Thermodynamics and Statistical Mechanics Review for Quiz 1

Thermodynamics and Statistical Mechanics Review for Quiz 1 Thermo & Stat Mech Spring 2006 Class 11

Laws of Thermodynamics First law: đQ – đW = d. U Energy is conserved Thermo & Stat Mech - Spring 2006 Class 11 2

Laws of Thermodynamics Second Law: The entropy of an isolated system increases in any irreversible process and is unaltered in any reversible process. This is the principle of increasing entropy. DS ³ 0 Thermo & Stat Mech - Spring 2006 Class 11 3

Laws of Thermodynamics Third Law: The entropy of a true equilibrium state of a system at a temperature of absolute zero is zero. Equivalent to: It is impossible to reduce the temperature of a system to absolute zero using a finite number of processes. Thermo & Stat Mech - Spring 2006 Class 11 4

Second Law Variations No series of processes is possible whose sole result is the absorption of heat from a thermal reservoir and the complete conversion of this energy to work. There are no perfect engines! Thermo & Stat Mech - Spring 2006 Class 11 5

Second Law Variations No series of processes is possible whose sole result is the transfer of heat from a reservoir at a given temperature to a reservoir at a higher temperature. There are no perfect refrigerators! Thermo & Stat Mech - Spring 2006 Class 11 6

Zeroth Law If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other. Thermo & Stat Mech - Spring 2006 Class 11 7

Work done by a gas Thermo & Stat Mech - Spring 2006 Class 11 8

Ideal gas law: PV = n. RT In terms of molar volume, v = V/n, this becomes: Pv = RT, or P = RT/v Thermo & Stat Mech - Spring 2006 Class 11 9

van der Waals equation of state This equation has a critical value of T which suggests a phase change. The next slide shows graphs for several values of T. Thermo & Stat Mech - Spring 2006 Class 11 10

Thermal Expansion Expansivity or Coefficient of Volume Expansion, b. Thermo & Stat Mech - Spring 2006 Class 11 11

Compressibility Volume also depends on pressure. Isothermal Compressibility: Thermo & Stat Mech - Spring 2006 Class 11 12

Cyclical Relation Thermo & Stat Mech - Spring 2006 Class 11 13

Carnot Cycle A Carnot cycle is an idealized reversible cycle that operates between two heat reservoirs at temperatures T 1 and T 2, where T 2 > T 1. It can operate as a heat engine, or a refrigerator. Thermo & Stat Mech - Spring 2006 Class 11 14

Thermal Efficiency (h) If T 1 = 0, h = 1 (100%) Thermo & Stat Mech - Spring 2006 Class 11 15

For a Carnot Engine or Thermo & Stat Mech - Spring 2006 Class 11 16

Entropy For reversible processes. Entropy is a state variable. Thermo & Stat Mech - Spring 2006 Class 11 17

First and Second Laws First Law: d. U = đQ – đW First law, combined with the second law: d. U = Td. S – Pd. V Thermo & Stat Mech - Spring 2006 Class 11 18

Tds Equations Thermo & Stat Mech - Spring 2006 Class 11 19

Ideal Gas Thermo & Stat Mech - Spring 2006 Class 11 20

Properties From first law: Td. S = d. U + Pd. V, or Internal Energy d. U = Td. S – Pd. V U(S, V) Enthalpy: H = U + PV d. H = Td. S + Vd. P Thermo & Stat Mech - Spring 2006 Class 11 H(S, P) 21

New Potentials Helmholtz Function: F = U – TS Gibbs Function: G = U – TS + PV G = H – TS G = F + PV Thermo & Stat Mech - Spring 2006 Class 11 22

All Four d. U = Td. S – Pd. V d. H = Td. S + Vd. P d. F = – Pd. V – Sd. T d. G = – Sd. T + Vd. P Thermo & Stat Mech - Spring 2006 Class 11 U(S, V) H(S, P) F(V, T) G(T, P) 23

Maxwell Relations Thermo & Stat Mech - Spring 2006 Class 11 24

Clausius-Clapeyron Equation Thermo & Stat Mech - Spring 2006 Class 11 25