Example using the perfect gas relation:
Calculate the density of air at a pressure of 1 atmosphere and a temperature of 25 deg. C.
Pressure: 1 atmosphere = 101300 Newtons per square meter
Temperature: 25 deg. Celsius=273.15 + 25 =298.15Kelvin
The thermal equation of state relates the pressure P, absolute temperature T, and density of a gas:
P = (rho) RT, where
R=Ru / MW,
Ru being the Universal Gas Constant (8314.3 in SI units ),and MW the molecular weight of the gas.Air is composed of 79% Nitrogen, and 21% Oxygen. The molecular weight of Nitrogen (N2) is 28, and that of Oxygen (O2) is 32. Thus the mean molecular weight is
MW= 0.79 * 28 + 0.21*32= 28.84
Thus, the gas constant for air, R = 8314.3 / 28.84 = 288.29 mK-1s-2
rho = 101300 / (298.15 * 288.29)=1.1785 kg/m3.
( Note: A more exact representation of air at sea level is: 79% nitrogen, 20% oxygen, and 1% argon (MW=44), giving a molecular weight of 28.96. This makes R = 287.04 mK-1s-2)
It is useful to remember that in SI units, atmospheric pressure at sea-level is approximately 100,000, temperature is 300, and density is 1.2.
Caloric Equations of State
For a calorically perfect gas, internal energy per unit mass depends only on temperature.
e = e(T)
Enthalpyper unit mass
h = e + p/r,
so that h = h(T)as well.
Specific heat at constant volume
Specific heat at constant pressure
,and h = e + p/r,
At constant pressure, dp = 0, so that dq = dh