R, the gas constant expressed in units of kJ/kg.K for common gases is given below.

Air                   0.2870  kJ/kg.K

Hydrogen         4.1240  kJ/kg.K

Argon              0.2081  kJ/kg.K

Nitrogen          0.2986  kJ/kg.K

Oxygen            0.2598 kJ/kg.K

Steam              0.4615   kJ/kg.K

Most process gases are ideal at high temperatures and one atmospheric Pressure.     In the units, kJ/kg.K, the gas-specific heat capacity @ 300K is given below. The specific heat capacity is temperature independent if the gas is truly ideal. Note hydrogen behaves more like a monoatomic gas at low temperatures.

Air                   Cp= 1.005  kJ/kg.K      Cv=0.718 kJ/kg.K     Density @ STP 1.29kg/m³

Hydrogen       Cp=14.307   kJ/kg.K    Cv=10.183  kJ/kg.K  Density @ STP 0.09kg/m³

Argon              Cp=0.5203  kJ/kg.K    Cv=0.3122 kJ/kg.K    Density @ STP 1.78kg/m³

CO₂                Cp=0.8443  kJ/kg.K    Cv=0.6553 kJ/kg.K    Density @ STP 1.96kg/m³

Nitrogen        Cp=1.0396  kJ/kg.K    Cv=0.743 kJ/kg.K     Density @ STP 1.25kg/m³

Oxygen          Cp=0.918  kJ/kg.K     Cv=0.658 kJ/kg.K     Density @ STP 1.43kg/m³

Steam            Cp=1.8723  kJ/kg.K    Cv=1.4108 kJ/kg.K    – see steam tables.

At IUPAC standard temperature and pressure (0 °C and 101.325 kPa), dry air has a density of 1.2754 kg/m³. At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m^3, i.e.at, 70 °F, and 14.696 psia; dry air has a density of 0.074887lb_m/ft³.

Both energy and Enthalpy are measured from a base temperature. Therefore only a change in properties of this kind is measurable. The difference in Enthalpy (H) is DH = Mass. Cp. (Change in temperature in Kelvin). The Internal Energy per kg (or specific internal energy) is given the symbol u. The Enthalpy per kg (or specific Enthalpy) is shown in the symbol h. The change in internal energy (U) is DU = Mass. Cv. (Change in temperature in Kelvin).

The table below gives Enthalpy per kg (h), Energy per kg (u), and Density of Air at various temperatures achieved by the Airtorch™.  Base ~ 0K.

Please note that the above approximations should be verified from standard texts before use. Unintended typographical errors are possible.

Click for Steam Calculator

What is humidity?

Other Important Fluid Properties

Other important properties of a gas are dynamic Viscosity (defined below), kinematic Viscosity, and Prandtl number (defined below).   For an ideal gas, these are independent of temperature. The Prandtl Number is often used in heat transfer and free and forced convection calculations. It depends on the fluid properties. The Pr ranges from 0.7 to 1.0 for standard process gasses, and Pr ranges from 0.001 to 0.03 for simple liquid metals.   For polar liquids like water and oils, the Pr ranges from 1 – 2200  (the lower end for water and the higher for high molecular weight viscous oils).   The Prandtl Number is a dimensionless number that is the ratio of momentum diffusivity (kinematic Viscosity) and thermal diffusivity. This number may, as you imagine, give a sense of comparison of viscous and thermal forces required for an objective and indicate what carries shear force to what carrier the thermal (heat) transport in a molecular sense!

Pr = v / α  or  Pr = μ c_p / k  where;

c_p= specific heat capacity (J/kg K) at constant pressure,

k = thermal conductivity (W/m K)

μ = absolute or dynamic Viscosity (kg/ms). The dynamic ( or absolute) Viscosity is the tangential force per unit area required to move one horizontal plane of a fluid concerning the other at unit velocity when maintained a unit distance apart.

α = thermal diffusivity (m²/s)

v = kinematic viscosity or momentum diffusivity (m²/s). Kinematic Viscosity is the ratio of absolute or dynamic Viscosity to density. Kinematic Viscosity can be obtained by dividing the absolute Viscosity of a fluid by density.

