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PHY1039 Properties of Matter

PHY1039 Properties of Matter Entropy Changes in a Thermodynamic Universe and the Maxwell Equations May 14, 2012 Lectures 21. Res. 1. Res. 2. Q 1. System. Res. 3. Q 2. Q 3. Thermodynamic Universe: Thermally Isolated System and Reservoirs. Adiabatic Wall.

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PHY1039 Properties of Matter

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  1. PHY1039 Properties of Matter Entropy Changes in a Thermodynamic Universe and the Maxwell Equations May 14, 2012 Lectures 21

  2. Res. 1 Res. 2 Q1 System Res. 3 Q2 Q3 Thermodynamic Universe: Thermally Isolated System and Reservoirs Adiabatic Wall Not the same as THE Universe

  3. Entropy Change,DS, in a Thermodynamic Universe DSuniv = DSsyst + DSres1 + DSres2 + …. Entropy can decrease or increase within the various parts of the thermodynamic universe. For an irreversible process within the universe, DSuniv0. For a reversible process within the universe, DSuniv=0. Thus, S goes to a maximum within a thermodynamic universe (i.e., a thermally-isolated system). Implication: In a thermodynamic universe, a higher entropy state must follow a lower entropy state. Entropy gives us the “arrow of time”!

  4. Which Carnot Engine Will Do More Work? T1 T1 Q1 Irreversible heat flow T1* < T1 Q1 T1* Q1 W C W* C Q2 Q2 T2 T2

  5. How Much Less Work is Being Done by the Modified Carnot Engine? As the second (modified) Carnot engine is operating from a reservoir at a lower T, it is less efficient. With the same amount of heat input, it is doing less work. How much less? Simplify: Factor out T2: As T1* < T1, we see that DW is > 0. We do more work without the irreversible heat flow.

  6. Entropy Change in the Modified Carnot Engine Entropy change in hot reservoir: T1 Q1 Irreversible heat flow T1* < T1 Entropy change in auxiliary reservoir: T1* Q1 The modified Carnot engine has some additional entropy change because of the auxiliary reservoir. W* C DS = 0 Reversible heat flow Q2 T2

  7. What is the Difference in DS for the Two Carnot Engines? DS for the original Carnot engine is simply 0, because it only has reversible heat flows. DS for the modified Carnot engine is given as: This equation represents the extra entropy associated with the irreversible process of heat flow from the hot reservoir to the auxiliary reservoir. What can we conclude?

  8. Helmholtz Free Energy, F For any irreversible process in a thermodynamic universe, the energy that is “unavailable” for work is ToDSuniverse. The potential for work in the universe decreases by ToDS for every irreversible process. The total energy is still conserved, however, as required by the First Law of Thermodynamics. We can define a state function to provide the energy that is “available” (or free) to do work: F = U – TS DF = DU – TDS – SDT F is the Helmholtz free energy.

  9. Maxwell Relations -S P V T -S P V T -S P V T -S P V T

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