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

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( ((aT_(c))/(b + T)b + lnRH)/(a - (aT_(c))/(b + T) + lnRH))`

where

a = 17.625

b = 237.7

Now, using the above formula and given values:

`23.34 = (237.7((17.625* 35)/( 237.7 + 35) + lnRH)/(17.625 - (17.625* 35)/(237.7 + 35) + lnRH))`

`23.34(17.625 - 2.26 + lnRH) = (237.7* 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