Second Law of Thermodynamics -

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1 Second Law of Thermodynamics - REVIEW ENTROPY EXAMPLE Dr. Garrick 1/19/09

2 First Law of Thermodynamics you can t win! First Law of Thermodynamics: Energy cannot be Created or Destroyed the total energy of the universe cannot change though you can transfer it from one place to another E universe = 0 = E system + E surroundings 2

3 Recap: 1st Law of Thermodynamics energy conservation Q = U + W 3 Heat flow into system work done is area under curve for closed cycle U=0 Q=W Increase in internal energy of system Work done by system P V 09

4 Review - Thermodynamics 4 The 1 st Law of Thermodynamics U = Q + W It is energy conservation The 2 nd Law of Thermodynamics Engines and refrigerators --> Efficiency of doing work < 100% Entropy and disorder --> Direction for thermal processes 1/20/2009

5 Energy Tax you can t break even! to recharge a battery with 100 kj of useful energy will require more than 100 kj every energy transition results in a loss of energy conversion of energy to heat which is lost by heating up the surroundings 5

6 Heat Tax fewer steps generally results in a lower total heat tax 6

7 Engines and Refrigerators 7 HEAT ENGINE REFRIGERATOR T H T H Q H system Q H W W Q C Q C T C T C 11

8 Heat Engine: A gas system in cyclic process Since it is a cyclical process, U = 0 8 Therefore, Q net = W eng The work done by the engine equals the net energy absorbed by the engine The work is equal to the area enclosed by the curve of the PV diagram 1/20/2009 8

9 HEAT ENGINE REFRIGERATOR T H T H Q H system Q H System of interest W eng W ref Q C Q C T C T C Q = U - W Q = U - W Q H - Q C 0 Q C - Q H 0 Q H - Q C = -W = W eng Q H - Q C = + W = W ref for a heat engine for refrigerator 9 1/20/2009

10 Heat Engine Efficiency vs. Refrigerator Coefficient Of Performance HEAT ENGINE 10 REFRIGERATOR/heat pump T H T H Q H Q H W eng W ref Q C Q C T C T C Q H - Q C = W eng Q H - Q C = W ref Eff = W eng / Q H Eff = 1 - Q C / Q H COP refrig = Q C / W ref = Q C / (Q H - Q C ) COP ht. pump = Q H / W hp = Q H / (Q H - Q C ) 1/20/2009

11 Second Law of Thermodynamics 1. The heat engine statement, or Kelvin-Planck statement: No engine operating in a cycle can absorb heat from a reservoir and convert it entirely to equal amount of work Eff =1 - Q c /Q H < 1 Or Q c /Q H > 0 2. The refrigerator statement, or Clausius statement: 11 No engine operating in a cycle can transfer heat from one object to another at a higher temperature without the input of work ==> Heat doesn t automatically go from a cold object to a hot one. 1/20/2009

12 Two kinds of processes and entropy 1. Irreversible processes 12 (a) All naturally occurring processes proceed in one direction only. They never, of their own accord, proceed in the opposite direction. Such spontaneous one-way processes are irreversible. (b) Although the wrong-way events do not occur, none of them would violate the law of conservation of energy.

13 2. Reversible process In reversible process, we make a small change in a system and its environment; by reversing that change, the system and environment will return to their original conditions. In a truly reversible process, there would be no friction, turbulence, or other dissipative effects, which will cause non-compensatory losses of energy.

Reversibility of Process any spontaneous process is irreversible it will proceed in only one direction a reversible process will proceed back and forth between the

14 Reversibility of Process any spontaneous process is irreversible it will proceed in only one direction a reversible process will proceed back and forth between the two end conditions equilibrium results in no change in free energy if a process is spontaneous in one direction, it must be nonspontaneous in the opposite direction 14

Spontaneous Processes A waterfall runs downhill A lump of sugar dissolves in a cup of coffee At 1 atm, water freezes below 0 0 C and ice melts above 0 0 C

15 Spontaneous Processes A waterfall runs downhill A lump of sugar dissolves in a cup of coffee At 1 atm, water freezes below 0 0 C and ice melts above 0 0 C Heat flows from a hotter object to a colder object A gas expands in an evacuated bulb Iron exposed to oxygen and water forms rust spontaneous nonspontaneous

16 spontaneous nonspontaneous

17 Second Law of Thermodynamics The entropy change (Q/T) of the system+environment 0 never < 0 order to disorder Consequences A disordered state cannot spontaneously transform into an ordered state No engine operating between two reservoirs can be more efficient than one that produces 0 change in entropy. This is called a Carnot engine 17

18 Carnot Cycle Idealized Heat Engine No Friction S = Q/T = 0 Reversible Process Isothermal Expansion Adiabatic Expansion Isothermal Compression Adiabatic Compression 18 32

19 Carnot Cycle: based on ideal reversible processes 19 1 Isothermal Expansion 2 Adiabatic Expansion 3 Isothermal Compression 4 Adiabatic Compression 1/20/2009

20 Heat Engine: Carnot Cycle 20 Efficiency: Eff 1 Q c Q h 1 T c T h No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two temperatues. -- Carnot Theorem, by Sadi Carnot 1/20/2009

