Review of Concepts from Thermal Physics

 

Temperature

 

Kelvin – Celsius – Fahrenheit – Rankin

 

Ttriple point = 273.16 K = 0°C

 

TC = T – 273.16°

 

TF = 9/5 TC + 32°

 

Heat

 

1 cal = 3.969 X 10-3 BTU = 4.186 J

 

1 Cal = 1000 cal = 1 kcal

Thermal Expansion

 

DL = LaDT

 

DV = VbDT

 

Specific Heat

 

dQ = cmdT = cmolarndT

 

C = cm

Heat of Transformation

 

Q = Lm

 

Work and Changes in Volume

 

 

First Law of Thermodynamics

 

dU = dQ - dW

 

Conservation of energy

Thermodynamic Processes

 

Adiabatic – no heat flow dQ = 0

 

Isometric – no volume change dV = 0

 

Isobaric – constant pressure

 

Isothermal – constant temp. dT = 0

 

Conduction

 

 

Radiation – Stefan – Boltzmann Law

 

Pr = seAT4

Avogadro’s Number

 

NA = 6.022 X 1023 part/mol

 

Ideal Gas

 

PV = nRT     PV = kBNT

 

N = nNA 

 

R = 8.31 J/mol K

kB = 1.38 X 10-23 J/K

 

Work - Isothermal Process

 

W = nRTln(Vf / Vi)     (ideal gas)

 

Temperature and Kinetic Energy

 

KERMS = (3/2)kBT

Molar specific heat

 

    

 

Ideal Gas Specific Heats

 

CV = 3/2 R

 

CP = CV + R

 

dU = nCVdT

 

Equipartition Theorem

 

U = f(1/2)kBT     f = degrees of freedom

 

Adiabatic Process – Ideal Gas

 

PVg = constant

 

g = CP / CV 

Entropy

 

dS = dQ/T

 

 

Entropy in Spontaneous Processes

 

DS > 0  across the whole systems for and spontaneous process

Combined first and second laws

 

dU = TdSdW

 

dU = TdSPdV     ideal gas

 

Efficiency of an Ideal Engine

 

e = (TH – TC)/TH 

Coefficient of Performance of an Ideal Refrigerator

 

K = TC/(TH – TC)

 

Carnot Cycle (ideal cycle)

Boltzmann’s Entropy Equation

 

S = kBlnW

 

W = the multiplicity or density of states