1. Entropy

2. Quantifying Quality
A Carnot cycle found a relationship between the temperatures and heat.
The heat in and out are of opposite sign.

3. Closed Cycle
Any closed cycle can be approximated by a sum of Carnot cycles.
On a PV diagram this is any reversible cycle.
The heat to temperature ratios can be added.

4. Entropy Defined
Entropy is defined as the heat flow at an absolute temperature.
The path doesn’t matter, so entropy is a macroscopic state variable.

5. Melting Ice The latent heat of ice is 79.7 kcal/kg.
What is the change of entropy for a very slowly melting 1.00 kg piece of ice?
What is the change in entropy for the surroundings?
Find the heat transfer.
Q = mL = 79.9 kcal
Find the entropy change.
DS = Q/T = kcal/K
The process is reversible.
DSsurr = kcal/K

6. Mixing
A sample of 50.0 kg water at 20.0 C is mixed with 50.0 kg water at 24 C.
Estimate the change in total entropy.
Find the heat transfer. There are equal amounts of heat in each sample.
Q = mcDT = 100. kcal
Find the entropy change in each sample using the average temperature.
DSH = Q/T = kcal/296K = kcal/K
DSL = Q/T = kcal/294K = kcal/K
The difference is the net change.
DS = kcal/K

7. Second Law III
The second law of thermodynamics can be described in terms of entropy:
The entropy of an isolated system never decreases. It only stays the same for reversible processes.