Heat expansion

ΔLL=αΔT\frac{\Delta L}{L}=\alpha\Delta T
ΔVV=βΔT\frac{\Delta V}{V}=\beta\Delta T
β=3α\beta=3\alpha

Heat

Q=mcΔTQ=mc\Delta T
ls=Qsml_s=\frac{Q_s}{m}
la=Qaml_a=\frac{Q_a}{m}

%a ska egentligen vara å

Fluid preassure

ptot=pfluid+pair=ρgh+pairp_{tot} = p_\textup{fluid} + p_\textup{air} = \rho gh + p_\textup{air}

%funkar det att skirva ä eller måste det vara så här?

Ideal gas law

pV=NkTpV=NkT
pV=nRTpV=nRT

Gas density and particle density

ρ=mtotV=pMRT,no=NV=pkT\rho = \frac{m_{tot}}{V} = \frac{pM}{RT}, \quad n_o = \frac{N}{V} = \frac{p}{kT}

Barometric height formula

p=p0e−ρ0gh/p0,h=p0ρ0gln⁡p0pp = p_0e^{-\rho_0gh/p_0}, \quad h = \frac{p_0}{\rho_0g}\ln{\frac{p_0}{p}}

Relative humidity

RM=pwaterpsaturationR_{M} = \frac{p_\textup{water}}{p_\textup{saturation}}

van der Waals' equation

(p+an2V2)(V−nb)=nRT\left(p + a\frac{n^2}{V^2}\right)(V - nb) = nRT

Critical point

Vk=3nb,Tk=8a27Rb,pk=a27b2V_k = 3nb, \quad T_k = \frac{8a}{27Rb}, \quad p_k = \frac{a}{27b^2}