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This document discusses entropy and the three laws of thermodynamics. It defines entropy statistically as S = k ln W, where W is the number of accessible microstates. Entropy is a measure of disorder and reaches a minimum of 0 only for a perfect crystal at absolute zero. The three laws are: 1) Energy is conserved in isolated systems, 2) Entropy always increases, 3) Entropy reaches a minimum of 0 only for perfect crystals at absolute zero. Standard entropy values are tabulated for substances at reference temperatures.

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Marc Chartouny
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20 views6 pages

Lec5 Post

This document discusses entropy and the three laws of thermodynamics. It defines entropy statistically as S = k ln W, where W is the number of accessible microstates. Entropy is a measure of disorder and reaches a minimum of 0 only for a perfect crystal at absolute zero. The three laws are: 1) Energy is conserved in isolated systems, 2) Entropy always increases, 3) Entropy reaches a minimum of 0 only for perfect crystals at absolute zero. Standard entropy values are tabulated for substances at reference temperatures.

Uploaded by

Marc Chartouny
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Absolute Entropy:

T2 C Because there is an absolute zero for


∆S = ∫T1 pdT
T temperature, the entropy for any state
can be calculated ... if we know S(0).

T
∫0
Cp(T´) dT´
S(T) = + S(0)
T´

We also defined entropy statistically:


W(T) ∝ number of
accessible states at T
SS==kkln
lnW
W or S(T) = k lnW(T)
W(T) depends on T through
Boltzmann population factors:
W ∝ probability of a given −∆E/kT
state being populated Pn ∝ e
Lets change the definition of W slightly:

Flip three coins W = W = #


S of states S
probability
HHH A 1/8 -2.08 k 1 0k
“isoenergetic”

HHT
HTH B 4 possible 3/8 -0.98 k 3 1.10 k
THH “states”
TTH 8 possible
THT C outcomes 3/8 -0.98 k 3 1.10 k
HTT
TTT D 1/8 -2.08 k 1 0k

If there is only one accessible microstate, the entropy of the


system is given by:
This is consistent with our view of
entropy as a measure of disorder.
SS==kkln W = k ln 1 = 0
ln W = k ln 1 = 0 No disorder (only one possible state)
⇒ S = 0.
Third Law of Thermodynamics:
SS==00for
forall
allperfectly
perfectlycrystalline
crystallinematerials
materialsat
atTT==00K
K

If there is only one possible arrangement of atoms: (i.e. a perfect


crystal):

SS==kkln
lnW
W==kkln
ln11==00

Every substance has a finite (nonzero) heat capacity.


T C (T´) dT´
S(T) =
∫
0
p
T´
+ S(0)

∴ except for a perfect crystal at absolute zero, every substance


has a finite positive entropy.

Standard absolute or “third law” molar entropies are tabulated,


generally at 298 K.
Third Law Entropy: Consider the absolute molar entropy of HCl
at 1 atm, 298.15K

98.36 K 158.91 K 188.07 K


Solid I Solid II Liquid
12.1 12.6 85.9
Gas
1.3 + 29.5 21.1 9.9
13.5
SS298.15
298.15
=
= 185.9
185.9 JK
JK -1mol
-1
mol
-1
-1

S = ∫ Cp dlnT from 0 K to 16 K using Debye formula: Cp = aT3


Solid I
S = ∫ Cp dlnT from 16 K to 98.36 K using experimental Cp

S = ∆H/T for each phase transition

Solid II S = ∫ Cp dlnT from 98.36 K to 158.91 K using experimental Cp

Liquid S = ∫ Cp dlnT from 158.91 K to 188.07 K using experimental Cp


Gas S = ∫ Cp dlnT from 188.07 K to 298.15 K using experimental Cp
Residual Entropy:
The entropy of a substance may not go to zero - even at 0 K.
Consider CO.
If there is no preferred orientation
O C µ = 0.12 D W = 2N
For one mole: W = 2NA

S = k ln W
Actual ca.
= k ln 2NA
4.2 J K-1 mol-1
= NAk ln 2
= R ln 2 = 5.8 J K-1 mol-1

Consider CH3D. No dipole moment, same number of electrons


No preferred orientation!
W = 4N or for one mole W = 4NA

S = R ln 4 = 11.5 J K-1 mol-1

Actual 11.7 J K-1 mol-1


The Three Laws of Thermodynamics:
Atkins Moore

The internal energy You can’t win,


∆U = q + W
1. of an isolated system the best you can
Energy Conservation
is constant do is break even

∆S ≥ 0
The entropy of the You can only
everything tends
2. universe tends to break even at
toward increasing
increase absolute zero
disorder
The entropy of a
S > 0 except for You can never
perfectly crystalline
3. perfect crystals reach absolute
substance is zero at
at T = 0 K zero
T = 0 K

Summary:
The energy of the universe is constant; the entropy
of the universe tends always toward a maximum.
Rudolf Julius Clausius (1822-1888)

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