Thermodynamics, Radiation, Oscillations and Cosmology

$pV = NkT$

$\tfrac{1}{2}m\langle c^2\rangle = \tfrac{3}{2}kT$

$T(\text{K}) = \theta(^\circ\text{C}) + 273$

$A = \lambda N$

$N = N_0e^{-\lambda t}$

$t_{1/2} = \dfrac{\ln 2}{\lambda}$

$\Delta E = c^2\Delta m$

$a = -\omega^2x$

$x = A\cos\omega t$

$v_{\text{max}} = \omega A$

$T = 2\pi\sqrt{\dfrac{m}{k}}$

$T = 2\pi\sqrt{\dfrac{l}{g}}$

$F = \dfrac{Gm_1m_2}{r^2}$

$g = \dfrac{GM}{r^2}$

$V_{\text{grav}} = -\dfrac{GM}{r}$

$L = \sigma AT^4$

$\lambda_{\text{max}}T = 2.898\times10^{-3}\,\text{m K}$

$I = \dfrac{L}{4\pi d^2}$

$z = \dfrac{\Delta\lambda}{\lambda} \approx \dfrac{v}{c}$

$v = H_0d$