lecture 06 2010

# lecture 06 2010 - 29 So now lets consider the reversible...

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29 So, now let’s consider the reversible isothermal expansion of an ideal gas. Let the volume double in this expansion. Δ E = q rev + w rev = 0, so q rev = -w rev = +RT ln (V f /V i ) Now, let’s define Δ S = q rev /T, so Δ S = +R ln (V f /V i ). ] In this particular case, Δ S = +R ln 2 So, we see that the entropy change is positive for this expansion. We claim that this expansion is thermodynamically favorable . Note that we must calculate the entropy change using the heat transferred reversibly . So, if we want to calculate entropy changes, we need to be sure that we know the heat transfer for a reversible process that takes us from the initial to the final state. Before we examine the implications of this idea, let’s compare this results with the statistical definition of entropy. According to Boltzmann, Δ S = S f – S i = k ln Ω f - k ln Ω i If we use our simple model for configurational entropy, there is only one microstate of the system in which all N particle are on the left side of the chamber. Ω i = 1. S i = 0. If we have Avogadro’s number of molecules distributed over both halves of the box in the final state, then Ω f = . So, S f = k ln = kN 0 ln 2 = R ln 2. This is exactly the result we got from the thermodynamic definition Δ S = q rev /T. The thermodynamic definition is actually the most fundamental definition of the entropy change. When is a process irreversible? Reversibility and Irreversibility The quantity q irrev /T has no meaning . The Second Law of Thermodynamics says that a process is irreversible if the entropy change for the Universe (system + surroundings) is positive. So, we need to calculate the entropy change for the system and the surrounding to know whether a process is spontaneous or not. P gas P gas P ext

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30 Let’s go back to our expansion of an ideal gas from V to 2V. Let’s compare reversible and irreversible processes. We saw that the Carnot cycle, comprised of reversible processes, was a very efficient way to convert heat into work. When we compared the Carnot cycle with a simpler “square” cycle operating under similar conditions, we found that the efficiency of converting heat
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lecture 06 2010 - 29 So now lets consider the reversible...

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