Dew Point and Relative Humidity
This blog entry has programs for the HP 50g and TI84+. 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%)
ClausiusClapeyron 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*(1/2731/Td))] / [611*e^(5423*(1/2731/T))]
RH = [e^(5423*(1/2731/Td))] / [e^(5423*(1/2731/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  TI84+:
: 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*(1/2731/T)) * RH = 611 * e^(5423*(1/2731/Td))
e^(5423*(1/2731/T)) * RH = e^(5423*(1/2731/Td))
5423*(1/2731/T) + ln RH = 5423*(1/2731/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  TI84+
: 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 TI84+: Dew Point and Relative Humidity
Subscribe to:
Post Comments (Atom)
How to Rotate Graphs
How to Rotate Graphs Introduction The key is to use parametric equations in our rotation. Using the rotation angle θ, the rotatio...

Casio fx991EX Classwiz Review Casio FX991EX The next incarnation of the fx991 line of Casio calculators is the fx991 EX. ...

TI36X Pro Review This is a review of the TI36X Pro Calculator by Texas Instruments. History Originally, this was the TI30X Pro that w...

One of the missing features of the TI82/83/84 family is the ability to convert between bases. Here are two programs in TIBasic to help...
No comments:
Post a Comment