**Dew Point and Relative Humidity**

This blog entry has programs for the HP 50g and TI-84+. RELHUMID is finding the relative humidity given actual temperature and dew point (both in °F).

Source: Michael Bell

"How do I calculate dew point when I know the temperature and relative humidity?"

Retrieve 6/10/2014

http://iridl.ldeo.columbia.edu/dochelp/QA/Basic/dewpoint.html

Relative Humidity

RH = E/Es (* 100%)

Clausius-Clapeyron Equations

Vapor Pressure:

E = 611 * e^(5423 * (1/273 - 1/Td)) [Pascal]

Saturation Pressure (Maximum):

Es = 611 * e^(5423 * (1/273 - 1/T)) [Pascal]

611: reference pressure

5423: L/Rv = ΔH/R; enthalpy of vapor water/Universal Gas Constant

R = 8.31452 J/(gmol K)

273 K: reference vapor pressure (at 0°K)

T = actual temperature

Td = Dew Point

RH = relative humidity

Temperature is in Kelvin

Kelvin to Fahrenheit

K = 5/9 * (F - 32) + 273.15

Equations and Programs:

Given T and Td, find RH

T and Td are in Kelvins

°F to °K: K = 5/9 * (F - 32) + 273.15

Derivation:

RH = E / Es

RH = [611*e^(5423*(1/273-1/Td))] / [611*e^(5423*(1/273-1/T))]

RH = [e^(5423*(1/273-1/Td))] / [e^(5423*(1/273-1/T))]

RH = e^( 5423 * (1/273 - 1/Td - 1/273 + 1/T ) )

RH = e^( 5423 * (1/T - 1/Td) )

Example:

Given T = 62.2°F and Td = 61°F, RH ≈ 95.7807%

Programs

RELHUMID - HP 50g:

Input: T on level 2, Td on level 1

<< 2 →LIST 1_°F * 1_K CONVERT

UVAL INV OBJ→ DUP - 5423 * EXP

100 * "Humidity (%)" →TAG >>

RELHUMID - TI-84+:

: Input "TEMP (°F):", T

: Input "DEW PT:", D

: 5/9 * (T - 32) + 273.15 → T

: 5/9 * (D - 32) + 273.15 → D

: e^( 5423( T⁻¹ - D⁻¹ → R

: 100R → R

: Disp "HUMIDITY:", R

T (in °K) and RH (in decimal), find Td

Derivation:

Es * RH = E

611 * e^(5423*(1/273-1/T)) * RH = 611 * e^(5423*(1/273-1/Td))

e^(5423*(1/273-1/T)) * RH = e^(5423*(1/273-1/Td))

5423*(1/273-1/T) + ln RH = 5423*(1/273-1/Td))

(1/273 - 1/T) + ln RH/5423 = 1/273 - 1/Td

-1/T + ln RH/5423 = -1/Td

1/Td = 1/T - ln RH/5423

Td = 1/( 1/T - ln RH/5423) = (1/T - ln RH/5423)^(-1)

°K to °F: F = 9/5 * K - 459.67

Example:

Given: T = 91°F and RH = 23%, Td ≈ 48.8400 °F

Programs:

DEWPOINT - HP 50g

Input: T on level 2, RH on level 1

<< 1 % LN 5423 / NEG

SWAP 1_°F * 1_K CONVERT UVAL INV

+ INV 1_K * 1_°F CONVERT "Dew Point" →TAG >>

DEWPOINT - TI-84+

: Input "TEMP (°F):", T

: Input "HUMIDITY", R

: R/100 → R

: 5/9 * (T - 32) + 273.15 → T

: (-ln(R)/5423 + T⁻¹ )⁻¹ → D

: 9/5 * D - 459.67 → D

: Disp "DEW PT.", D

Hope this is helpful. I am grateful for the many compliments. Talk to you next time, Eddie

This blog is property of Edward Shore. 2014

A blog is that is all about mathematics and calculators, two of my passions in life.

## Wednesday, June 11, 2014

### HP 50g and TI-84+: Dew Point and Relative Humidity

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