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Entropy

Entropy. Energy Quality. You are offered 1000 J of energy. Would you rather have it as A) mechanical work B) frictional work C) heat from an object at 1000 K D) heat from an object at 300 K. A Carnot cycle found a relationship between the temperatures and heat.

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Entropy

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  1. Entropy

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

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

  4. 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.

  5. 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.

  6. 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 = 0.292 kcal/K The process is reversible. DSsurr = -0.292 kcal/K Melting Ice

  7. 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 = -100. kcal/296K = -0.338 kcal/K DSL = Q/T = +100. kcal/294K = +0.340 kcal/K The difference is the net change. DS = +0.002 kcal/K Mixing

  8. 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.

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