1. 1 Lecture 2 Summary Summary 1) The Zeroth Law: Systems that have no tendency to transfer heat are at the same temperature. 2) Work: A process which transfers energy to or from a system by applying a force to cause a displacement. 3) Heat: A process which transfers energy between two systems at different temperatures. 4) The First Law: Energy is conserved for all processes. 5) The Second Law: The entropy of the universe increases for all processes except reversible ones, for which there is no change in S univ. 6) The absolute temperature scale relates two temperatures by the heat flow of a Carnot cycle at those temperatures. 7) The Third Law: There exists a zero of temperature which is unobtainable and at which the change in entropy for any process becomes zero.

2. 2 Lecture 3: Equilibrium Main Points: 1) Definitions (system, phase, component) 2) Reversible processes produce no entropy 3) Infinitesimal processes about equilibrium points are reversible 4) Energy functions 5) Criteria for reversibility in different systems The concept of equilibrium plays an important role in thermodynamics. Here we explore the meaning of equilibrium and the related concept of reversibility after defining some important terms.

3. 3 Additional Definitions Definitions: A chemical system is any system made up of one or more elements. We generally restrict ourselves to interest in the bulk physical and chemical properties for simplicity, although we could extend our treatment to other properties, including stress, surface properties, etc. A phase is any distinguishable region of a chemical system which is in a well-defined state of internal equilibrium. Phases can be open or closed depending on whether they change or do not change the amount of material in the phase, respectively. A component is any independently variable chemical species of the system: For example, P in Si, Ga and As, (C 2 H 5 )OH in H 2 O.

4. 4 Criteria for Equilibrium For irreversible processes For reversible processes Never Irreversible processes are also called spontaneous or natural Remember, that disorder can never be destroyed once created and thus for a process to be reversible it must create no entropy. Process Result

5. 5 The Equilibrium Postulate In a system that is in internal equilibrium, any infinitesimal process about a point of equilibrium is reversible. An infinitesimal change in a system introduces no finite driving forces and thus no dissipative processes if the system is in equilibrium. Examples of reversible and irreversible processes? Striking a match Expansion of a gas into a vacuum Slow expansion of a gas in a cylinder with a piston Slow stretch of a rubber band Drop of dye in a swimming pool T1T1 T2T2 T3T3

6. 6 The Equilibrium Postulate For an infinitesimal process performed on a single-phase closed chemical system: From our definition of entropy In a simple chemical system only mechanical work is done. If the process is reversible we can substitute: If the process is reversible then T is well defined for the process and we can relate the heat flow to the temperature and change in entropy. If the process is reversible then P is well defined for the process and we can relate the mechanical work done on the system to the volume and pressure.

7. 7 The Equilibrium Postulate So for a closed simple system in internal equilibrium a reversible infinitesimal process changes the internal energy by an amount: To generalize this to an open system we need to take into account the amount the internal energy changes as the amount of matter in the system changes. We do this generally by adding the term: Where we define the derivative of U with respect to the amount of component i at constant S, V and the amount of other components as the chemical potential Then n dn If the system is open, then removing a small amount of material removes the internal energy of that part of the material (U is extensive).

8. 8 Enthalpy Helmholtz Free Energy Gibbs Free Energy Energy Functions Internal Energy: We can define three additional energy functions using Legendre transformations on our expression for the change in internal energy: dP=0? dT=0? Substituting in dU:

9. 9 Criteria for Reversibility The mathematical form of the Second Law states that: And for an infinitesimal, reversible process: Gas M Heat Q Work W If the process involves a reversible transfer of an infinitesimal amount of heat then: On substitution: And for a chemical system we can substitute in: Criteria for Reversibility:

10. 10 Isolated System If a system is isolated, it cannot interact with the surroundings. The system cannot do work, or have work done on it nor can it change its internal energy (the First Law). Energy can only be transferred. It cannot be created or destroyed. Thus, for an isolated system the internal energy is a constant. The volume of an isolated system cannot change Equilibrium is reached in an isolated system when it maximizes its entropy. General criteria for reversibility:

11. 11 Closed Isometric and Isothermal System For a closed, isometric and isothermal system heat can flow in or out, although the temperature, volume and amount of material are constant: dV=0, dT=0 and dn i =0 Since dT = 0: Inserting the constant volume expression into the criteria for equilibrium: And from our expression for the Helmholtz Free energy: Equilibrium is reached in a closed isometric and isothermal system when it minimizes F. Then on substitution:

12. 12 Closed Isobaric and Isothermal System For a closed isobaric and isothermal system, heat can flow into or out of the system, but the pressure, temperature, and amount of material are constant: dP=0, dT=0 and dn i =0 From our expression for the Gibbs Free energy: Equilibrium is reached in a closed isothermal, isobaric system when it minimizes G. Then Substituting the following into our expression for the equilibrium: We see that:

13. 13 Lecture 3: Equilibrium Main Points: 1) Definitions (chemical system, phase, component) 2) Reversible processes produce no entropy 3) Infinitesimal processes about equilibrium points are reversible 4) Energy functions U, H, F, and G 5) Criteria for reversibility in different systems The concept of equilibrium plays an important role in thermodynamics. We have derived criteria that must be satisfied for systems under various conditions for them to be in equilibrium.