Pr = Prandtl’s number. (Note dimensionless).

Viscosity of Steam The Viscosity of gases with temperature Pressure Enthalpy Diagram for Water-Steam

Flow Rate of 0.3g/min (~0.3ml/min) Water Conversion at Various Temperatures Constant Pressure at 1 bar with Water Inlet g/min= 0.3 Temp (°C) Specific Volume v (m3/kg) Volume flow rate (mL/min) (steam) 100 1.6959 509 150 1.9367 581 200 2.1724 652 250 2.4062 722 300 2.6389 792 400 3.1027 931 500 3.5655 1070 600 4.0279 1208 700 4.4900 1347 800 4.9519 1486 900 5.4137 1624 1000 5.8755 1763 1100 6.3372 1901 1200 6.7988 2040 1300 7.2605 2178

Water vapor pressure

The water vapor exerts Pressure on the walls of the container. In a closed container partly filled with water, water vapor will be in the space above the water. The concentration of water vapor depends only on the temperature. It is not dependent on the amount of water and is only slightly influenced by the air pressure in the container. The empirical equations below give a good approximation to the saturation water vapor pressure at temperatures within the limits of the earth’s climate.

Saturation vapor pressure (svp), ps, in pascals:
ps = 610.78 *exp( t / ( t + 238.3 ) *17.2694 )
where t is the temperature in degrees Celsius

The svp below freezing can be corrected after using the equation above, thus:
ps ice = -4.86 + 0.855*ps + 0.000244*ps2

The next formula gives a direct result for the saturation vapor pressure over ice:
ps ice = exp( -6140.4 / ( 273 + t ) + 28.916 )

Pascal is the SI unit of Pressure = newtons / m2. Atmospheric Pressure is about 100,000 Pa (standard atmospheric Pressure is defined as 101,300 Pa).

Water vapor concentration

The relationship between vapor pressure and concentration is defined for any gas by the equation:
p = nRT/V
p is the Pressure in Pa, V is the volume in cubic meters, T is the temperature in degrees Kelvin (degrees Celsius + 273.16), n is the quantity of gas expressed in molar Mass ( 0.018 kg in the case of water ), R is the gas constant: 8.31 Joules/mol.K

To convert the water vapor pressure to concentration in kg/m3: ( Kg / 0.018 ) / V = p / RT

kg/m3 = 0.002166 *p / ( t + 273.16 )   where p is the actual vapor pressure

Relative Humidity

Relative Humidity (RH) is the ratio of the actual water vapor pressure to the saturation water vapor pressure at the prevailing temperature.

RH = p/ps

RH is usually expressed as a percentage rather than as a fraction.

The RH is a ratio. It does not define the water content of the air unless the temperature is given. RH is so much used in conservation because most organic materials have an equilibrium water content that is mainly determined by the RH and is only slightly influenced by temperature.

Notice that air is not involved in the definition of RH. Air is the transporter of water vapor in the atmosphere and air conditioning systems, so the phrase “RH of the air” is commonly used and occasionally misleading. Airless space can have an RH. The independence of RH from atmospheric Pressure is not important on the ground. Still, it does have some relevance to calculations concerning the air transport of works of art and conservation by freeze-drying.

The Dew Point

The water vapor content of air is often quoted as a dew point. This is the temperature to which the air must be cooled before dew condenses. At this temperature, the actual water vapor content of the air is equal to the saturation water vapor pressure. The dew point is usually calculated from the RH. The first one calculates ps, the saturation vapor pressure at the ambient temperature. The actual water vapor pressure, pa, is:

pa= ps * RH% / 100

The next step is calculating the temperature at which pa would be the saturation vapor pressure. This means running backward the equation given above for deriving saturation vapor pressure from temperature:

Let w = ln ( pa/ 610.78 )
Dew point = w *238.3 / ( 17.294 – w )

This calculation is often used to judge the probability of condensation on windows and within walls and roofs of humidified buildings.

The dew point can also be measured directly by cooling a mirror until it fogs. The following ratio then gives the RH.

