Question

Suppose outside temperature is 55◦F, while the temperature inside a building is 72◦F. The building is heated but not air conditioned, so the partial pressure of water vapor is the same both inside and outside the building. Finally, suppose the dew point outside is 40◦F. What is the dew point inside? What are the relative humidities inside and outside the building? (We are most comfortable if relative humidity is between 30% and 50%. This question shows why air in heated buildings can be uncomfortably dry.)

Answer 1

Dew point is the temperature at which the saturation vapour pressure is equal to the present vapour pressure.

Here dew point outside is given 40⁰F. So the saturation vapour pressure of water at this temperature is 0.0085 atm. this is the pressure outside the building

to find the pressure inside the building we could use Charles law of pressure.

that is,

therefore p2(pressure inside)=p1*t2/t1=0.0085*72/55=0.01112 atm

so, for this pressure to be equal to saturation vapour pressure the temperature is found to be 48⁰F(approx.).This is the dew point.

to find relative humidity inside-

relative humidity=vapour pressure of air / SVP at same temperature. / SVP-saturation vapour pressure

=0.01112 / SVP at 72⁰F=0.01112 / 0.026= 0.427=42.79%

relative humidity outside-

=0.0085 / SVP at 55⁰F= 0.0085 / 0.0145=58.6%

note: the saturation vapour pressure at a given temperature can be found using an approximate equation given by,

​​​​​​​

where P is the vapour pressure in mmHg and T is the temperature in kelvins.