The volume of a number (n) of gas molecules depends on the thermodynamic temperature (T) and the ambient pressure (P). The following relationship holds for dry gas:
V = n·R·T/P
where R = gas constant, and T is expressed in Kelvin (K = 273.2 + ºC). Air and expired gas are made up of gas molecules and water vapor. In a gas mixture saturated with water vapor and in contact with water (such as occurs in the lung) the number of water molecules in the gas phase varies with temperature and pressure. As the number of molecules is not constant, the above gas law should be applied to dry gas. This also holds outside the lung when gas saturated with water vapor is compressed or cools down. As gas volumes vary with temperature and pressure, the conditions during which they are measured must be recorded. To that end volume displacement spirometers need to be equipped with a thermometer; if meters employ other measuring principles the manufacturer should state clearly how corrections need be performed as the composition of the gas and gas viscosity may then come into play.
The water vapor pressure of a saturated gas is temperature dependent. The table below can be used to convert from ATPS to BTPS conditions; e.g. 1 L ATPS at 20 ºC equals 1.102 L BTPS.
It is uncommon to express the oxygen uptake and carbon dioxide delivery as mol per unit of time. The volume is not converted but expressed in STPD conditions: standard temperature and dry gas at standard barometric pressure: 0º C, 101.3 kPa, dry.
Convert Fahrenheit to Celsius temperature, v.v.
One can approximate the water vapour pressure (PH2O, in kPa) of saturated air at temperatures (t, in °C) between 10-45 °C with sufficient accuracy as follows:
Pt,H2O = 0.42013 + 0.07985·t - 0.000751·t² + 0.000078·t³
In obsolete units (mmHg):
Pt,H2O = 3.10594 + 0.59886·t -0.00561·t² + 0.00058·t³