Air with a relative humidity of 30% at 20°C is pumped into a container. What is the maximum pressure inside the container so that water does not condense on the inside of the container? Assume the air temperature inside the container is 20°C.
Answers
For air at atmospheric pressure and at a temperature of 20°C, containing water vapor such that the relative humidity is 30%, the partial pressure of the water vapor is Pw = 0.30×Pg (according to the definition of relative humidity), where Pg is the pressure of saturated water vapor. Referring to a thermodynamics table containing the properties of saturated water (H2O), Pg = 0.002338 MPa. So, Pw = 0.30×0.002338 = 0.0007 MPa. We wish to calculate the air pressure inside the container so that Pw = Pg. This means that the partial pressure of the water vapor inside the container is equal to the pressure of saturated water vapor (at 20°C). If we increase the air pressure by some multiple M, then the partial pressure of the water vapor present in the air will increase by the same multiple M (based on Dalton's law of partial pressures). Therefore, M = 0.002338/0.0007 = 3.34. The maximum pressure inside the container is then 3.34×(atmospheric pressure) = 340 kPa, approximately, for atmospheric pressure = 101.3 kPa. At this pressure the water vapor will begin to condense inside the container (at the dew point temperature of 20°C). Note that having water condense inside the container can be undesirable given that it can cause corrosion or mold growth. This is prevented by keeping the pressure inside the container less than 340 kPa, so that water condensation doesn't occur.