Termodynamik

Värmeutvidgning

\frac{\Delta L}{L} = \alpha \Delta T, \quad \frac{\Delta V}{V} = \beta \Delta T, \quad \beta =3\alpha

Q = mc \Delta T, \quad l_s = \frac{Q_s}{m}, \quad l_\textup{å} = \frac{Q_\textup{å}}{m}

p_{tot} = p_\textup{vätska} + p_\textup{luft} = \rho gh + p_\textup{luft}

\begin{gathered} pV = NkT \quad \textup{eller} \quad pV = nRT \\ \textup{där} \quad n = \frac{m_{tot}}{M} = \frac{N}{N_A} \quad \textup{och} \quad R = kN_A \end{gathered}

\rho = \frac{m_{tot}}{V} = \frac{pM}{RT}, \quad n_o = \frac{N}{V} = \frac{p}{kT}

p = p_0e^{-\rho_0gh/p_0}, \quad h = \frac{p_0}{\rho_0g}\ln{\frac{p_0}{p}}

R_{LF} = \frac{p_\textup{vatten}}{p_\textup{mättnad}}

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

V_k = 3nb, \quad T_k = \frac{8a}{27Rb}, \quad p_k = \frac{a}{27b^2}

r = \left(\frac{3b}{16\pi N_A}\right)^{1/3}

p = Ae^{-Ml_\textup{å}/(RT)}

Re = \frac{\rho vd}{\eta}, \quad Re < 2300 \; \textup{laminär}

\Phi = \frac{\textup{d}V}{\textup{d}t} = A_1v_1 = A_2v_2

p_1 + \frac{\rho v_1^2}{2} + \rho gy_1 = p_2 + \frac{\rho v_2^2}{2} + \rho gy_2

\Phi = \frac{\pi R^4}{8\eta}\frac{(p_1 - p_2)}{L}

p = \frac{2}{3}n_o\frac{m_\textup{en}}{2}\langle v^2 \rangle = \frac{2}{3}n_o\left\langle W_\textup{kin}\right\rangle_\textup{en}

\left\langle W_\textup{kin} \right\rangle_\textup{en} = \frac{3}{2}kT

\Delta U = \frac{f}{2}Nk\Delta T = \frac{f}{2}nR\Delta T

Q = \Delta U + W \quad \textup{med} \quad W = \int_1^2pdV

W \equiv 0

W = p\left(V_2 - V_1\right)

W = nRT\ln\left(\frac{V_2}{V_1}\right)

W = -\Delta U

c_V = \frac{f}{2}R, \quad c_p = c_V + R

\begin{gathered} T_1V_1^{(\gamma - 1)} = T_2V_2^{(\gamma - 1)} \\ p_1V_1^\gamma = p_2V_2^\gamma \end{gathered}

\gamma \equiv \frac{C_p}{C_V} = \frac{c_p}{c_V} = 1 + \frac{2}{f}

Q_\textup{netto} = W_\textup{netto} = \oint pdV

\eta = \frac{W_\textup{netto}}{Q_\textup{in}} = \frac{Q_\textup{in} -|Q_\textup{ut}|}{Q_\textup{in}}= 1 - \frac{|Q_\textup{ut}|}{Q_\textup{in}}

\eta = \frac{T_\textup{varm} - T_\textup{kall}}{T_\textup{varm}} = 1 - \frac{T_\textup{kall}}{T_\textup{varm}}

K_f \equiv \frac{Q_\textup{in}}{|W_\textup{netto}|}, \quad K_f = \frac{T_\textup{kall}}{T_\textup{varm} - T_\textup{kall}}

V_f \equiv \frac{Q_\textup{ut}}{|W_\textup{netto}|}, \quad V_f = \frac{T_\textup{varm}}{T_\textup{varm} - T_\textup{kall}}

f(v_z) = \sqrt{\frac{m_\textup{en}}{2\pi kT}}e^{-m_\textup{en}v_z^2/(2kT)}

f(v) = 4\pi v^2 \left(\frac{m_\textup{en}}{2\pi kT}\right)^{3/2}e^{-m_\textup{en}v^2/(2kT)}

\begin{gathered} \langle v \rangle = \sqrt{\frac{8kT}{\pi m_\textup{en}}}, \quad \langle v\rangle = 2\langle |v_x| \rangle \\ \langle W_\textup{kin} \rangle = \left\langle \frac{m_\textup{en}v^2}{2}\right\rangle = \frac{m_\textup{en}}{2}\langle v^2 \rangle = \frac{3}{2}kT \end{gathered}

n^* = \frac{n_o}{4}\langle v \rangle

l = \frac{1}{n_o\pi d^2 \sqrt{2}}

P = -\lambda A \frac{\textup{d}T}{\textup{d}x}, \quad P = \lambda A \frac{T_1 - T_2}{L}

P = \alpha A \Delta T

P_\textup{ideal} = \sigma A T^4, \quad P_\textup{verklig} = eP_\textup{ideal}