Question

The weatherman states that the current temperature is 95 F and the dew point is 74 F. What is the current relative humidity?

Answer 1

Answer:

Current Relative Humidity is 29.623

Given:

Current Temperature, $T_{c} = 95 F = 35^{\circ}C$

Dew point temperature, $T_{d} = 74 F = 23.34^{\circ}C$

Solution:

Now, in order to calculate the Relative Humidity, RH, we use the given formula:

$T_{d} =100( \frac{\frac{aT_{c}}{b + T}b + lnRH}{a - \frac{aT_{c}}{b + T} + lnRH})$

where

a = 17.625

b = 237.7

Now, using the above formula and given values:

$23.34 = (237.7\frac{\frac{17.625\times 35}{ 237.7 + 35} + lnRH}{17.625 - \frac{17.625\times 35}{237.7 + 35} + lnRH})$

$23.34(17.625 - 2.26 + lnRH) = (237.7\times 2.26 + lnRH)$

$358.62 + 23.34lnRH) = (537.20 + lnRH)$

$358.62 + 23.34lnRH) = (537.20 + lnRH)$

On solving the above eqn, we get:

RH = 29.623