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

Answer:

47 %  

Step-by-step explanation:

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

$a_{d} = 6.112e^{\frac{17.502T_{d} }{240.97+T_{d}}}$

$a_{w} = 6.112e^{\frac{17.502T_{w} }{240.97+T_{w}}}$

$RH = \frac{ a_{w}-0.668 745(1+0.00115T_{w})(T_{d}-T_{w})}{a_{d}}\times100$

Data:

$T_{d} = 28 ^{\circ}\text{C}; T_{w} = 20^{\circ}\text{C}$

Calculations:

$a_{d} = 6.112e^{\frac{17.502\times28}{240.97+ 28}}$

$a_{d} = 6.112e^{\frac{490.1}{238.97}}$

$a_{d} = 6.112e^{1.822}$

$a_{d} = 6.112\times 6.184$

$a_{d} = 37.88$

$a_{w} = 6.112e^{\frac{17.502\times20}{240.97+ 20}}$

$a_{w} = 6.112e^{\frac{350.0}{260.97}}$

$a_{w} = 6.112e^{1.341}$

$a_{w} = 6.112\times 3.824$

$a _{w} = 23.37$

$RH = \frac{ 23.37 - 0.668 745(1+0.00115\times20)(28 - 20)}{37.88}\times100$

$RH = \frac{ 23.37 - 0.668 745(1+0.02300)\times8}{37.88}\times100$

$RH = \frac{ 23.37 - 0.668 745\times1.02300\times8}{37.88}\times100$

$RH = \frac{ 23.37 - 5.4738}{37.88}\times100$

$RH = \frac{ 17.90}{37.88}\times100$

$RH = 47.3 \%$

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

Answer 2

10 i think not sure