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