K = °C + 273.15 °C = K – 273.15

∆L = Li∆T ∆V =  Vi ∆T

 (density) = mass / Volume

n = m / M (number of moles equals mass over molar mass)

NA (Avogadro’s number) = 6.022 x 1023 atoms or molecules per 1 mole

c
Water (liq) / 4186
Iron / 448
Copper / 387
Silver / 234
Gold / 129
Mercury (liq) / 140

P V = n R T (ideal gas law) where R = 8.314 J / ( mol * K) = 0.082 L * atm / ( mol * K) And P V = ( N / NA ) * R * T = N * kB *T where Boltzmann’s constant kB =R/NA = 1.38x10^-23 J/ K

1 cal = 4.186 J and 1 kCal = 1 Cal (food) = 1,000 calories

Q = m * c * ∆T or Q = m Lf or Q = m L v

cX = mW * cW * ( Tf – TW ) / [ mX * ( TX – Tf ), for object X in water W

Density of water is ~1 g/cc = 1 g/mL = 1 g/cm^3 = 1 kg / L

Melting Pt. / Latent heat / Boiling Pt. / Latent heat
of fusion / of vaporization
[J per kg] / [J per kg]
Water (Liq) / 0°C / 3.33E+05 / 100°C / 2.26E+06
Copper / 1,083°C / 1.34E+05 / 1,187°C / 5.06E+06
Silver / 960.8°C / 8.82E+04 / 2,193°C / 2.33E+06
Liquid Nitrogen (LN2) / -196° / 2.00E+05

W done ON gas = -∫P dV. W done by gas = -W done by gas or ∫P dV (positive)

∆Eint = Q + W, where Q is the work done ON gas (otherwise, it is Q – W). First law of thermo

Units of pressure: 1 atm = 1.013e5 N / m ^ 2 = 1.013e5 Pa = 101.3 kPa (Remember: e or E is short-hand or calculator/computer notation for “x 10 ^”)

Adiabatic => Q=0, PV^  = Const. TV^Const. Isothermal => T unchanging. Isobaric => P is unchanging (so Work on gas= -P∆V) If V unchanging (iso-volumetric),no work is being done.

Power = energy or work per unit time in general. For blackbody, P =  * A *  * T4

Sigma: constant = 5.67e-8 W / ( m^2 * K^4 ). Perfect blackbody => epsilon = to 1

P = (2/3)(N/V)(1/2)m0v2

KEtot = (3/2)NkBT = (3/2)nRT for mono-atomic gas. KE = (3/2)kBT per atom/molecule

Energy per degree of freedom = (1/2)kBT. KEtot = (#/2)nRT for # degrees of freedom

nV(E) = noe-E/(kBT) (Boltzmann energy distribution)

Nv= 4 p N ( m0 / (2pkBT) ) 3/2 v2 e –m0v^2/(2kBT) (Maxwell-Boltzmann speed distribution)

vmp is where dNv/dv = 0. It is 1.41 √ [ (kBT) / m0 ]

vavg = ∫ (v Nv dv) / N = 1.60 √ [ (kBT) / m0 ]

vrms = √v2 = √[∫(v2 Nv dv) / N] = 1.73 √ [ (kBT) / m0 ]

QV = nCV∆T and QP = nCP∆T and CV = (3/2)R = 12.5 J/(mol*K), mono-atomic gas

CP = CV + R = 12.5 + 8.3 = 20.8 J / ( mol – K), mono-atomic gas. Gamma = CP/ CV

Experimental Values (at some temp.)
C_P / C_V / C_P - C_V
Mono-atomic gases / ~20.8 / ~12.5 / ~8.3
Di-atomic gases / ~30 / ~21.7 / ~8.3
Tri-atomic gases / 35-40 / 27-31 / ~8.5

Carnot Efficiency = W / Qh = 1 – Qc / Qh = 1 – Tc / Th (max possible for ANY engine)

COP = |Qc| / W (cooling mode) for a refrigerator

COP = |Qh| / W (heating mode) for a heat pump, which is 1 over efficiency

Otto cycle efficiency (car or truck ICE on gas or diesel) = 1 – (Vbig /Vsmall)1-

S = kB ln W, where W is Multiplicity (NOT work)

S = nR ln(V/Vm) where Vm is the volume of an individual atom or molecule

∆S = ∫dQr/T, where r stands for “reversible” process (∆S = Q / T simply, if T is fixed)

∆S = kB ln (Wf / Wi )

∆S = 0 for a idealized cyclical, reversible process (like Carnot)

∆S = nR ln ( Vf / Vi ) for an isothermal process (ideal gas)

Entropy is always increasing for the universe as a whole (2nd law)