### Equilibrium and the Second Law of Thermodynamics

When two systems can exchange energy, they are in thermal contact.

In thermal contact, energy is exchanged between the two systems until thermal equilibrium is reached---heat flows from the hotter to the colder system.

Thermal equilibrium is defined by T1 = T2.

#### Second Law of Thermodynamics

Question: Can heat from from a colder to a hotter system?

Answer: Heat flow in the "wrong" direction is so unlikely that it is impossible!

The flow of heat from the hotter to a colder system corresponds to evolution to the most probable state of the combined system.

The leads to a new concept: Entropy ≡ S
A measure of the probability for a given microscopic state to occur.
Evolving to most probable state   →   increase in entropy!

Example: melting ice cube (mass m1) in warm water (mass m2)
initial: ice (low entropy), warm water (high entropy)
final: tepid water (medium entropy)
(m1 + m2)stepid > m1sice + m1swarm

Statement of the Second Law:

The entropy of an isolated system never decreases:

• in equilibrium, the entropy stays the same;
• otherwise the entropy increases until equilibrium is reached.

The second law stems from the extremely large number of particles in a thermodynamic system---1023.