Entropy Time’s Arrow

Objectives Explain the tendency of matter and energy to spread out over time. Identify entropy changes in familiar processes.

Poll Question I heard of “entropy” before this course. True. False.

Poll Question I think I know what “entropy” means. True. False.

The Flow of Matter particles disperse

Gas Molecule in a Box No energy transfer to walls: elastic collisions

Gas Molecule in a Box Double the size of the box!

Gas Molecule in a Box Double the size of the box!

Poll Question What portion of the time will the molecule spend in the original volume (left half of the box)? a. All b. Half c. none d. 75%

Poll Question What portion of the time will the molecule spend in the original space if we quadruple the volume of the box?

Poll Question What portion of the time will the molecule spend in the original space if we quadruple the volume of the box? a. All b. Half c. 1/3 d. 1/4

Poll Question What is the probability that the molecule will be in the original space at any given time? a. 1 b. 1/2 c. 1/3 d. 1/4 V V/4

Two Molecules (Poll) What is the probability that both will be in the left half of the container at the same time? a. 1 b. 1/2 c. 1/4 d. 0

Three Molecules (Poll) What is the probability that all three will be in the left half of the container at the same time? a. 1/2 b. 1/3 c. 1/4 d. 1/8

Whiteboard Work What is the probability that all N will be in the given sector of the container at the same time? xV V

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.

Group It! Discuss all succeeding poll questions with your group before answering.

The Flow of Energy energy disperses

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

Group Poll Question What happens to the kinetic energy after the collision? All of it goes to the target. The projectile and target have equal kinetic energies. The projectile keeps it all. It depends; there isn’t enough information to know for sure.

I did the math! I calculated the kinetic energies of object 1 (projectile) and object 2 (target) as a function of Offset Relative masses

Energy Transfer: Mass Effect

Energy Transfer: Mass Effect

Energy Transfer: Offset Effect

Energy Transfer: Offset Effect

Energy Transfer: Offset Effect

Collision Summary Before impact, all the kinetic energy is in the motion of the projectile. At impact, the kinetic energy almost always distributes to motion of both the projectile and target. When two objects collide, their kinetic energies are usually closer after the collision than before. Spreading out is irreversible.

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

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

multiple interactions Heat Transfer multiple interactions

Heat Flow Two solids with different temperatures (average molecular kinetic energies) are brought into contact.

Heat Flow Two solids with different temperatures (average molecular kinetic energies) are brought into contact. What happens to the atoms’ kinetic energies (temperatures)?

Heat Flow Summary Molecular kinetic energy flows from high temperature objects to low temperature objects, but not the other way around. This is because kinetic energy tends to even out between colliding objects. There are more ways to distribute energy among many molecules than among few molecules.

Heat Generation Any energy  molecular motion Raises entropy Energy less constrained Effect more important at low temperatures DS = q/T Greater proportional increase in thermal energy at low T

Temperature Difference Hot Cold heat Until Warm Equilibrium

Temperature Difference Hot Cold heat low DS DU high DS DU Heat flows until total entropy stops increasing Thermal equilibrium Same temperature

Thermodynamic Temperature Hot Cold heat low DS DU high DS DU 1/T = DS/DU DS = q/T

Overall Summary Particles and energy tend to become spread out uniformly. Entropy is a measure of how many different ways a state can be arranged. library analogy Total entropy increases in all processes that actually occur.

What It Means examples

Interesting but vital point We cannot see most of the motion that occurs in our world.

The Funnel and the Ice Pack How can matter ever become localized? Stars form Rain falls How can thermal motion ever decrease? Refrigerators and heat pumps First aid cold packs Any time one thing becomes localized, something else spreads out more

Entropy, Technically W = number of “configurations” of a state S = kB ln(W) = entropy of the state DS = entropy change DS = S2 − S1 = kB ln(W2) − kB ln(W1) = kB ln(W2/W1)

Free Expansion Example xV V N W2/W1 = = xN DS = kN ln(x) xV V

Ice Melting Example Solid  liquid disperses matter DSc > 0 constrains energy DST < 0 temp DS DSc DS melting temperature DST

Add Salt Salt dissolves in liquid only Raises S of liquid (+ salt) Raises DSc lower melting temperature temp DS DSc DSc DS DS original melting temperature DST

General Physics L03_entropy.ppt Group Work Explain how your process increases entropy. Think about: Could the reverse process occur? What spreads out: matter, energy or both? How? Why does total entropy increase? Processes: 1. Humpty Dumpty 2. NH4NO3 in water 3. coffee freezes outside 4. Log burns 5. Student tidies his room 6. vinegar + baking soda 7. quartz crystallizes underground 8. egg develops into a chick

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

Chemical Thermodynamics Enthalpy (DH) is heat transfer to surroundings Spontaneous if DG = DH – TDS < 0 Equivalent to DS – DH/T > 0 DS is entropy change of system DH/T is entropy change of surroundings If a state changes spontaneously, entropy increases.

Entropy and Evolution Darwinian evolution is perfectly consistent with thermodynamics. Energy from the sun powers life processes. Energy from earth radiates into space. Material order on earth can increase because energy is dispersed. Entropy always increases!

General Physics L03_entropy.ppt Sun, Earth, and Life Tsun = 6000 K, Tearth = 300 K, Tspace = 3 K DSsun = –Q/Tsun; DSearth = ±Q/Tearth In a year, Q  8 GJ/m2 of earth surface DSsun = –1.3 MJ/K m2 DSearth = 0 DSsurr = +2.7 GJ/K m2 1000 kg/m2 “orderly” life diverts > 1.3 MJ/K Plenty of entropy is created

Congratulations! “[Asking someone to] describe the Second law of thermodynamics is about the scientific equivalent of: Have you read a work of Shakespeare’s?” – C.P. Snow, Rede Lecture, Cambridge, May 7, 1959.