RH = 100 * ps dewpoint/ps ambient

The concentration of water vapor in the air

It is sometimes convenient to quote water vapor concentration as kg/kg of dry air. This is used in air conditioning calculations and is mentioned on psychrometric charts. The following calculations for water vapor concentration in air apply at ground level.

Dry air has a molar mass of 0.029 kg. It is denser than water vapor, with a molar mass of 0.018 kg. Therefore, humid air is lighter than dry air. If the total atmospheric Pressure is P and the water vapor pressure is p, the partial pressure of the dry air component is P – p. The weight ratio of the two components, water vapor, and dry air, is:

kg water vapor / kg dry air = 0.018 *p / ( 0.029 *(P – p ) )
= 0.62 *p / (P – p )

At room temperature, P – p is nearly equal to P, which at ground level is close to 100,000 Pa, so approximately:

kg water vapor / kg dry air = 0.62 *10-5 *p

Thermal properties of damp air

Heat transfer control can be used to control the drying and wetting of materials during conservation treatment. The transfer of heat from an air stream to a wet surface, which releases water vapor to the airstream at the same time as it cools it, is the basis for psychrometry and many other microclimatic phenomena. The heat content, usually called the Enthalpy of the air, rises with increasing water content. This hidden heat, called latent heat by air conditioning engineers, has to be supplied or removed to change the relative humidity of the air, even at a constant temperature. This is relevant to conservators.

The Enthalpy of dry air is not known. Air at zero degrees Celsius is defined as having zero enthalpies. The Enthalpy, in kJ/kg, at any temperature, t, between 0 and 60C is approximate:

h = 1.007t – 0.026   below zero: h = 1.005t

The Enthalpy of liquid water is sometimes defined as zero at zero degrees Celsius. Turning liquid water to vapor at the same temperature requires considerable heat energy: 2501 kJ/kg at 0C.

At temperature t, the heat content of water vapor is:

hw = 2501 + 1.84t 

Notice that water vapor, once generated, also requires more heat than dry air to raise its temperature further: 1.84 kJ/kg.C against about one kJ/kg.C for dry air.

The Enthalpy of moist air, in kJ/kg, is, therefore:

h = (1.007*t – 0.026) + g*(2501 + 1.84*t)
g is the water content (specific humidity) in kg/kg of dry air

The Psychrometer

The final formula in this collection is the psychrometric equation. The psychrometer is the nearest to an absolute method of measuring RH that the conservator ever needs. It is more reliable than electronic devices because it depends on the calibration of thermometers or temperature sensors, which are much more reliable than electrical RH sensors. The only limitation of the psychrometer is that it is difficult to use in confined spaces (not because it needs to be whirled around but because it releases water vapor).

The psychrometer, or wet and dry bulb thermometer, responds to the RH of the air in this way:

Unsaturated air evaporates water from the wet wick. The heat required to evaporate the water into the air stream is taken from it, which cools in contact with the wet surface, thus cooling the thermometer beneath it. An equilibrium wet surface temperature is reached, roughly halfway between ambient and dew point temperatures.

The air’s potential to absorb water is proportional to the difference between the mole fraction, ma, of water vapor in the ambient air and the mole fraction, mw, of water vapor in the saturated air at the wet surface. It is this capacity to carry away water vapor that drives the temperature down to, tw, the wet thermometer temperature, from the ambient temperature ta :
(mw – ma) = B(ta- tw)
B is a constant whose numerical value can be derived theoretically by some rather complicated physics (see the reference below).

The water vapor concentration is expressed here as a mole fraction in the air rather than as vapor pressure. Air is involved in the psychrometric equation because it brings the heat required to evaporate water from the wet surface. Therefore, the constant B depends on total air pressure, P. However, the mole fraction, m, is simply the ratio of vapor pressure p to total pressure P:  p/P. The air pressure is the same for both ambient air and air in contact with the wet surface, so the constant B can be modified to a new value, A, which incorporates the Pressure, allowing the molar fractions to be replaced by the corresponding vapor pressures:

pw – pa= A* ( ta- tw)

The relative humidity (as already defined) is the ratio of pa, the actual water vapor pressure of the air, tops, and the saturation water vapor pressure at ambient temperature.

