Answer to Question #86009 in Molecular Physics | Thermodynamics for Beast

Question

The humidity meter shows the relative humidity of the room air at 78% when the temperature
is 22 ° C. What is the absolute humidity in g / m3 of air and what is Dew point (temperature)?

Answer 1

1) Calculate the absolute humidity in $\text{ g/m}^3$ substituting the relative humidity in % and the temperature in Celsius degrees:

$$AH=\frac{6.112\cdot 2.1674\cdot e^{17.67T/(243.5+T)}\cdot RH}{273.15+T}=15.14\text{ g/m}^3.$$

2) Calculate the parameter $\gamma (T, RH)$ for $T=22^\circ\text{C}$ (Celsius) and $RH=0.78$ (not %) using Magnus formula:

$$\gamma (T, RH)=\frac{17.27\cdot T}{237.7+T}+\text{ln}RH=1.215.$$

Calculate the dew point:

$$T_{DP}=\frac{237.7\cdot \gamma (T, RH)}{17.27-\gamma (T, RH)}=17.98^\circ\text{C}.$$

The formula has a maximum error $\pm 0.4^\circ\text{C}.$