Answer:
47 %
Step-by-step explanation:
The formula for relative humidity (RH) consists of three parts:
[tex]a_{d} = 6.112e^{\frac{17.502T_{d} }{240.97+T_{d}}}[/tex]
[tex]a_{w} = 6.112e^{\frac{17.502T_{w} }{240.97+T_{w}}}[/tex]
[tex]RH = \frac{ a_{w}-0.668 745(1+0.00115T_{w})(T_{d}-T_{w})}{a_{d}}\times100[/tex]
Data:
[tex]T_{d} = 28 ^{\circ}\text{C}; T_{w} = 20^{\circ}\text{C}[/tex]
Calculations:
[tex]a_{d} = 6.112e^{\frac{17.502\times28}{240.97+ 28}}[/tex]
[tex]a_{d} = 6.112e^{\frac{490.1}{238.97}}[/tex]
[tex]a_{d} = 6.112e^{1.822}[/tex]
[tex]a_{d} = 6.112\times 6.184[/tex]
[tex]a_{d} = 37.88[/tex]
[tex]a_{w} = 6.112e^{\frac{17.502\times20}{240.97+ 20}}[/tex]
[tex]a_{w} = 6.112e^{\frac{350.0}{260.97}}[/tex]
[tex]a_{w} = 6.112e^{1.341}[/tex]
[tex]a_{w} = 6.112\times 3.824[/tex]
[tex]a _{w} = 23.37[/tex]
[tex]RH = \frac{ 23.37 - 0.668 745(1+0.00115\times20)(28 - 20)}{37.88}\times100[/tex]
[tex]RH = \frac{ 23.37 - 0.668 745(1+0.02300)\times8}{37.88}\times100[/tex]
[tex]RH = \frac{ 23.37 - 0.668 745\times1.02300\times8}{37.88}\times100[/tex]
[tex]RH = \frac{ 23.37 - 5.4738}{37.88}\times100[/tex]
[tex]RH = \frac{ 17.90}{37.88}\times100[/tex]
[tex]RH = 47.3 \%[/tex]
It's much easier to use a RH table (see below) and get the same result.
