Entropy

1. Entropy As a general rule of thumb systems proceed naturally or spontaneously, i.e., of their own accord, from states of high energy to states of low energy. Think of a ball rolling down hill from a state of high potential energy at the top of the hill to a state of lower potential energy at the bottom of the hill. Balls, for example, do not spontaneously roll uphill. Now consider that a dish of water left in a large room will eventually evaporate. Evaporation is a process in which molecules move from a state of lower energy, the liquid phase, to a state of higher energy, the vapor phase. The spontaneous evaporation of the water in the dish is an apparent contradiction to the statement in the proceeding paragraph. We must not have the whole picture - something else must be going on that we have overlooked. What we are overlooking is probability. Not only do systems proceed from states of higher to lower energy, but systems also naturally proceed from states of lower to higher probability. Since disordered states are more probable than ordered states, systems tend to proceed naturally to states of greater disorder. Entropyis the thermodynamic measure of probability and disorder. The more disordered a system the more probable it is and the greater and more positive is its entropy. Does ice have a greater or smaller entropy than liquid water? 19.1

2. In determining the spontaneous direction of a process we have to consider both energy (or enthalpy for a constant pressure process) and entropy. In the case of the evaporating water the unfavorable (with respect to a spontaneous process) increase in energy associated with evaporation is offset by a more favorable (again with respect to a spontaneous process) increase in entropy, as the more ordered liquid evaporates to form the more disordered vapor. We have been using the word spontaneous quite a bit in the foregoing discussion and, since our usage differs a bit from conventional usage, we will define a thermodynamically spontaneous process as a process that will eventually happen without external intervention. Note the use of the word eventually indicating that spontaneous in the sense that we are using the word and contrary to common usage implies nothing about how fast the process takes place and in fact a process may require an essentially infinite amount of time and still be spontaneous! Systems spontaneously convert to their thermodynamically stable form. At 25 oC and 1 bar what is the thermodynamically stable form of carbon, diamond or graphite? At this temperature and pressure all carbon should eventually exist as what phase? Do you think this spontaneous process occurs very rapidly? 19.2

3. The 2nd law of thermodynamicssays that in a spontaneous process the entropy of the universe always increases. DSuniverse = DStotal = DSisolatedsystem = DS system + DS surroundings > 0 Consider the abstract process: state 1 ---------> state 2 If the considered or defined process (in the direction of the arrow) is spontaneous, then the total entropy change is greater than zero: DStotal = Sstate 2 - Sstate 1 > 0. If the reverse of the defined process (in the direction opposite that of the arrow) is spontaneous, then: DStotal < 0 If the process is equally probable or sponataneous in either direction, then: DStotal = 0 and the system is at equilibrium, a situation often indicated by a double arrow: state 1 <======> state 2 19.3

4. Consider the vaporization of water at 105 oC and 1 bar: 105 oC H2O (l) ---------> H2O (g) 1 bar What is the sign on the entropy change for the system (the water), DSsystem? Hint, did the disorder increase or decrease? At the above temperature and pressure, which phase is stable, liquid water or water vapor? Which direction is the spontaneous direction? What is the sign on the total entropy change, DStotal ? Can you determine the sign on the entropy change in the surroundings, DSsurroundings ? 19.4

5. Consider the melting of water at 0 oC and 0.5 bar: 0 oC H2O (s) ---------> H2O (l) 0.5 bar What is the stable phase of water under these conditions (be careful - you may want to consult a phase diagram for water that can be found in your text book)? What are the signs on DSsystem, DStotal, and DSsurroundings? 19.5