Answer:
Current Relative Humidity is 29.623
Given:
Current Temperature, [tex]T_{c} = 95 F = 35^{\circ}C[/tex]
Dew point temperature, [tex]T_{d} = 74 F = 23.34^{\circ}C[/tex]
Solution:
Now, in order to calculate the Relative Humidity, RH, we use the given formula:
[tex]T_{d} =100( \frac{\frac{aT_{c}}{b + T}b + lnRH}{a - \frac{aT_{c}}{b + T} + lnRH})[/tex]
where
a = 17.625
b = 237.7
Now, using the above formula and given values:
[tex]23.34 = (237.7\frac{\frac{17.625\times 35}{ 237.7 + 35} + lnRH}{17.625 - \frac{17.625\times 35}{237.7 + 35} + lnRH})[/tex]
[tex]23.34(17.625 - 2.26 + lnRH) = (237.7\times 2.26 + lnRH)[/tex]
[tex]358.62 + 23.34lnRH) = (537.20 + lnRH)[/tex]
[tex]358.62 + 23.34lnRH) = (537.20 + lnRH)[/tex]
On solving the above eqn, we get:
RH = 29.623
