The Laws of Thermodynamics - Revisited

1. The Laws of Thermodynamics - Revisited Arthur Shavit, Professor Emeritus Department of Mechanical Engineering Technion – Israel Institue of Technology Haifa, ISRAEL

2. The second Law Usual statement A PMM2 is impossible A PMM2 is cyclic device that produces positive work while interacting with a single reservoir Questions: Is that a law of thermodynamics? What is a law of thermodynamics? To answer these question some introduction is needed

3. The Structure of Thermodynamics • • Definitions • • Experimental facts • • Laws (axioms) • • Theorems and Corollaries • Applications

4. Definitions • Body • Environment • Primitive property • State • Allowed states • Identical states • System • Change of state • Path • Interaction • Process • Cycle

5. Definitions – some examples BodyA body is a part of space enclosed by a well defined boundary. The boundary may be physical or mathematical, fixed or changing in time, closed or open to passage of matter. Environment Everything outside the boundary of the body Primitive Property Primitive property of a body is specified by subjecting the body to an operation or a test, that requires no previous knowledge of the body, the result of which at a specific time is the value of the primitive property at that time. A primitive property may be determined without the need to change the conditions of the body.

6. Definitions – examples cont. State The condition of the body identified by all its primitive properties Identical statesStates that have the same values of thecorresponding primitive properties. Change of stateOccurs when the value of at least one primitive property is changed. Allowed states Allowed states of a body are all the states which the body may inherently attain consistent with the definition of the body.

7. System An idealization of a body that may includes only part of the allowed states of the body. It is also required that the system could be isolated from its environment The allowed states may be given as an explicit list. or implicitly, by describing one state and all possible variations of state. These variations must be consistent with: 1. the laws of matter, 2. the constraints. 3. the passive resistances. Closed System A system where matter may not cross its boundary. Open System A system where matter may cross its boundary.

8. General Property An observable characteristic of the system, whose change between two end states is independent of the path. Derived property: A property that is not primitive Examples: – Ampere-hour on a battery. – Life time of an incandescent lamp.

9. Classifications of properties • Primitive – Derived • Extensive – Intensive • Independent – Dependent • Conservative – Non conservative

10. Equilibrium An equilibrium state is one that can not be changed without a corresponding change in the environment. 4 types according to the changes required in the environment Unstable Stable Neutral Metastable Mutual equilibrium

11. Types of Equilibria The type of equilibrium is characterized by the required change in the environment for a finite change in the system

12. Neutral vs Themodynamic property Neutral Property A property of neutral equilibrium that can change in both directions by only temporary changes in the environment. Example: The horizontal position of the system in a gravity field. Substate A state different from others only by neutral properties. Thermodynamic Property Any property that is not neutral. Note: A thermodynamic property may have several substates. Thermodynamic State A state that includes only thermodynamic properties

13. Work Interaction Work is an interaction between two systems such that whatever happened in each system and its boundary could be repeated exactly while the sole external effect is a change of level of a weight. Measure of work The work of a system equals the number of weights, in the test, that underwent a unit change of level. Adiabatic processA process having no interactions other than work. Dislacement of a wire pulled by a force Modes of quasistatic work Change of volume under pressure. Change of magnetization in magnetic field. Change of surface area with surface tension . Etc.

14. First law / Energy First law The work of a system undergoing an adiabatic process depends only on the end states. Energy A property whose change between two end states is determined by the adiabatic work.

15. The Laws of Thermodynamics A law is a generalization of all known experimental facts. Zeroth Law Maxwell, 1891 First Law Clausius, 1850 (Joule, 1848) Clausius, 1850 (Carnot, 1824) Second Law State principle Kline & Koenig, 1957 Third Law Nernst, 1906

16. Work of a system in a stable state Theorem: A system, in a stable equilibrium state, cannot change its state while the only external effect is the rise of the level of weight. Proof Assume that the theorem is incorrect then there should be at least one case where a the stable state changes while the only external effect is a rise in a level of a weight. It possible to lower the weight and impart a velocity to the system. In this case the net external effect is zero while the state of the system changed from a stable state to another. That violates the definition of a stable state.

17. Quasi-stable State Some non equilibrium states can be made stable by eliminating some of the allowed stated, while retaining others. This can be achieved by altering passive resistances and constraints. A state made stable by altering passive resistances and/or constraints is called a quasi-stable state. The stable state so produced is called corresponding stable state.

18. Heat Interaction Heat is an interaction between two systems each in a stable state with no change in the constraints and the passive resistances. Heat Interaction between systems not in stable states. Interaction during which the system vary only through the corresponding stable states.

