คำนวณหำควำมชื ้นสัมพัทธ์ที่ถกู ต้ องใน Calibration Certificate จำกหน่วย
dew-point temperature
?
% RH 
?
?
e ' w ( t s ) f ( t s , Ps )
e ' w ( t c ) f ( t c , Pc )

Pa
Pa
 100
?
where
 and e’w(ts) and e’w(tc) are the saturation water vapor pressure over a plane surface of the
pure phase of liquid water or solid ice at the saturator temperature ts and test chamber
temperature tc
 The temperature and pressure have units of Kelvin and Pascal
 f ( Ps,ts ) is the enhancement factor of water vapor-air mixture at saturator pressure Ps
and temperature ts
 f ( Pc ,tc) is the enhancement factor of water vapor-air mixture at test chamber pressure
Pc and temperature tc
 P is Pressure on temperature chamber (Pc) and temperature on saturation (Ps)
เรารู้อะไรบ้าง ?
Dew-point/Frost-point temperature ( oC)
 ได้จาก ?
2. Ambient temperture ( oC)
1.

3.
ได้จาก ?
สูตรการคานวณ ew และ f
 Bob Hardy, Formulation for vapor pressure…,
 Institute of measurement control, A guide to the measurement of humidity
 ฯลฯ
Dew-point/ Frostpoint temperature
Dew-point
hygrometer
Pout = 101325 Pa
td = Average of calibration
dew-point temperature
reading
ta = Average of calibration
ambient temperature
reading
ta &td & Pa
ค่าเฉลี่ยจากการบันทึกผล
การวัด
td
ed '
e w ( t d ) f ( t d , Pa )
คานวนหา ew และ f ของ td
ta
ea '
e w ( t a ) f ( t a , Pa )
e '
% RH  d 
e '
a
P
a  100
P
a
คานวนหา ew และ f ของ ta
Actual water
vapor pressure
e'  e  f
ตัวแปรที่ไม่ทราบค่า (1)
By Wexler’s equation and Sonntag’s equation;
 6

i 2
e w  exp  ai (T  273.15)  a ln(T  273.15) 
7
i

0


By Magnus’s equation

 a t


e  exp  lna   1
a t
w
0


 2






Wexler
Range: above water
Sonntag
Hardy
Wagner and Pruss
ITS-90
Magnus
a0
a1
a2
a3
a4
a5
a6
a7
-2.9912729·103
-6.0170128·103
1.887643854·101
-2.8354721·10-2
1.7838301·10-5
-8.4150417·10-10
4.4412543·10-13
2.858487
0
-6.0969385·103
2.12409642·101
-2.711193·10-2
1.673952·10-5
0
0
2.433502
-2.8365744·103
-6.028076559·103
1.954263612·101
-2.737830188·10-2
1.6261698·10-5
7.0229056·10-10
-1.8680009·10-13
2.7150305
0
-7.85951783
1.84408259
-11.7866497
22.6807411
-15.9618719
1.80122502
0
611.2
17.62
243.12
ur(e)
for the range
0oC ≤ t ≤ 100oC:
ur(e) < 0.005%
as for Wexler
as for Wexler
for the range
-45 oC ≤ t ≤60oC:
ur(e) < 0.3%
a0
a1
a2
a3
a4
a5
a6
a7
ur(e)
Wexler
above ice Equation
Sonntag
Hardy
Wagner and Pruss
ITS-90
Magnus
0
-5.6745359·103
-5.6745359
-9.677843·10-3
6.22157·10-7
2.0747825·10-9
-9.484024·10-13
4.1635019
0
-6.0245282·103
2.932707·101
1.0613868·10-2
-1.3198825·10-5
0
0
-4.9382577·10-1
0
-5.8666426·103
2.232870244·101
1.39387003·10-2
-3.4262402·10-5
2.7040955·10-8
0
6.7063522·10-1
0
-13.928169
34.7078238
611.2
22.46
272.62
for the range
-100oC ≤ t ≤
0.01oC:
ur(e) < (0.010.005t)% of value
as for Wexler
as for Wexler
for the range
-65 oC ≤ t ≤0.01oC:
ur(e) < 0.5%
Actual water
vapor pressure
ตัวแปรที่ไม่ทราบค่า (2)
e'  e  f
 
 P

ed 
Water pressure enhancement factor f  exp  α  1    β   1  
P 
 ed

 
4
4
 

i 1
Ai t
( i  1)
 

i 1
Bi t
( i  1)
ไอนำ้ เป็ นแก๊สอุดมคติหรือไม่ ?
Sensitivity Coefficient (Ci)
สามารถหาได้จาก
For Dew-point Temperature =
dRH
dt d
for magnus
equation
dRH
dt d
for sonntag
equation
dRH
dt d
 4283 . 774
 RH  
  243 . 12  t d
2




a7 
2
 RH    a 1T d  a 3  2 a 4 T d 

T
d 

Sensitivity Coefficient (Ci)
for Wexler
equation
dRH
dt d

a7 
3
2
2
3
 RH    2 a 0 T d  a 1T d  a 3  2 a 4 T d  3 a 5T d  4 a 6 T d 

T
d 

for air temper ature sensitivit
y coefficien
t
dRH
dT a
for magnus
equation
dRH
dt a
for sonntag
equation
dRH
dt a
 4283 . 774 
 - RH  
2 
  243 . 12  t a  

a7 
2
 - RH    a 1T a  a 3  2 a 4 T a 

T
a 

Sensitivity Coefficient (Ci)
for Wexler
equation
dRH
dt a

a7 
3
2
2
3
 RH    2 a 0 T a  a 1T a  a 3  2 a 4 T a  3 a 5 T a  4 a 6 T a 

T
a 
