On a winter day, the outside temperature is 0°C and relative humidity 40%. The air from outside comes into a room and is heated to 20°C. What is the relative humidity in the room? The saturation vapor pressure at 0°C is 4.6 mm of mercury and at 20°C it is 18 mm of mercury.

Question

Philoid · Accepted Answer

Given:

Temperature of air outside the room=0=273.15K

Temperature of air inside the room=20=293.15K

Relative humidity at 0 =40%

Let vapor pressure of air P₁.

SVP at 0=4.6mm of Hg

P₁=0.44.6=1.84mm of Hg

Volume of room is not changed so, applying ideal gas equation at 0 and 20.

We know ideal gas equation

PV=nRT

Where V= volume of gas

R=gas constant =8.3JK^-1mol^-1

T=temperature

n=number of moles of gas

P=pressure of gas.

We get,

Relative humidity inside home i.e. at temperature 20

SVP at 20=18mm of Hg

The relative humidity in the room is 10.9%.