Atmospheric & gas law toolkit

1. Gas laws solver (Boyle, Charles, ideal gas)
2. Dew point & relative humidity
3. Wind chill index
4. Heat index (apparent temperature)

$$PV = nRT, \quad \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$

Ideal gas law combines Boyle's ($PV=\text{const}$ at fixed $T$) and Charles's ($V/T=\text{const}$ at fixed $P$) laws. $R=8.314$ J/(mol·K). Source: standard thermodynamics.

$$T_{dp} = \frac{243.04 \left(\ln\left(\frac{RH}{100}\right) + \frac{17.625T}{243.04+T}\right)}{17.625 - \ln\left(\frac{RH}{100}\right) - \frac{17.625T}{243.04+T}}$$

Magnus-Tetens approximation for dew point given dry-bulb temperature $T$ (°C) and relative humidity $RH$ (%). Source: NOAA / standard meteorology.

$$WCI = 13.12 + 0.6215T - 11.37V^{0.16} + 0.3965TV^{0.16}$$

NWS/Environment Canada wind chill formula, $T$ in °C, $V$ in km/h wind speed at 10 m. Source: NOAA National Weather Service.

Rothfusz regression: a multi-term polynomial in dry-bulb temperature $T$ (°F) and relative humidity $RH$ (%), valid for $T\ge80°F$. Source: NOAA National Weather Service.