17.9 Ideal Gas Law: PV = nRT
R = 8.31J/mole.K = .08205 atm l/(mole K) Note: T must be in Kelvins for all this stuff!
k=R/N_A = 1.38x10^-23 J/K
N_A = 6.02x10²³
M_N2 = molecular mass of nitrogen gas = 28 g/mole
n = number of moles = Mass / Molecular wt of substance = m/M
1 atm = 1.013x10⁵N/m² = 1 Pascal
Note the alternate form of Ideal Gas Law:

Chapter 19: First Law of Thermodynamics:

Total Energy of the system DU = Q-W and W =ÝPdV or
DU = Heat gained by the system - Work done by the system
= Energy gained by heat + Energy gained due to work

Heat added: Q > 0
Heat lost: Q < 0
Work done by system DV >0 W > 0
Work done on system DV <0 W < 0
Adiabatic Process: Q = 0 => DU = -W
Cyclic Process: DU = 0 Þ Q = W
Isobaraic Process: DP = 0 Þ W = PDV
Isovolumetric Process: DV = 0 Þ W = 0 Þ DU = Q
Isothermal Process: DT = 0 Þ DU = 0 Þ Q = W =
Boiling Process: DU = Q-W = mL_V - P(V_V - V_L)

Chapter 18 Notes on Kinetic Theory of Gases

P= (2/3(N/V)(1/2)(mv_avg²) so
PV=(2/3)N(1/2)(mv_avg²) = NkT so
T = (This is a RBD!)
Average Kinetic Energy of a molecule (1/2) mv_avg² = (3/2)kT, But v_x² = (1/3) v_avg² so
(1/2) mv_x² = (1/2)kT or v_{x avg}² = kT/m and v_avg² = 3kT/m where m = mass of 1 molecule of the gas Total Energy U of a system of an Ideal Gas
E = N(1/2)(m…v²) = (3/2)NkT = (3/2)nRT so
U = (3/2)NkT = (3/2)nRT (monatomic Gas)
Isovolumetric Process DU = Q = (3/2)nRDT(monatomic Gas)

Molar Specific Heat Q = nC_v DT = (3/2)nRDT, or, Cv = (3/2)R = 2.98(cal/K.mole) = 12.5(J/k.mole) for all monatomic gases, so U = nC_vT for constant volume, or U = nC_pT for constant pressure problems.

For non-monatomic gases, Q=nC_pDT (isobaric processes)
Q=nC_vDT )isovolumetric processes)

C_p-C_v = R for all ideal gases R = 1.99 cal/(Mole.K)

For all monatomic gases C_p= 4.98 cal/(Mole.K)
C_v= 2.98cal/(Mole.K) and C_p/C_v = 1.67
Adiabatic Process (no Heat exchanged with surroundings)
PV = constant so T_oV_o - = T_fV_f -

Sum-up:
Heat: energy transferred from one object to another because of a temperature difference.
Temperature: The average kinetic energy of the molecules in an object.
Internal (mechanical) energy: The total kinetic energy of all the molecules in an object.

Chapter 22 Notes: Laws of Thermodynamics
First Law of Thermo: Total Energy of the system U = Q-W

Heat Engines: In1 cycle , DU = 0 so W = Q_net = Q_h - Q_c

Q_h - Q_c
efficiency (eff) = --------------
Q_h

Carnot Engine: Ideal Heat Engine, maximum efficiency of any heat engine is that of a carnot engine.

efficiency of a carnot engine (effc) = 1 - (T_c/T_h) Where T_c is the temperature of the cold source and Th is the temperature of the hot source in Kelvins.
Coefficient of Performance for Heat Pumps (and air conditioners)
COP (heating) = Q_H/W ,
COP(cooling) = Q_C/W,
Otto Cycle: eff = 1 - 1/(V₁/V₂)g-1
Expansion 10 point Bonus Problem.

A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 18.7 m when the temperature is 21.2 ° C, what is the measured length when the temperature rises to 29.4° C? (Note: Do NOT neglect the expansion of the steel tape.)