ব্যবহারকারী:Ahammad Ullah Bappy/পানির বাষ্পীয় চাপ

পানির বাষ্পীয় চাপ হচেছ এমন চাপ যেখানে‌ জলীয়বাষ্প তাপগতীয় সাম্যাবস্থার ঘণীভূত অবস্থায় থাকে। উচ্চ তাপমাত্রায় পানি ঘনীভূত হয়ে থাকে। পানির বাষ্পীয় চাপ হলো কঠিন অথবা তরল পানির সাম্যাবস্থার যে কোনো গ্যাস মিশ্রনের জলীয়বাস্পের আংশিক চাপ। অন্যান্য পদার্থের জন্য, পানির বাষ্পীয় চাপ হলো তাপমাত্রার ফাংশন এবং ক্লসিয়াস-ক্ল্যাপেরন সম্পর্কের মাধ্যমে নির্ণয় করা হয়।

Approximation formulas

There are many published approximations for calculating saturated vapour pressure over water and over ice. Some of these are (in approximate order of increasing accuracy):

• $P=\exp \left(20.386-{\frac {5132}{T}}\right),\ \ \ \ (Eq.1)$

where P is the vapour pressure in mmHg and T is the temperature in kelvins.

• The Antoine equation

$\log _{10}P=A-{\frac {B}{C+T}},$

where the temperature T is in degrees Celsius (°C) and the vapour pressure P is in mmHg. The constants are given as

A	B	C	Tmin, °C	Tmax, °C
8.07131	1730.63	233.426	1	99
8.14019	1810.94	244.485	100	374

• The August-Roche-Magnus (or Magnus-Tetens or Magnus) equation, as described in Alduchov and Eskridge (1996). Equation 25 in provides the coefficients used here. See also discussion of Clausius-Clapeyron approximations used in meteorology and climatology.

$P=0.61094\exp \left({\frac {17.625T}{T+243.04}}\right),$

where temperature T is in °C and vapour pressure P is in kilopascals (kPa)

• The Tetens equation

$P=0.61078\exp \left({\frac {17.27T}{T+237.3}}\right),$

where temperature T is in °C and  P is in kPa

• The Buck equation.

$P=0.61121\exp \left(\left(18.678-{\frac {T}{234.5}}\right)\left({\frac {T}{257.14+T}}\right)\right),$

where T is in °C and P is in kPa.

• The Goff-Gratch (1946) equation.

Accuracy of different formulations

Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005):

T (°C)	P (Lide Table)	P (Eq 1)	P (Antoine)	P (Magnus)	P (Tetens)	P (Buck)	P (Goff-Gratch)
0	0.6113	0.6593 (+7.85%)	0.6056 (-0.93%)	0.6109 (-0.06%)	0.6108 (-0.09%)	0.6112 (-0.01%)	0.6089 (-0.40%)
20	2.3388	2.3755 (+1.57%)	2.3296 (-0.39%)	2.3334 (-0.23%)	2.3382 (+0.05%)	2.3383 (-0.02%)	2.3355 (-0.14%)
35	5.6267	5.5696 (-1.01%)	5.6090 (-0.31%)	5.6176 (-0.16%)	5.6225 (+0.04%)	5.6268 (+0.00%)	5.6221 (-0.08%)
50	12.344	12.065 (-2.26%)	12.306 (-0.31%)	12.361 (+0.13%)	12.336 (+0.08%)	12.349 (+0.04%)	12.338 (-0.05%)
75	38.563	37.738 (-2.14%)	38.463 (-0.26%)	39.000 (+1.13%)	38.646 (+0.40%)	38.595 (+0.08%)	38.555 (-0.02%)
100	101.32	101.31 (-0.01%)	101.34 (+0.02%)	104.077 (+2.72%)	102.21 (+1.10%)	101.31 (-0.01%)	101.32 (0.00%)

A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). The analysis here shows the simple unattributed formula and the Antoine equation are reasonably accurate at 100 °C, but quite poor for lower temperatures above freezing. Tetens is much more accurate over the range from 0 to 50 °C and very competitive at 75 °C, but Antoine's is superior at 75 °C and above. The unattributed formula must have zero error at around 26 °C, but is of very poor accuracy outside a very narrow range. Tetens' equations are generally much more accurate and arguably simpler for use at everyday temperatures (e.g., in meteorology). As expected, Buck's equation for T > 0 °C is significantly more accurate than Tetens, and its superiority increases markedly above 50 °C, though it is more complicated to use. The Buck equation is even superior to the more complex Goff-Gratch equation over the range needed for practical meteorology.

Numerical approximations

For serious computation, Lowe (1977) developed two pairs of equations for temperatures above and below freezing, with different levels of accuracy. They are all very accurate (compared to Clausius-Clapeyron and the Goff-Gratch) but use nested polynomials for very efficient computation. However, there are more recent reviews of possibly superior formulations, notably Wexler (1976, 1977), reported by Flatau et al. (1992).

Graphical pressure dependency on temperature

Vapour pressure diagrams of water; data taken from Dortmund Data Bank. Graphics shows triple point, critical point and boiling point of water.

See also

• Dew point
• Gas laws
• Molar mass
• Clausius–Clapeyron relation
• Goff-Gratch equation
• Antoine equation
• Tetens equation
• Arden Buck equation
• Lee–Kesler method

Further reading

• "Thermophysical properties of seawater"। Matlab, EES and Excel VBA library routines। MIT। ২০ ফেব্রুয়ারি ২০১৭। উদ্ধৃতি টেমপ্লেট ইংরেজি প্যারামিটার ব্যবহার করেছে (link)
• Garnett, Pat; Anderton, John D; Garnett, Pamela J (১৯৯৭)। Chemistry Laboratory Manual For Senior Secondary School। Longman। আইএসবিএন 978-0-582-86764-2। উদ্ধৃতি টেমপ্লেট ইংরেজি প্যারামিটার ব্যবহার করেছে (link)
• Murphy, D.M.; Koop, T. (২০০৫)। "Review of the vapour pressures of ice and supercooled water for atmospheric applications"। Quarterly Journal of the Royal Meteorological Society। 131 (608): 1539–65। ডিওআই:10.1256/qj.04.94। বিবকোড:2005QJRMS.131.1539M। উদ্ধৃতি টেমপ্লেট ইংরেজি প্যারামিটার ব্যবহার করেছে (link)
• Speight, James G. (২০০৪)। Lange's Handbook of Chemistry (16th সংস্করণ)। McGraw-Hil। আইএসবিএন 978-0071432207। উদ্ধৃতি টেমপ্লেট ইংরেজি প্যারামিটার ব্যবহার করেছে (link)

External links

• Vömel, Holger (২০১৬)। "Saturation vapor pressure formulations"। Boulder CO: Earth Observing Laboratory, National Center for Atmospheric Research। জুন ২৩, ২০১৭ তারিখে মূল থেকে আর্কাইভ করা। উদ্ধৃতি টেমপ্লেট ইংরেজি প্যারামিটার ব্যবহার করেছে (link)
• "Vapor Pressure Calculator"। National Weather Service, National Oceanic and Atmospheric Administration। উদ্ধৃতি টেমপ্লেট ইংরেজি প্যারামিটার ব্যবহার করেছে (link)