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

3 pages55 viewsSpring 2017

Department

University College - ChemistryCourse Code

University College - Chemistry Chem 402Professor

Barnes AlexanderLecture

17This

**preview**shows half of the first page. to view the full**3 pages of the document.**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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