Thermodynamics

• System: Part of Universe to Study. Open or Closed boundaries. Isolated.

• Equilibrium: Unchanging State. Detailed balance

• State of System: Defined at Equilibrium. Specification of state allows reproduction of system. Variable that describe system.

• Extensive properties depends on size of system. Intensive properties do not.

• Reversible and Irreversible changes between equilibrium states. Change by infinitesimal change in system.

• Heat, q: Energy transferred into or out of the system by temperature differences

• Work, w: Any other exchange of energy

• Internal Energy, E: Energy within the system (kinetic + potential)

• Enthalpy, H=E+PV:

• First Law: dE = dq - dw

• Collection of Particles with number of energy states accessible to it. Quantized states. All states equally probable. Most probable distribution is one that corresponds to largest number of ways of arranging particles in the states. N particles.

!!!!

!

321 tnnnn

NW

6 ways 60 ways 15 ways

Using standard techniques and maximizing number of ways, W,with N and total energy E constants, for large number of particles:

)(1

21 enniWhere ni is number of particles in state i. Boltzmann Distribution.

If energy levels are degenerate with factor gi

kTii eng

gn /)(

11

21

Total number of particles are:

kT

ii

ii

iegg

nnN /)(

1

1 1

kT

ii

kTii

i

i

eg

eg

N

n/)(

/)(

1

1

Denominator is the molecular Partition Function (Z)

Entropy

• Equilibrium state favored because it is more probable

• Randomness of ways particles can be distributed over energy states of system

• Measure of disorder or randomness is entropy

• S=k ln W

Free Energy

• System at constant temperature and pressure• Gibbs Free Energy: Energy available for work• dG = dH - T dS• Negative: Exothermic and spontaneous• Positive: Endothermic• Statistical Thermodynamics

BAMolecule can exist in two forms, A and B.

Equilibrium constant:

RTGABK Beq exp][

][

Z

RTG

BA

B

K

KP B

eq

eqB

exp

][][

][

1