It will be necessary to know the air density in order to convert between masses and volumes of air. For example, in a bioreactor model, the aeration rate may be input into the model in terms of the volumetric flow rate (m3-air s-1) while the heat capacity used may contain units of mass (i.e., J kg-air-1 °C-1). In this case, in order to calculate the amount of energy stored within a given volume of air for a given temperature rise, it is necessary to first multiply the air volume by its density to calculate the mass of air, before multiplying the mass of air by the heat capacity and the temperature rise.
Air density is a function of temperature and pressure. At low pressures ideal gas behavior can be assumed:
where P is the pressure (Pa), n is the number of moles (mol), V is the volume (m3), Tk is the temperature (K), and R is the universal gas constant (8.314 J mol-1 K-1). The number of moles can be replaced with the mass of the gas (mg, kg) divided by its molecular weight (Mg, kg mol-1). This leads to a term in which the mass of gas is divided by the volume, and this combination can be replaced by the gas density
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