Question

50 m3 of saturated vapour is cooled down from 30°C to 20°C. Find the mass of the water condensed. The absolute humidity of saturated water vapour is 30 g m−3 at 30°C and 16 g m−3 at 20°C.

Answer 1

The mass of the water condensed is 700 g.

Explanation:

We realize there is $30 \mathrm{g}$ of water vapor in $1 \mathrm{m}^{3}$ of air at $30^{\circ} \mathrm{C}$.

Therefore, water vapor in $50 \mathrm{m}^{3}$ of air in $30^{\circ} \mathrm{C}=30 \times 50 g=1500 g$

Even, at $20^{\circ} \mathrm{C}, 1 \mathrm{m} 3$ of air produces $16 \mathrm{g}$ water vapour.

Intake of water vapor in $50 m^{3}$ of air,  $20^{\circ} \mathrm{C}=16 \times 50 g=800 g$

Amount of condensed water vapour $=1500-800 \mathrm{g}=700 \mathrm{g}$

Answer 2

The mass of the water condensed is 700 g.

Explanation:

From question, we know that, 1 m³ of air contains 30 g of water vapor at 30°C

Density = Mass/Volume

The amount of water vapor at 30°C in 50 m³ is:

Amount of water vapor = 30 × 50 = 1500 g

From question, we know that, 1 m³ of air contains 16 g of water vapor at 20°C

The amount of water vapor at 20°C in 50 m³ is:

Amount of water vapor = 16 × 50 = 800 g

The amount of water vapor condensed is:

⇒ 1500 g - 800 g = 700 g