[Physics] How to calculate relative humidity from specific humidity and temperature

Question

If I know specific humidity and temperature at a location, can I calculate relative humidity using these two?

Answer 1

From Psychrometry in Refrigeration & Air Conditioning

Let $t_d$ be D.B.T. (dry bulb temperature) & $t_w$ be W.B.T. (wet bulb temperature) and $p_s$ & $p_w$ are saturation pressures at D.B.T. & W.B.T. respectively (refer to "Steam Table" for saturation pressures at given temperatures) then using Carrrier's Equation, the partial pressure ($p_v$) of water vapor is given as $$p_v=p_w-\frac{(p_b-p_w)(t_d-t_w)}{1544-1.44t_w}\tag 1$$ Where, $p_b$ is barometric pressure

Now, use the formula for given specific humidity say $W$ given as $$W=0.622 \left(\frac{p_v}{p_b-p_v}\right) $$ $$\implies p_b=\frac{0.622p_v}{W}+p_v$$ Substitute the value of $p_b$ in the eq(1) to get the value of $p_v$ Then apply the formula of $\color{blue}{\text{Relative Humidity}\ \phi}$ as follows $$\color{blue}{\phi=\frac{p_v}{p_s}}$$

Where, $p_v$ (partial pressure) & $p_s$ (saturation pressure at D.B.T.) are known.