Q. 584.5( 2 Votes )
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.
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
Where V= volume of gas
R=gas constant =8.3JK-1mol-1
n=number of moles of gas
P=pressure of gas.
Relative humidity inside home i.e. at temperature 20
SVP at 20=18mm of Hg
The relative humidity in the room is 10.9%.
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