Question

The inside temperature of a wall in a dwelling is 16°C. If the air in the room is at 21°C, what is the maximum relative humidity, in percent, the air can have before condensation occurs on the wall?

Answer 1

The maximum relative humidity is 77.7 %

Step-by-step explanation:

The actual vapor pressure at the given temperature is equal to:

`E=6.11*10*((T)/(237.7+T) )=6.11*10*((16)/(237.7+16) )=28.9mbar`

The saturation vapor pressure at room temperature is equal to:

`E_(s) =6.11*10*((21)/(237.7+21) )=37.19mbar`

The maximum relative humidity is equal to:

`Relative-humidity=(E)/(E_(s) ) *100=(28.9)/(37.19) *100=77.7%`%

Answer 2

`\phi_(max) = 0.731\,(73.1\,\%)`

Step-by-step explanation:

The relative humidity is equal to the ratio of the vapor pressure to the saturation pressure at dry-bulb temperature. Maximum relative occurs when air temperature is equal to the dew-point temperature, related to the temperature of the wall. Then:

`\phi = (P_(v))/(P_(sat))`

Saturation Pressure (21°C): (Taken from water tables)

`P_(sat) = 2.5053\,kPa`

Vapor Pressure (16°C): (Taken from water tables)

`P_(v) = 1.8324\,kPa`

The maximum relative humidity is:

`\phi_(max) = (1.8324\,kPa)/(2.5053\,kPa)`

`\phi_(max) = 0.731\,(73.1\,\%)`