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.

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%.


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