0.22 Entropy and the second law of thermodynamics  (Page 7/9)

One thing we have failed to take into consideration is that these phase transitions involve changes of energy and thus heat flow. Condensation of gas to liquid and freezing of liquid to solid both involve evolution of heat. This heat flow is of consequence because our observations also revealed that the entropy of a substance can be significantly increased by elevating its temperature.

One way to preserve our conclusions about spontaneity and entropy is to place a condition on their validity: a spontaneous process produces the final state of greatest probability and entropy provided that the process does not involve the evolution of heat. This is an unsatisfying result, however, since most physical and chemical processes involve heat transfer. As an alternative, we can force the process not to evolve heat by isolating the system undergoing the process: no heat can be released if there is no sink to receive the heat, and no heat can be absorbed if there is no source of heat. Therefore, we conclude from our observations that, for a spontaneous process in an isolated system the entropy always increases and leads us to the final state of greatest probability and entropy. This is one statement of the Second Law of Thermodynamics:

∆S>0 spontaneous process in an isolated system

It is interesting to consider one particular “isolated system,” which is the entire universe. Since no energy or matter can transfer in or out of the universe, the universe qualifies as “isolated.” So, another statement of the Second Law of Thermodynamics is:

∆S _universe >0 for any spontaneous process

Though interesting and quite general, this statement is not yet all that useful because calculating S for the entire universe seems very difficult. In the next Concept Development Study, we will develop a means to do that calculation fairly easily.

Observation 4: heat transfer and entropy changes

We will begin with a simple and common observation about heat flow. Let’s take two pieces of metal of the same mass. It doesn’t matter what type of metal or what mass, so let’s say 100.0 g of copper. Let’s heat one of the samples (call it sample A) to 100 ºC and cool the other (call it sample B) to 0 ºC. Then let’s place them in contact with each other but insulated from everything surrounded them. We know from everyday experience what is going to happen, but of course, when we run the experiment, the cold metal B warms up, the hot metal A cools off, and both pieces of metal stop changing temperature only when they come to the same temperature, in this case, 50 ºC. We say that they have reached “thermal equilibrium.”

The approach to thermal equilibrium is clearly a spontaneous process: it happens automatically, and indeed there is nothing we can do to stop it other than to isolate the two pieces of metal from each other. Since this is a spontaneous process and since we isolated the two pieces of metal from their surroundings, then the work of the previous study tells us that, in total for system consisting of the two pieces of metal, ∆S>0.