Wednesday, June 11, 2014

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

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

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