Theme Music: Desi Arnaz - UMD Physics · Physics 132 2/10/17 Prof. E. F. Redish 4 How is entropy extensive? W A = number of microstates for system A W B = number of microstates for

Physics 132 2/10/17

Prof. E. F. Redish 1

2/10/17 1 Physics 132

■ Theme Music: Desi Arnaz Perhaps, perhaps, perhaps

■ Cartoon: Pat Brady Rose is Rose

February 10, 2017 Physics 132 Prof. E. F. Redish

The structure of science knowledge

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Synthesis: How does it fit together?

Mechanism: How does it work?

Facts: What is there?

Process: What happens?

Equations

Physics 132 2/10/17

Prof. E. F. Redish 2

Entropy (Thermodynamics

definition)

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ΔS = QT

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Foothold ideas: Entropy

■ Entropy – an extensive* measure of how well energy is spread in an object.

■ Change in entropy upon heat flow (exchange of thermal energy)

ΔS = QT

* Extensive = proportional to the amount of stuff you have (like mass) Intensive = independent of the amount of stuff you have (like density)

Physics 132 2/10/17

Prof. E. F. Redish 3

Entropy (Information

definition)

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S = kB lnW

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Foothold ideas: Entropy

■ Entropy – an extensive* measure of how well energy is spread in an object.

■ Entropy measures – The number of microstates in a given

macrostate – The amount that the energy of a system is

spread among the various degrees of freedom

S = kB ln(W )* Extensive = proportional to the amount of stuff you have (like mass) Intensive = independent of the amount of stuff you have (like density)

Physics 132 2/10/17

Prof. E. F. Redish 4

How is entropy extensive?

■ WA = number of microstates for system A ■ WB = number of microstates for system B ■ Wtotal = WAWB ■  SA = kB ln WA

■  SB = kB ln WB

■  SAB = kB ln (WAWB) = kB ln WA + kB ln WB ■  SAB = SA + SB

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Foothold ideas: Exponents and logarithms

■  Power law: a variable raised to a fixed power.

■ Exponential: a fixed constant raised to a variable power.

■ Logarithm: the inverse of the exponential.

f (x) = x2 g(x) = Ax7

f (x) = ex g(N ) = 2N h(z) = 10z

x = eln(x )

y = 10log(y)

log(2) = 0.3010log(e) = 0.4343

2N = 100.3010( )N ≈100.3N

ex = 100.4343( )x ≈100.4 x2N = B

N log2 = logB⇒ N = logBlog2

x = ln ex( )y = log 10y( )