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ATPS, ATP, BTPS, STPD

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.

BTPS
in respiratory physiology lung volumes and flows are standardized to ambient barometric pressure at sea level, body temperature, saturated with water vapor: body temperature and pressure, saturated.
ATPS
measured at ambient temperature, pressure, saturated with water vapor (e.g. expired gas, which has cooled down): ambient temperature and pressure, saturated.
ATP
like ATPS, but not saturated with water vapor (e.g. room air).
STPD
oxygen consumption and carbon dioxide delivery are standardized to standard temperature (0 ºC), barometric pressure at sea level (101.3 kPa) and dry gas: standard temperature and pressure, dry.


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.

Conversion from ATPS to BTPS conditions
Temp.
ºC
Corr.
factor
Temp.
ºC
Corr.
factor
Temp.
ºC
Corr.
factor
Temp.
ºC
Corr.
factor
16 1.123 21 1.097 26 1.069 31 1.039
17 1.118 22 1.091 27 1.063 32 1.033
18 1.113 23 1.086 28 1.057 33 1.026
19 1.107 24 1.080 29 1.051 34 1.020
20 1.102 25 1.074 30 1.045 35 1.013

It is uncommon to express the oxygen uptake and 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

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