Page Description Equation
conversion between $\text{C}$ and $\text{K}$ \[ T_\mathrm{C}=T-273.15 \]
conversion between $\text{C}$ and $\text{F}$ \[ T_\mathrm{F}=\frac{9}{5}T_\mathrm{C}+32^\circ F \]
proportions between $\text{K}$, $\text{C}$ and $\text{F}$. \[ \Delta T_\mathrm{C}=\Delta T=\frac{5}{9}\Delta T_\mathrm{F} \]
average coefficient of linear expansion, depends on material. \[ \alpha=\frac{\Delta L/L_i}{\Delta T} \]
alphas for some common materials Table 19.2
587 for sufficiently small changes in $\Delta T$ or for sufficiently small $\frac{\Delta L}{L_i},$ $\alpha$ is constant.
$\alpha=$ average coefficient of linear expansion. Holds for small changes \[ L_f-L_i=\alpha L_i\left(T_f-T_i\right) \]
$2\alpha=$ average coefficient of area expansion \[ A_f-A_i=2\alpha A_i\left(T_f-T_i\right) \]
$3\alpha=$ average coefficient of volume expansion \[ V_f-V_i=3\alpha V_i\left(T_f-T_i\right) \]
Ideal gas law. $P=$ Pressure, $V=$ Volume, $n=$ number of moles molecules, $T=$ temperature, $R=$ universal gas constant. The gas must be trapped, which is to say that $n$ is constant. \[ PV=nRT \]
universal gas constant. \[ R=8.315\frac{\mathrm{J}}{\mathrm{mol\cdot K}} \]
Ideal gas law expressed in terms of number of molecules instead of number of moles. ($k_B$ is Boltzmann's Constant.) \[ PV=Nk_BT \]
Boltzmann’s Constant. \[ k_B=\frac{R}{N_A}=1.38\times{10}^{-23}\frac{\mathrm{J} }{\mathrm{K}} \]
Boyle’s Law. This law is captured by the Ideal Gas Law. \[ P\propto V^{-1} \]
Law of Charles Gay-Lussac. This law is captured by the Ideal Gas Law. \[ V\propto T \]
pressure \[ \left[P\right]=\frac{\left[F\right]}{\left[L^2\right]}=\frac{\left[F\right]}{\left[A\right]} \]
pressure $\times$ volume = energy \[ \left[PV\right]=\left[E\right] \]
SI units for pressure $\times$ volume \[ \left[PV\right]_{\mathrm{SI}}=\mathrm{J}=N\cdot m \]
pascal, pressure units \[ 1\ \mathrm{Pa}=1=\frac{\mathrm{N}}{\mathrm{m}^2} \]