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Lecture 17

University College - Chemistry Chem 402 Lecture Notes - Lecture 17: Isothermal Process, Carnot Cycle, Path DependencePremium

3 pages55 viewsSpring 2017

Department
University College - Chemistry
Course Code
University College - Chemistry Chem 402
Professor
Barnes Alexander
Lecture
17

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27 February 2017
L17: The Carnot Cycle and Third Law of Thermodynamics
I. Second Law of Thermodynamics
A. Entropy
1. Derivation by thermocycler path using an isotherm, adiabat, and constant volume
process to find   
was path independent
2. Derivation of Entropy as a State Function (Math Proof for Ideal gas)
a.     
b.      (P = nRT/V)
c.    

Now check to see if the cross terms are equal, if so, it is a state function, if
not, it is path dependent

  
 ?
  
these are not equal, and thus  is path dependent
d. Now, consider


  (divide through by T)

  
   they are equal, so this function is a state function

 , thus entropy is a state function
B. Heat Engines and Refrigerators
1. Clausius
a. It is impossible for any system to operate in a cycle that takes heat from a cold
reservoir and transfers it to a hot reservoir without at the same time converting
some work into heat
b. The left violates the 2nd law if |q1| = |q2|
Consider  
On a number line: have ∆Scold (q2/T2) which is negative, and ∆Shot (q1/T1)
Suni = ∆Scold - ∆Shot < 0 (violates second law!)
c. The right side is ok since work in will increase ∆Suni, for a reversible process,
Suni = 0
When work is added, ∆Scold is the same, but ∆Shot increases because work is
added for going into the hot reservoir
Since S = kln, as you ad heat there is a larger distribution of energies and
microstates, adding the same amount of heat again spreads out energy levels a
little bit more
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