## Liquids, gases, thermal properties of matter

#### Fluid Mechanics:

Bernoulli's equation:    P + ρgh + ½ρv2= constant.
Poiseuille's law Q = π∆Pr4/(8ηL)
Volume flow rate = π*(pressure difference)*(pipe radius)4/[8*(pipe length)*viscosity)

#### Kinetic Theory:

Ideal gas law: PV = nRT = NkBT
Kinetic theory: PV = (2/3)N(m<v2>/2)
Avg. kinetic energy per particle: <KE> = (3/2)kBT

#### Temperature and Heat:

Linear expansion: Δl = αlΔT.
Volume expansion: ΔV = βVΔT
Thermal conductivity:    ΔQ/Δt = -kA ΔT/Δx.
Specific heat capacity:   c = ΔQ/(m ΔT).
Wien's law: λmax  ∝ 1/T.
Stefan-Boltzmann Law Radiated power = emissivity * σ * T4 * Area

#### Thermodynamics

First law of thermodynamics:   ΔU = ΔQ - ΔW
Carnot cycle: Q1/T1 = Q2/T2
Efficiency of a heat engine: e = W/Qhigh = (Qhigh - Qlow)/Qhigh
COP of refrigerator: COP = Qlow/(-W) = Qlow/(Qhigh - Qlow)
COP of heat pump: COP = Qhigh/(-W) = Qhigh/(Qhigh - Qlow)
Change in entropy: ΔS = ∫if dQr/T,  dS = dQ/T

1 Cal = 1 kcal = 4186 J

kB = 1.381*10-23 J/K,  R = 8.31 J/(mol K)