Question

what is the relative humidity when the air temperature is 28 degrees celcius and the wet bulb temperature is 20 degrees celcius?

Answer 1

10 i think not sure

Answer 2

47 %

Step-by-step explanation:

The formula for relative humidity (RH) consists of three parts:

`a_(d) = 6.112e^{(17.502T_(d) )/(240.97+T_(d))}`

`a_(w) = 6.112e^{(17.502T_(w) )/(240.97+T_(w))}`

`RH = ( a_(w)-0.668 745(1+0.00115T_(w))(T_(d)-T_(w)))/(a_(d))*100`

Data:

`T_(d) = 28 ^(\circ)\text{C}; T_(w) = 20^(\circ)\text{C}`

Calculations:

`a_(d) = 6.112e^{(17.502*28)/(240.97+ 28)}`

`a_(d) = 6.112e^{(490.1)/(238.97)}`

`a_(d) = 6.112e^(1.822)`

`a_(d) = 6.112* 6.184`

`a_(d) = 37.88`

`a_(w) = 6.112e^{(17.502*20)/(240.97+ 20)}`

`a_(w) = 6.112e^{(350.0)/(260.97)}`

`a_(w) = 6.112e^(1.341)`

`a_(w) = 6.112* 3.824`

`a _(w) = 23.37`

`RH = ( 23.37 - 0.668 745(1+0.00115*20)(28 - 20))/(37.88)*100`

`RH = ( 23.37 - 0.668 745(1+0.02300)*8)/(37.88)*100`

`RH = ( 23.37 - 0.668 745*1.02300*8)/(37.88)*100`

`RH = ( 23.37 - 5.4738)/(37.88)*100`

`RH = ( 17.90)/(37.88)*100`

`RH = 47.3 \%`

It's much easier to use a RH table (see below) and get the same result.