The general gas law
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(2.8) |
It is possible to combine Boyle’s and Charles’ laws as one equation; pV = mRT
Where p = the pressure of the gas in Pa,
V = the volume of the gas in m3, m = the mass of the gas in kg,
R = a constant of proportionality,
T = the absolute temperature of the gas in K.
Avogadro’s hypothesis argues that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. Accepting this and taking as the unit of mass the kilomole (kmol), a mass in kilograms numerically equal to the molecular mass of the gas, a value for the universal gas constant can be established:
PVm = R0T (2.9)
Where Vm is the volume in m3 of 1 kmol and is the same for all gases having the same
Values of p and T. Using the values p = 101 325 Pa and T = 273.15 K, it has been
Experimentally determined that Vm equals 22.41383 m3 kmol-1. Hence the universal gas constant is determined
. —~2^f —- — S314.41 J tool — K-*
Dividing both sides of equation (2.9) by the molecular mass, M, of any gas in question allows the determination of the particular gas constant, R, for the gas. This may then be used for a mass of 1 kg in equation (2.8) and we can write
R0T nrr( u n 8314.41 ^
Pv = ~Jf = [whence/? = —y—J
Where v is the volume of 1 kg.
If a larger mass, m kg, is used, the expression becomes equation (2.8)
PV = mRT (2.8)
Where V is the volume of m kg and R has units of J kg“1 K_1.
For dry air, Ra = = 287 J kg“1 K"1
For steam, Rs = = 461 J kg_1K_1
A suitable transposition of the general gas law yields expressions for density, pressure and volume.
EXAMPLE 2.2
Calculate the density of a sample of dry air which is at a pressure of 101325 Pa and at a temperature of 20°C.
Answer
^ . mass of the gas
Ensity — vojume 0f tjje gas
M
_ _P_
101 325 “ 287 x (273 + 20)
= 1.2049 kg nT3
We may compare this answer with that obtained by referring to the CIBSE tables of psychrometric data, which quote the volume of air at 20°C dry bulb and 0 per cent saturation as 0.8301 m3kg_1 of dry air.
The reciprocal of density is specific volume, hence the density of the air quoted by the tables is given by the reciprocal of 0.8301 m3 kg-1 and is 1.2047 kg rrf3.
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