Code: Select all
\begin{align}
RH :&= \cfrac{m_w}{m_\text{sat}(w)} = \cfrac{M_w \cdot n_w}{M_\text{sat}(w) \cdot n_\text{sat}(w)} = \cfrac{M_w \cdot \frac{p_w \cdot \cancel{V}}{\cancel{R \cdot T}}}{M_\text{sat}(w) \cdot \cfrac{p_\text{sat}(w) \cdot \cancel{V}}{\cancel{R \cdot T}}} = \frac{p_w}{p_\text{sat}(w)}\\
&= \frac{\frac{W \times p}{W + `r M_w_TO_M_d`}}{p_\text{sat}(w)} = \frac{W \times p}{(W + `r M_w_TO_M_d`) \cdot p_\text{sat}(w)} = \frac{x_w}{x_\text{sat}(w)}|_{T, P}
(\#eq:relative-humidity)
\end{align}
Code: Select all
\begin{align}
RH :&= \cfrac{m_w}{m_\text{sat}(w)} = \cfrac{M_w \cdot n_w}{M_\text{sat}(w) \cdot n_\text{sat}(w)} = \cfrac{M_w \cdot \frac{p_w \cdot \cancel{V}}{\cancel{R \cdot T}}}{M_\text{sat}(w) \cdot \cfrac{p_\text{sat}(w) \cdot \cancel{V}}{\cancel{R \cdot T}}} = \frac{p_w}{p_\text{sat}(w)}\\(\#eq:relative-humidity-ratio-of-pressures)
&= \frac{\frac{W \times p}{W + `r M_w_TO_M_d`}}{p_\text{sat}(w)} = \frac{W \times p}{(W + `r M_w_TO_M_d`) \cdot p_\text{sat}(w)} = \frac{x_w}{x_\text{sat}(w)}|_{T, P}
(\#eq:relative-humidity)
\end{align}
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