = Q/T - Q/T If T > T, then!s > 0 System will achieve more randomness by exchanging heat until T = T Efficiencies of Engines onsider a cycle described by: W= work done by engine = heat that flows into engine Idealized engine Most efficient possible arnot Engines from source at = heat exhausted from engine at lower temperature, T cold engine: Efficiency is defined: e = W =! =! Since!S = Q / T > 0, >! T cold > T cold! engines : e <! T cold engine W e = W =! T cold arnot ycle Example 2.9 n ideal engine (arnot) is rated at 50% efficiency when it is able to exhaust heat at a temperature of 20 º. If the exhaust temperature is lowered to -30 º, what is the new efficiency. e =
8 Since!S = Q / T > 0, Refrigerators Given: Refrigerated region is at T cold Find: Efficiency refrigerator: Heat exhausted to region with e = W = =! /! > T cold! > T cold! refrigerator: e < fridge Note: Highest efficiency for small T differences / T cold! W Given: Inside is at Outside is at T cold Find: Efficiency heat pump: e = W = =! Since, > T cold!s = Q / T > 0 Heat umps! > T cold! heat pump Like Refrigerator: Highest efficiency for small!t! / heat pump: e <! T cold / W Example 2.0 modern gas furnace can work at practically 00% efficiency, i.e., 00% of the heat from burning the gas is converted into heat for the home. ssume 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? ssume T inside = 295 ºK. Example 2.a n engine does an amount of work W, and exhausts heat at a temperature of 50 degrees. The chemical energy contained in the fuel must be greater than, and not equal to, W. a) True b) False T = = K = Example 2.b locomotive is powered by a large engine that exhausts heat into a large heat exchanger that stays close to the temperature of the atmosphere. The engine should be more efficient on a very cold day than on a warm day. Example 2.c n air conditioner uses an amount of electrical energy U to cool a home. The amount of heat removed from the home must be less than or equal to U. a) True b) False a) True b) False 47 48
9 Example 2.d heat pump uses an amount of electrical energy U to heat a home. The amount of heat added to a home must be less than or equal to U. a) True b) False 49
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