Second Law of Thermodynamics

1. Second Law of Thermodynamics • Introduction • Random Kinetic Energy and Probability • Early Observations • Kelvin-Planck and Clausius statements • Entropy statement • Allowed/Disallowed processes • Examples

2. Second Law of Thermodynamics • What “drives” heat? • Heat flows Q = (kA/l) ΔT • But always flows from hot to cold. • What’s the nature of this “driver”? • Force? - gravitation? • Force? - electrostatic? • No! - a desire to “spread out”, distribute more evenly • Random kinetic energy – governed by statistics • Go to most probable state. • Most probable is intermixed - requires flow from “Hot” to “Cold”. http://en.wikipedia.org/wiki/Statistical_mechanics

3. Dice Games • 2 Dice. • What’s the probability of rolling a “7” vs. a “2”? • 6 more ways to get “7”, so “7” more likely! • You’ll more likely get “7” (though you might beat the odds..)

4. Hot and Cold Molecules • Hot and cold molecules in a box. • What’s the probability of hot and cold molecules intermixing vs. separating at two ends? • ~Avogadro’s # more ways to intermix, so intermixed far more likely! • You’ll almostcertainly get mixing (and never beat the odds…)

5. 2nd Law - Early Observations • Cannot take heat and turn completely into work • Flow from hot to cold may be “diverted” to do work. • No perpetual motion machines. • Heat always flows from “Hot” to “Cold” • Hot gets colder, cold gets hotter • Never the other way!

6. 2nd Law – Early Statements • Kelvin-Planck • No device is possible whose sole effect it to transform a given amount of heat into work. • Clausius • No device is possible whose sole effect is to transfer heat from one system at a temperature TL into a second system at a higher temperature TH

7. 2nd Law – Equivalence of 2 statements • Violating Kelvin-Planck violates Clasius • Violating Clasius violates Kelvin-Planck

8. 2nd Law – Entropy statement • Entropy • For any process, the entropy S of the system either increases (if process is irreversible) or remains the same (if process is reversible). • Define entropy change as ratio of heat added or removed from an object to its absolute temperature. (“weighted random KE”) • 2nd Law Entropy - for all processes: • Whatever Q/T you take from one place you have to put back as much (or more) somewhere else!

9. 2nd Law Entropy - Examples • Can an ideal Carnot engine work? • Can the “Everything” problem work? • Can a heat pump deliver more heat than it takes in? • Can heat flow spontaneously hot to cold? • Can heat flow spontaneously cold to hot? (Clausis) • Can heat be completely converted to work? (Kelvin-Planck)

10. 1. Can Carnot cycle work? (yes!) • For Carnot cycle • -QH taken from hot • +QC given to cold • So entropy change to surroundings is zero

11. 2. Can “everything” problem work? (yes!) • Entropy change a->b (“everything” problem) • Entropy change b->c • Entropy change c->d • Entropy change d->a

12. 3. Can Heat Pump deliver more heat than it takes in ? (yes!) • For Carnot cycle • If TH > TLthen QH > QL • So entropy change to surroundings is zero Cycle running backwards

13. 4. Can heat flow spontaneously hot to cold? (yes!) • All heat Q from hot goes to cold Q

14. 5. Can heat flow spontaneously cold to hot? (no!) • All heat Q from cold goes to hot NOT ALLOWED! Q

15. 6. Can heat be completely converted to work? (no!) • Loss of entropy from hot • Gain of entropy by cold • So entropy change of surroundings is negative NOT ALLOWED!

16. Example 15-14 • Q absorbed by ice to melt 28 g • Entropy change of ice • Negative entropy change of room smaller, since temperature higher

17. Example 15-15 • Final temperature 22°C. Each exchanges heat • Should use integral, since each temperature’s changing. We’ll just do average. • Entropy changes • Total entropy change +10 J/K

18. Problem 38 • Heat lost by water freezing • Entropy change of water freezing (at 0 C) • Heat lost by frozen water cooling • Entropy change of frozen water cooling (average -5 C)

19. Problem 38 (cont) • Heat gained by great deal of ice • Entropy change of GD ice absorbing (-10 C) • Total entropy change

20. End Thermodynamics Next Electromagnetism