The Second Law of Thermodynamics this is cool § 18.2–18.3

Outline Multiplicity Free expansion Heat transfer Possibility and efficiency of heat engines Evolution and life Gibbs free energy

Multiplicity and Probability Order, disorder, and usefulness –Library analogy –Poker hands –Literature Configurations with more multiplicity are more common. Multiplicity tends to increase.

Probability and Time Multiplicity increases with time Maximum multiplicity ≡ equilibrium Time is the direction of increasing multiplicity!

V1V1 Sub-Space What is the probability that all N will be in the given sub-volume of the container at the same time? V2V2 N V1V1 V2V2

Expansion Summary Random motions cause particles to spread out. The chance that they will randomly come back together decreases tremendously as the number of molecules increases. Spreading out is irreversible.

Collision! A moving object rams a stationary object. Before impact: KE of projectile > 0 KE of target = 0

Energy Transfer: Mass Effect

Energy Transfer: Offset Effect

Collision Summary Before impact, projectile has all the kinetic energy. KE more evenly distributed after unless: –Equal masses –Direct hit Energy spreading out is irreversible.

Kinetic Energy Randomizes Spreads out over more objects Spreads out in more directions Work becomes internal energy

Example How does entropy increase when a ball is dropped, bounces, and eventually stops? How is energy conserved? PE  KE  random molecular KE

Entropy, Technically  = multiplicity of a state S = k ln(  = entropy of the state  S = entropy change –  S = S 2 − S 1 –= k ln(  2 ) − k ln(  1 ) –= k ln(  2 /  1 ) k = × J/K

Heat Transfer To thermal equilibrium

Temperature Difference Hot Cold heat Until Warm Equilibrium

Temperature Difference Hot Cold heat low SS UU high SS UU Heat flows until total entropy stops increasing –Thermal equilibrium –Same temperature

Thermodynamic Temperature Hot Cold heat low SS UU high SS UU 1/T =  S/  U  S = Q/T

Heat Engines Divert heat flow

Heat Engine Heat flow can be diverted to useful work As long as entropy still increases ThTh QhQh QcQc W TcTc Q h = W + Q c Q c /T c ≥ Q h /T h

Sun, Earth, and Life T sun = 6000 K, T earth = 300 K, T surr = 3 K  S sun = −Q/T sun ;  S earth = ±Q/T earth In a year, Q  8 GJ/m 2 of earth surface –  S sun = −1.3 MJ/K m 2 –  S earth = 0 –  S surr = MJ/K m kg/m 2 life diverts < 1.3 MJ/K Plenty of entropy is created

Chemical Thermodynamics Enthalpy (  H) is heat transfer to surroundings (const P) Spontaneous if  G =  H – T  S < 0 Equivalent to  S –  H/T > 0 –  S is entropy change of system – −  H/T is entropy change of surroundings In a spontaneous change, entropy increases.

Overall Pessimistic View –Energy degrades from more to less useful forms –Order becomes disorder Rather: Increasing entropy is how we know something will happen!