Question

The temperature and humidity of air are 27°C and 50% on a particular day. Calculate the amount of vapour that should be added to 1 cubic metre of air to saturate it. The saturation vapour pressure at 27°C = 3600 Pa.

Answer 1

The amount of vapour that should be added to 1 cubic metre of air to saturate is 13g.

Explanation:

Step 1:  

given data  

Saturated vapour pressure$=3600 P a$

$T=273+27=300 K$            

$V=1 m^{3}$

(mass for water ) $=18 g$

RH (Relative humidity)$=50 \%$  

( vapour pressure)/(Saturated vapour pressure)$=\frac{50}{100}=0.5$

vapour pressure=$0.5 \times 3600=1800$

Step 2:

Let be the water mass $m_{1}$ in the $50$percent moist air.

$P V=n R T$

$P V=\frac{m_{1}}{M} R T$

$1800=\frac{m_{1}}{18} \times 8.3 \times 300$

$m_{1}=13 g$

 Required Saturation pressure=$3600 \mathrm{Pa}$

Step 3:

Let $\mathrm{m}_{2}$ be the saturation needed amount of water.

$3600=\frac{m_{2}}{M} R T$

$m_{2}=\frac{3600 \times 18}{8,3 \times 300}$

$m_{2}=\frac{36 \times 18}{8.3 \times 3}$

$m_{2}=\frac{648}{24.9}=26.02 g \approx 26 g$

Maximum excess water vapour to be added = $m_{2}-m_{1}=26-13=13 g$