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**Author:** Bob Hardy, RH Systems, Albuquerque, NM, USA

Relative Humidity of a gas is defined as the percentage ratio of the amount of water vapor present in the gas to the maximum amount of water vapor possible at that same temperature. At temperatures above freezing, water can exist in only one of two thermodynamically stable states—water vapor or a liquid. At subzero temperatures, water can exist as either a gas or a solid, but contrary to intuition, water at subzero temperature can also exist in a third thermodynamic state, liquid. This subzero, liquid state is an achievable metastable state with an energy level between that of the gas and solid. In the temperature range 0 to –40°C, this super-cooling phenomenon is quite prevalent, and Relative Humidity may be computed in either of two distinct methods, termed Standard and WMO.

**Authors:**

Bob Hardy, RH Systems, Albuquerque, NM, USA

Daniel Mutter, MBW Calibration, Wettingen, Switzerland

Relative Humidity can be determined by the ratio of Saturation Vapor Pressure at the dew/frost point temperature to the Saturation Vapor Pressure at the air temperature. In accordance with NIST Guideline 12971, uncertainty is determined by analyzing the uncertainty of the individual components, then combining those uncertainties to obtain the total expanded uncertainty. As it applies here, we’ll analyze the uncertainties associated with the dew/frost point measurement and the air temperature measurement, then combine them to obtain the total expanded uncertainty in RH. In this analysis, we assume manufacturers stated specifications of ±0.1°C dew/frost point accuracy, and ±0.1 °C air temperature measurement accuracy. If these values differ from those given for a specific instrument, then this document can be used as a guide in recomputing the uncertainty due to the stated specifications.

Relative_Humidity_Uncertainty_Analysis_using_Dew FrostPoint_Measurements

**Author:** Bob Hardy, RH Systems, Albuquerque, NM, USA

With the change in the temperature scale of ITS-90, new temperature dependent equations were required which predict saturation vapor pressure over water and ice, enhancement factor over water and ice, frostpoint temperature, and dewpoint temperature. Internationally recognized formulas based on the previous temperature scale, viewed as self-consistent data sets for vapor pressures and enhancement factors, were chosen as initial defining equations. These formulas, coupled with those defining the temperature difference between the two scales, were used to compute new data sets consistent with the temperature scale of ITS-90. These new data sets were then fitted to equations of the original form, yielding new ITS-90 compatible coefficients to the familiar vapor pressure and enhancement factor equations. In addition, the resulting vapor pressure equations were used to produce a set of inverse approximating equations to yield frostpoint and dewpoint temperatures when the vapor pressure is known. The resulting coefficients, equations, and the conversion methods that produced them are presented.

**Author:** Bob Hardy, RH Systems, Albuquerque, NM, USA

Described here is the Relative Humidity Uncertainty Analysis, following NIST Guideline 12971, for a Model 2500 Humidity Generator that utilizes the NIST developed and proven two-pressure humidity generation principle.2,3 Generation of humidity in a system of this type does not require direct measurements of the water vapor content of the gas. Rather, the generated humidity is derived from the measurements of saturation and chamber pressures, and saturation and chamber temperatures.

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