Lecture 5 (1/16/2013)
• Statistics and Entropy (S):
o Boltzmann’s equation:
S = k ln W
k =1.38 ´ 10 J/K
W = # of accessible energy “microstates” (how dispersed
the energy in a system is)
• Thermodynamic Entropy:
o Isothermal Process:
A process that takes place at constant T.
o Reversible Process:
A process that can be run in the reverse, restoring the initial
system, with no net energy flow into or out of the system.
o For an isothermal process:
ΔS sys /rev /T sys
• qrev flow of heat into or out from a system during a
• Entropy Change & Spontaneity:
o Consider an ice cube at 0.0°C (273 K) placed on a counter top at room
temperature (293 K).
o Will it melt spontaneously?
ΔS univ= ΔSsys ΔS surr
Heat flows into ice cube: ΔS = q /273
Heat flows out of counter top: ΔS surr= −qrev93
• Negative because ice cube causes table top to lose heat
ΔS = (q /273) + (−q /293) > 0
univ rev rev
Yes, ice cubes melt spontaneously at room temperature. Who
• Entropy and Temperature:
o Entropy increases as temperature increases
o Decrease in temperature leads to decrease in entropy
• Third Law of Thermodynamics:
o Third Law of Thermodynamics:
The entropy of a perfect crystal is zero at absolute zero. (It has
only 1 microstate.)
o Absolute Entropy:
The entropy of a substance at some temperature
above 0 Kelvin.
Calculated from measurement of molar heat capacities
as a function of