RH% = 100 *pa/ ps = 100 *( pw – ( ta- tw) * 63) / ps
When the wet thermometer is frozen, the constant changes to 56

The psychrometric constant is taken from: R.G.Wylie & T. Lalas, “Accurate psychrometer coefficients for wet and ice-covered cylinders in laminar transverse air streams,” in Moisture and Humidity 1985, published by the Instrument Society of America, pp 37 – 56. These values are slightly lower than those in general use. There are tables and slide rules for calculating RH from the psychrometer, but a programmable calculator is convenient. Alternatively, click on the calculator.

Properties of Various Gases (at 300 K) that are close to ideal (i.e., close to the specific heat ratio k-1.667)
Gas	Molecular Formula	Molar Mass	Gas constant	Specific Heat at Constant Pressure, Cp.	Specific Heat at Constant Volume Cv	Specific Heat Ratio
Units		M[kg/kmol]	R[kJ/kg.K]	Cp[kJ/kg.K]	Cv[kJ/kg.K]	k = Cp/Cv
Air	Typical	28.97	0.287	1.005	0.718	1.4
Argon	Ar	39.948	0.2081	0.5203	0.3122	1.667
Butane	C4H10	58.124	0.1433	1.7164	1.5734	1.091
Carbon Dioxide	CO2	44.01	0.1889	0.846	0.657	1.289
Carbon Monoxide	CO	28.011	0.2968	1.04	0.744	1.4
Ethane	C2H6	30.07	0.2765	1.7662	1.4897	1.186
Ethylene	C2H4	28.054	0.2964	1.5482	1.2518	1.237
Helium	He	4.003	2.0769	5.1926	3.1156	1.667
Hydrogen	H2	2.016	4.124	14.307	10.183	1.405
Methane	CH4	16.043	0.5182	2.2537	1.7354	1.299
Neon	Ne	20.183	0.4119	1.0299	0.6179	1.667
Nitrogen	N2	28.013	0.2968	1.039	0.743	1.4
Octane	C8H18	114.231	0.0729	1.7113	1.6385	1.044
Oxygen	O2	31.999	0.2598	0.918	0.658	1.395
Propane	C3H8	44.097	0.1885	1.6794	1.4909	1.126
Steam	H2O	18.015	0.4615	1.8723	1.4108	1.327

Heat Values of Various Fuels

A fuel’s “heat value,” or energy or calorific value, is the heat released during combustion. The heat value measures a fuel’s energy density and is expressed in energy (joules) per specified amount (kilograms, kg).

Fuel	Heat value
Hydrogen (H2)	120-142 MJ/kg
Methane (CH4)	50-55 MJ/kg
Methanol (CH3OH)	22.7 MJ/kg
Propane (C3H8)	46 MJ/kg
Dimethyl ether – DME (CH3OCH3)	29 MJ/kg
Petrol/gasoline	44-46 MJ/kg
Diesel fuel	42-46 MJ/kg
Crude oil	42-47 MJ/kg
Liquefied petroleum gas (LPG)	46-51 MJ/kg
Natural gas	42-55 MJ/kg
Hard black coal (IEA definition)	>~23.9 MJ/kg
Hard black coal (Australia & Canada)	c. 25 MJ/kg
Sub-bituminous coal (IEA definition)	17.4-23.9 MJ/kg
Sub-bituminous coal (Australia & Canada)	c. 18 MJ/kg
Lignite/brown coal (IEA definition)	<17.4 MJ/kg
Lignite/brown coal (Australia, electricity)	c. 10 MJ/kg
Firewood (dry)	16 MJ/kg
Natural uranium in LWR (normal reactor)	500 GJ/kg
Natural uranium, in LWR with U & Pu, recycle	650 GJ/kg
Natural uranium, in FNR	28,000 GJ/kg
Uranium enriched to 3.5% in LWR	3900 GJ/kg

Uranium figures are based on 45,000 MWd/t burn-up of 3.5% enriched U in LWR
MJ = 10⁶ Joule, GJ = 10⁹ J
One tonne of oil equivalent is equal to 41.868 GJ