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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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Energy quality
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


Quantifying quality

A Carnot cycle found a relationship between the temperatures and heat.

The heat in and out are of opposite sign.

Quantifying Quality


Closed cycle
Closed Cycle and heat.

  • 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.


Entropy defined
Entropy Defined and heat.

  • 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. and heat.

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


Mixing

A sample of 50.0 kg water at 20.0 and heat.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


Second law iii
Second Law III and heat.

  • 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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