21 Real Engines vs Carnot Engines 21 All real engines are less efficient than the Carnot engine Real engines are irreversible because of friction Real engines are irreversible because they complete cycles in short amounts of time 1/20/2009

22 Second Law of Thermodynamics - ENTROPY

23 Entropy 23 The 0 th law of Thermodynamics defines a state variable: T The 1 st law of Thermodynamics defines a state variable: U The 2 nd law of Thermodynamics defines a new state variable: S, the entropy The change in entropy, S, between two equilibrium states is given by the heat energy, Q r, transferred along the reversible path divided by the absolute temperature, T, of the system in this interval 1/20/2009

24 Entropy, cont. 24 This applies only to the reversible path, even if the system actually follows an irreversible path To calculate the entropy change for an irreversible process, model it as a reversible process When energy is absorbed, Q is positive and entropy increases When energy is expelled, Q is negative and entropy decreases Physics 103, Fall 2007, U. Wisconsin 1/20/2009

25 3. Entropy (S) Entropy is a physical quantity that controls the direction of irreversible processes. It is a property of the state of a system; like T, P, V, E int. 25 Entropy principle: If an irreversible process occurs in a closed system, the entropy of that system always increases; it never decreases.

26 Entropy State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. energy, enthalpy, pressure, volume, temperature, entropy Potential energy of hiker 1 and hiker 2 is the same even though they took different paths.

27 First Law of Thermodynamics Energy can be converted from one form to another but energy cannot be created or destroyed. Second Law of Thermodynamics The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. Spontaneous process: Equilibrium process: S univ = S sys + S surr > 0 S univ = S sys + S surr =

28 The 2 nd Law of Thermodynamics the total entropy change of the universe must be positive for a process to be spontaneous for reversible process S univ = 0, for irreversible (spontaneous) process S univ > 0 S universe = S system + S surroundings if the entropy of the system decreases, then the entropy of the surroundings must increase by a larger amount when S system is negative, S surroundings is positive the increase in S surroundings often comes from the heat released in an exothermic reaction 28

29 The Entropy definition change of entropy for reversible change for processes a reversible process: S i f dq T (reversible) (6.2) Here dq is the increment of heat energy that is transferred into (or out) of the closed system at temperature T. 29 If the process is isothermal, Q S Q 0 S 0 T the entropy of that system increases.( if Q<0 ). S 0

30 Adiabatic Compression During adiabatic compression of an ideal gas, the entropy of the gas Decreases. Stays constant. Increases. 30 No heat is transferred in or out of the system during an adiabatic process - therefore, entropy remains constant. Physics 103, Fall 2007, U. Wisconsin 1/20/2009

31 PROPERTY DIAGRAMS WITH ENTROPY AS A COORDINATE: 31 T-s diagram Processes on T-s diagram

32 Features of T-s diagram: Area on the diagram have the dimensions of heat 32 In the mixed-phase region, the constant pressure lines are horizontal In a reversible process the area under the curve is equal to the heat transfer in the corresponding process Vertical lines represents isentropic processes (no change in S, entropy) In a reversible cycle, the area enclosed by the curve representing the process is equal to the net heat transfer to the fluid and so, from the first law is also equal to the net work

33 Example: Brayton cycle on T-s diagram 33 Processes: 1-2s Isentropic compression 1-2 Actual compression 3-4s Isentropic expansion 3-4 Actual expansion

34 Entropy and Disorder Entropy increase indicates the natural direction for a thermal process. Entropy can be described in terms of disorder 34 A disorderly arrangement is much more probable than an orderly one if the laws of nature are allowed to act without interference This comes from a statistical mechanics development 1/20/2009

35 Entropy and Disorder, cont. Isolated systems tend toward greater disorder, and entropy is a measure of that disorder 35 This gives the Second Law as a statement of what is most probably rather than what must be The Second Law defines the direction of time of all events as the direction in which the entropy of the universe increases 1/20/2009

36 Entropy Question 36 Suppose your roommate is Mr. Clean and tidies up your messy room after a big party. What happens to the entropy of the room (assume that room and its contents are isolated from rest of the universe)? Decreases Stays the same Increases correct The books may be in order after Clean s work, but the work done by your roommate generates heat, resulting in increase of the room s (system+environment) entropy. 1/20/2009

37 Example 6.24 Example 37 One kg of water initially at 160 oc, 1.5 bar undergoes an isothermal internally reversible compression process to the saturated liquid state. Determine the work and heat transfer, each in KJ. Sketch the process on the p-v and T-s coordinates. Associate the work and heat transfer with the areas on the diagrams

38 Example 160 C (433K); 1.5 bar C (433K); saturated liquid Find W, Q in KJ Assume Closed system, internally reversible, no change in Kinetic or potential energy State 1 Superheated vapor (table A-4) State 2 Saturated water (Liquid-vapor) (table A-3)

Chapter 12. The Laws of Thermodynamics. First Law of Thermodynamics

Chapter 12. The Laws of Thermodynamics. First Law of Thermodynamics Chapter 12 The Laws of Thermodynamics First Law of Thermodynamics The First Law of Thermodynamics tells us that the internal energy of a system can be increased by Adding energy to the system Doing work