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( )