19. Zeroth Law If two systems, A and B, are each in mutual equilibrium with a system C then they are in mutual equilibrium with each other. Is that trivial???

20. Temperature Thermometer Temperature is a property that is common to all systems in mutual equilibrium.

21. State Principle The stable state of a system bounded by a fixed boundary and subjected to prescribed force fields is fully determined by its energy. The state principle fixes the number of independent properties of a system in a stable state. These are the parameters of the boundary and the force fields and the energy.

22. Heat Machines A closed system that undergoes a cycle while having interactions Heat Machine Heat Engine Heat Pump - Refrigerator

23. The Second Law Reservoir A system in a stable state whose temperaturestays constant under finite interactions. PMM2 A heat engine that communicates with a single reservoir The Second Law (Two statements) • A PMM2 is not possible • It is not possible to transfer heat from a reservoir at a low temperature to one at a higher with no other effects Are these really Laws (axioms)???

24. Clausius Inequality (a corollary of the second law) For a reversible process Leads to define a property

25. The Law of Stable Equilibrium A system having specified allowed states can reach, from any given state, one and only one stable state and leave no effect on the environment.

26. Gibbs Principle of General Inertia A finite rate of change (or a finite rate of a rate of change) cannot be stopped by means of infinitesimal alteration in the circumstances. (J.W. Gibbs, Collected Works, Yale University. Press, Vol. 1 p.56,1948)

27. The Unified Laws Second law First law State principle Law of stable equilibrium Zeroth Law Gibbs Principle Prague 14.04.2003 Structure of Thermodynamics

28. Pressure Pressure is a thermodynamic property. weight A weight is an idealized body whose only independent property is its level in a gravitational field. Theorem A process involving no effects except the lowering of weights is impossible.

29. Work Interaction Work is an interaction between two systems such that whatever happened in each system and its boundary could be repeated exactly while the sole external effect is a change of level of a weight.

30. Y1 X1 X1 A1 A2 X2 Y2 Y2 X2 B B Y0 X0 Y0 X0 C Y00 X00 weights Proof of first law

31. Proof of the State Principle According to the Law of Stable States one and only one stable state is possible for a system of fixed constraints (and passive resistances) that undergoes no interactions (constant energy) It follows that the stable state is determined by the constraints Thus Where is any property of the system in stable equilibrium are the constraints are the passive resistances

32. Work of a system in combination with a reservoir In general Called Available Work Define

33. Entropy Define entropy

34. Criterion of Equilibrium It is necessary and sufficient for equilibrium of an isolated system, not subdivided by adiabatic walls, that all possible variation in state satisfy: (dS)E ≤ 0

35. Stable Equilibrium For every possible variation for which

36. Unstable Equilibrium For at least one possible variation for which

37. Metastable Equilibrium For all possible variation for which And for p.v. smaller than a certain value And for some possible variation, larger than that value, at least one p.v. is

38. Neutral Equilibrium For at least one possible variation for which and

39. Proof of the Zeroth Law Any property Thus Consider two systems A and B in mutual equilibrium 39 Krakow 12.09.2011 The Laws of Thermodynamics Revisited

40. Proof of the Zeroth Law (cont.) For equilibrium

41. Temperature Kelvin scale For a system in equilibrium with the reservoir For the triple point of water 41 Krakow 12.09.2011 The Laws of Thermodynamics Revisited

42. Alternative Criteria of Equilibrium For all possible variations to states of equal E equal S } uniform T uniform and equal T } uniform T and equal T

43. Alternative Criteria of Equilibrium For all possible variations From states of to states of } uniform T equal S uniform p equal p and S } uniform p and T equal p uniform p and T equal p and T

44. Alternative Criteria of Equilibrium Kelvin scale For a system in equilibrium with the reservoir Select For the triple point of water

45. Many Thanks תודה רבה Dziękuję Bardzo 45 Krakow 12.09.2011 The Laws of Thermodynamics Revisited

46. Questions ??? Discussions ???

48. Notations A,aHelmholz free energy xdegree of reaction E,e energy xpassive resistance G,gGibbs free energy bconstraint H,henthalpy mchemical potential mmass ffugacity nnumber of moles Wwork ppressure Qheat S,sentropy Ttemperature U,uinternal energy V,vvolume

50. Simple system A system that has only one boundary quasistatic work parameter. If the parameter is the volume the system is called a simple compressible system. Such a system has exactly 2 independent properties: the volume and the energy. (V and E)