Entropy

Energy Quality  You are offered 1000 J of energy. Would you rather have it as A) mechanical work A) mechanical work B) frictional work B) frictional work C) heat from an object at 1000 K C) heat from an object at 1000 K D) heat from an object at 300 K D) heat from an object at 300 K

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

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.The heat to temperature ratios can be added.

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.

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.   S = Q/T = kcal/K  The process is reversible.   S surr = kcal/K

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 = mc  T = 100. kcal  Find the entropy change in each sample using the average temperature.   S H = Q/T = kcal/296K = kcal/K   S L = Q/T = kcal/294K = kcal/K  The difference is the net change.   S = kcal/K

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.