Posts Tagged ‘equation’

Relative humidity (RH) and temperature (T) data from an RH&T sensor like the DHT22 can be used to compute not only absolute humidity AH but also dewpoint temperature TD

There has been a fair amount of interest in my formula which computes AH from measured RH and T, since it adds value to the output of RH&T sensors. To further extend this value, I have developed another formula which computes dewpoint temperature TD from measured RH and T.

Formula for computing dewpoint temperature TD

In this formula (P Mander 2017) the measured temperature T and the computed dewpoint temperature TD are expressed in degrees Celsius, and the measured relative humidity RH is expressed in %

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Strategy for computing TD from RH and T

1. The dewpoint temperature TD is defined in the following relation where RH is expressed in %

2. To obtain values for Psat, we can use the Bolton formula[REF, eq.10] which generates saturated vapor pressure Psat (hectopascals) as a function of temperature T (Celsius)

These formulas are stated to be accurate to within 0.1% over the temperature range –30°C to +35°C

3. Substituting in the first equation yields

Taking logarithms

Rearranging

Separating TD terms on one side yields

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Spreadsheet formula for computing TD from RH and T

1) Set up data entry cells for RH in % and T in degrees Celsius.

2) Depending on whether your spreadsheet uses a full point (.) or comma (,) for the decimal separator, copy the appropriate formula below and paste it into the computation cell for TD.

Formula for TD (decimal separator = .)

=243.5*(LN(RH/100)+((17.67*T)/(243.5+T)))/(17.67-LN(RH/100)-((17.67*T)/(243.5+T)))

Formula for TD (decimal separator = ,)

=243,5*(LN(RH/100)+((17,67*T)/(243,5+T)))/(17,67-LN(RH/100)-((17,67*T)/(243,5+T)))

3) Replace T and RH in the formula with the respective cell references. (see comment)

Your spreadsheet is now complete. Enter values for RH and T, and the TD computation cell will return the dewpoint temperature. If an object whose temperature is at or below this temperature is present in the local space, the thermodynamic conditions are satisfied for water vapor to condense (or freeze if TD is below 0°C) on the surface of the object.

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© P Mander August 2017