Thermodynamics and Statistical Physics

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Presentation transcript:

Thermodynamics and Statistical Physics Lecture 5 Entropy Second law of thermodynamics Variable dependences of thermodynamic relationships 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Note that dS is an “exact differential” dQ is not. Entropy for a reversible process (quasi-static via continuous changes in the variables): Note that dS is an “exact differential” dQ is not. Carnot cycle. 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Square cycle: 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Second law of thermodynamics Kelvin-Planck: It is impossible to construct an engine which, operation in a cycle, will produce no other effect than the extraction of energy from a reservoir and the performance of an equivalent amount of work. Clausius: No process is possible whose sole result is cooling a colder body and heating a hotter body. Gould-Tobochnik:There exists an additive function of state known as the entropy S that can never decrease in an isolated system. 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Comment on “quasi-static” restrictions Consider the free expansion of an isolated ideal gas, initially in left chamber at V1 with vacuum in right chamber and finally occupying full volume V2. In order to use the laws of thermodynamics, we must envision a quasi-static process that accomplishes the free expansion 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Variables and functions: 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Assume N constant -- 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Further relations: 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Mathematical transformations for continuous functions of several variables & Legendre transforms: 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

Mathematical transformations for continuous functions of several variables & Legendre transforms continued: 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

For thermodynamic functions: 7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5

7/24/2019 PHY 341/641 Spring 2012 -- Lecture 5