Thermal expansion

ΔLL=α⋅ΔT\frac{\Delta L}L = \alpha\cdot\Delta T
ΔVV=β⋅ΔT\frac{\Delta V}V = \beta\cdot\Delta T
β=3⋅α\beta = 3\cdot\alpha

Specific Heat Capacity

Q=m⋅c⋅(Tend−Tstart)Q = m\cdot c\cdot (T_\textup{end} - T_\textup{start})

Melting Heat

Q=m⋅lmQ = m\cdot l_\textup{m}

Steam Generation Heat

Q=m⋅lsQ = m\cdot l_\textup{s}

Effect

P=dWdtP = \frac{dW}{dt}

Density

ρ=mV\rho = \frac mV

Force

F=m⋅gF = m\cdot g

Pressure

p=FAp = \frac FA

Water Pressure

ptot=ρ⋅g⋅h+pabovep_\textup{tot} = \rho\cdot g\cdot h + p_\textup{above}

Ideal Gas Law

p⋅V=n⋅R⋅Tp\cdot V = n\cdot R\cdot T
p⋅V=N⋅k⋅Tp\cdot V = N\cdot k\cdot T
n=NNA=mtotMn = \frac N{N_A} = \frac{m_\textup{tot}}{M}
ρ=p⋅MR⋅Tn0=pk⋅T\rho = \frac{p\cdot M}{R\cdot T} \qquad n_0 = \frac p{k\cdot T}

Barometric Height Formula

p=p0⋅e−ρ0⋅g⋅hp0h=p0ρ0⋅g⋅ln⁡p0pp = p_0\cdot e^{-\frac{\rho_0\cdot g\cdot h}{p_0}} \qquad h = \frac{p_0}{\rho_0\cdot g}\cdot\ln\frac{p_0}{p}

Relative Air Moisture

RLF=pwaterpsaturatedR_{LF} = \frac{p_\textup{water}}{p_\textup{saturated}}

Van der Waal's Equation

(p+a⋅n2V2)⋅(V−n⋅b)=n⋅R⋅T\left(p + a\cdot\frac{n^2}{V^2}\right)\cdot(V - n\cdot b) = n\cdot R\cdot T

Critical Point

VK=3⋅n⋅b,TK=8⋅a27⋅R⋅bV_K = 3\cdot n\cdot b, T_K = \frac{8\cdot a}{27\cdot R\cdot b}
pK=a27⋅b2p_K = \frac a{27\cdot b^2}

The Vapor Pressure Curve

p=A⋅eM⋅IvR⋅Tp = A\cdot e^{\frac{M\cdot I_\textup{v}}{R\cdot T}}

Reynold's Number

Re=ρ⋅v⋅dηRe = \frac{\rho\cdot v\cdot d}{\eta}

Laminar if

Re<2300Re < 2300

, Turbulent if

Re>2300Re > 2300

.

Volume Flow

ϕ=v⋅A\phi = v\cdot A

Bernoulli's Equation

p1+ρ⋅v122+ρ⋅g⋅y1=p2+ρ⋅v222+ρ⋅g⋅y2p_1 + \frac{\rho\cdot v_1^2}{2} + \rho\cdot g\cdot y_1 = p_2 + \frac{\rho\cdot v_2^2}2 + \rho\cdot g\cdot y_2

Poiseuille's Law

ϕ=π⋅R48⋅η⋅(p1−p2)L\phi = \frac{\pi\cdot R^4}{8\cdot\eta}\cdot\frac{(p_1 - p_2)}{L}

Heat Conduction

P=−λ⋅A⋅dTdx(general)P = -\lambda\cdot A\cdot\frac{dT}{dx} \quad \textup{(general)}
P=λ⋅A⋅T1−T2L(linear)P = \lambda\cdot A\cdot\frac{T_1 - T_2}L \quad \textup{(linear)}
P=λ⋅2π⋅L⋅T1−T2ln⁡(R2R1)(cylindrical)P = \lambda\cdot 2\pi\cdot L\cdot\frac{T_1 - T_2}{\ln(\frac{R_2}{R_1})} \quad \textup{(cylindrical)}

Heat Transfer

P=α⋅A⋅ΔTP = \alpha\cdot A\cdot \Delta T

k-number (U-number)

1k=1α1+L1λ1+L2λ2+⋯+1α2\frac 1k = \frac 1{\alpha_1} + \frac{L_1}{\lambda_1} + \frac{L_2}{\lambda_2} + \cdots + \frac 1{\alpha_2}
P=A⋅k⋅ΔTP = A \cdot k \cdot \Delta T

Heat flow(intensity)

I=PA=λ⋅T1−T2L(linear)I = \frac PA = \lambda\cdot\frac{T_1 - T_2}L \quad \textup{(linear)}

Heat Radiation

Pideal=σ⋅A⋅T4P_\textup{ideal} = \sigma\cdot A\cdot T^4
Preal=e⋅PidealP_\textup{real} = e\cdot P_\textup{ideal}
Pnet=Pout−Pin=e⋅σ⋅A⋅(Tout4−Tin4)P_\textup{net} = P_\textup{out} - P_\textup{in} = e\cdot\sigma\cdot A\cdot (T_\textup{out}^4 - T_\textup{in}^4)
σ=5.67⋅10−8 J/(s⋅m2⋅K4)\sigma = 5.67\cdot 10^{-8}\:\textup{J/(s$\cdot$m$^2\cdot$K$^4$)}

Wien's Displacement Law

λmax⋅T=2.898⋅10−3 m⋅K\lambda_\textup{max}\cdot T = 2.898\cdot 10^{-3}\:\textup{m}\cdot\textup{K}