PHY 341641 Thermodynamics and Statistical Physics Lecture 5

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PHY 341/641 Thermodynamics and Statistical Physics Lecture 5 1. Entropy 2. Second law of

PHY 341/641 Thermodynamics and Statistical Physics Lecture 5 1. Entropy 2. Second law of thermodynamics 3. Variable dependences of thermodynamic relationships 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 1

Entropy for a reversible process (quasi-static via continuous changes in the variables): Note that

Entropy for a reversible process (quasi-static via continuous changes in the variables): Note that d. S is an “exact differential” d. Q is not. Carnot cycle. 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 2

Square cycle: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 3

Square cycle: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 3

Second law of thermodynamics • Kelvin-Planck: It is impossible to construct an engine which,

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. 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 4

Comment on “quasi-static” restrictions Consider the free expansion of an isolated ideal gas, initially

Comment on “quasi-static” restrictions Consider the free expansion of an isolated ideal gas, initially in left chamber at V 1 with vacuum in right chamber and finally occupying full volume V 2. In order to use the laws of thermodynamics, we must envision a quasi-static process that accomplishes the free expansion 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 5

Variables and functions: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 6

Variables and functions: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 6

Assume N constant -- 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 7

Assume N constant -- 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 7

Further relations: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 8

Further relations: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 8

Mathematical transformations for continuous functions of several variables & Legendre transforms: 9/21/2021 PHY 341/641

Mathematical transformations for continuous functions of several variables & Legendre transforms: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 9

Mathematical transformations for continuous functions of several variables & Legendre transforms continued: 9/21/2021 PHY

Mathematical transformations for continuous functions of several variables & Legendre transforms continued: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 10

For thermodynamic functions: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 11

For thermodynamic functions: 9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 11

9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 12

9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 12

9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 13

9/21/2021 PHY 341/641 Spring 2012 -- Lecture 5 13

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PHY 341641 Thermodynamics and Statistical Physics Lecture 10PHY 341641 Thermodynamics and Statistical Physics Lecture 10