The symbol for the Universal Gas Constant is Ru= 8.314 J/mol.K (0.0831 bar dm3 mol-1 K-1). The Specific-Heat, C, is defined as the amount of heat required to raise the temperature by 1K per mole or per kg. The Specific Heat is reported at constant pressure (Cp) or constant volume conditions (Cv) respectively.
For monoatomic gases Cp=2.5Ru J/mol.K and Cv=1.5Ru J/mol.K.
The ratio of the two specific heats is called the adiabatic ratio. The symbol for the adiabatic ratio is g (gamma) and equal to 1.667 for all monoatomic gases like He, Ar, Ne.
For diatomic gases, Cp, Cv and g are 3.5Ru, 2.5Ru and 1.4 respectively. For ideal gases the specific-heats, dynamic-viscosity, and Prandelt number are independent of temperature.
For solids and liquids the two Specific Heats (Cp and Cv) are almost equal (because they fall into the class of incompressible condensed substances) and very approximately equal to 3Ru=24.942 J/mol.K
Although Ru is the same number 8.314 for all substances when expressed in the units J/mol.K. The gas constant R, however when expressed in the units of kJ/kg.K is equal to Ru/M where M is the molecular weight in moles/kg.
R, the gas constant expressed in 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
At high temperatures and one atmospheric pressure most gases can be considered close to ideal.
In the units kJ/kg.K the ideal gas specific heat @ 300K is given below.
If the gas is trully ideal then the Specific Heat is temperature independent.
Air Cp= 1.005 kJ/kg.K Cv=0.718 kJ/kg.K
Hydrogen Cp=14.307 kJ/kg.K Cv=10.183 kJ/kg.K
Argon Cp=0.5203 kJ/kg.K Cv=0.3122 kJ/kg.K
Nitrogen Cp=1.0396 kJ/kg.K Cv=0.743 kJ/kg.K
Oxygen Cp=0.918 kJ/kg.K Cv=0.658 kJ/kg.K
Steam Cp=1.8723 kJ/kg.K Cv=1.4108 kJ/kg.K
Enthalpy change DH = Mass. Cp. (change in temperature in Kelvin). Enthalpy per kg (specific enthalpy) is given the symbol h.
Internal Energy change DU = Mass. Cv. (change in temperature in Kelvin). Internal Energy per kg (specific internal energy) is given the symbol u.
The table below gives Enthalpy per kg (h) and Energy per kg (u), and Density of Air, at various temperatures achieved by the Airtorch™
Base ~ 0K.
Temperature of Air in Kelvin (K) |
Enthalpy |
Internal Energy |
Density Kg/m3 |
---|---|---|---|
200 |
200 |
143 |
0.7459 |
300 |
300 |
214 |
0.6158 |
400 |
401 |
286 |
0.5243 |
500 |
503 |
359 |
0.4565 |
600 |
607 |
435 |
0.4042 |
700 |
713 |
512 |
0.3627 |
800 |
822 |
592 |
0.3289 |
900 |
933 |
675 |
0.3008 |
1000 |
1046 |
759 |
0.2772 |
1500 |
1636 |
1205 |
0.1553 |
Please note the above are approximations and should be verified from standard texts prior to use.
Unintended typographical errors are possible.
Equations for the physical properties of moist air
Water vapor pressure
In a closed container partly filled with water there will be some water vapor 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 very slightly influenced by the pressure of air in the container.
The water vapor exerts a pressure on the walls of the container. The empirical equations given below give a good approximation to the saturation water vapor pressure at temperatures within the limits of the earth's climate.
Saturation vapor pressure, 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 )
The 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 metres, 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
The 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. The reason RH is so much used in conservation is that 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. Airless space can have a RH. Air is the transporter of water vapor in the atmosphere and in air conditioning systems, so the phrase "RH of the air" is commonly used, and only occasionally misleading. The independence of RH from atmospheric pressure is not important on the ground, but it does have some relevance to calculations concerning air transport of works of art and conservation by freeze drying.
The Dew Point
The water vapor content of air is often quoted as dew point. This is the temperature to which the air must be cooled before dew condenses from it. 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. 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 to calculate the temperature at which pa would be the saturation vapor pressure. This means running backwards 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 RH is then given by the ratio
RH = 100 * ps dewpoint/psambient
Concentration of water vapor in 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 quoted 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, which has 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
The heat content, usually called the enthalpy, of air rises with increasing water content. This hidden heat, called latent heat by air conditioning engineers, has to be supplied or removed in order to change the relative humidity of air, even at a constant temperature. This is relevant to conservators. The transfer of heat from an air stream to a wet surface, which releases water vapor to the air stream at the same time as it cools it, is the basis for psychrometry and many other microclimatic phenomena. Control of heat transfer can be used to control the drying and wetting of materials during conservation treatment.
The enthalpy of dry air is not known. Air at zero degrees Celsius is defined to have zero enthalpy. The enthalpy, in kJ/kg, at any temperature, t, between 0 and 60C is approximately:
h = 1.007t - 0.026 below zero: h = 1.005t
The enthalpy of liquid water is also sometimes defined to be zero at zero degrees Celsius. To turn liquid water to vapor at the same temperature requires a very considerable amount of 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 1 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 to 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 the air stream, which cools in contact with the wet surface, thus cooling the thermometer beneath it. An equilibrium wet surface temperature is reached which is very roughly half way between ambient temperature and dew point temperature.
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 which 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 mole fraction in 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. The constant B is therefore dependent 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, to ps, 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 very handy for this job. Alternatively, click to calculator. Psychrometric charts have graphical versions that can be emailed to you.