For ideal gases the properties of temperature, pressure, volume, and others are related to each other according to two simple laws. The first is known as the ideal gas law, which can be written down in several different forms all of which are all related to each other. For example :
(1) p V = m Rs T or p V = n Ru T or p v = Rs T
p [N/m²] = absolute pressure ( p=0 for vaccuum )
V [m³] = volume occupied by ideal gas
v [m³/kg] = specific volume = volume occupied by 1 kg of gas = inverse of density ρ
m [kg] = mass of ideal gas
Rs [kJ/(kg K)] = specific gas constants, its value depends on the gas at hand.
T [K] = absolute temperature
n [kmol] = number of moles of gas , 1 mol = 6.023×1023 molecules (Avogadro's number)
Ru = universal gas constant = 8.31434 kJ/(kmol K)
The above two forms of the ideal gas law are equivalent because :
m/n = M [kg/kmol] = molecular mass of gas , often but falsly called the molecular weight
Rs = Ru/M
Another property of ideal gases, much less known, is that the internal
energy, u, of an ideal gas does not depend on pressure which was
originally verified experimentally by the English physicist
James Prescott Joule (1818-1889). In that experiment two spherical
containers, A and B, are immersed in a water bath. They connected by a small
tube closed off initially by a stop. Container A is filled with a gas at
a high pressure while container B is empty. Everything is at the same
temperature. Now the stop is opened and some gas streams from container A into
B until the pressure is equal in both containers. Because of the larger
volume the gas now occupies the pressure is lower. Despite that, measurements
show that the temperature of the gas has not changed. Because during this
process no heat has been supplied nor any work has been done. As a
consequence the internal energy, u, of the gas is unchanged.
(2) cp - cv = Rs
For some ideal gases, specifically all the noble gases He, Ne, Ar, Kr, and Xe, the specific heat capacities are completely temperature independent and their ratio is :
(3) κ = cp/cv = 1.667For many diatomic gases like N2, O2, air, and CO the specific heats and their ratio are nearly temperature independent over a wide range of tempratures. A generally accepted value is :
κ = 1.4 for diatomic gases
A last question of course arises : Under which circumstances does a real life gas behave like an ideal gas ? The answer is somewhat ambiguous because the ideal gas is an abstraction which is approached by every gas as the pressure is lowered and the temperature is raised. If a few percent accuracy is sufficient then a good guideline would that if the absolute temperature of interest is more than twice that of the critical temperature ( listed as Tcrit in above table ) you are in good shape. If your temperatures are lower than that, your pressure of interest better be below 0.2 times the critical pressure ( listed as pcrit in above table). If you need a clearer answer, then you either have to get the property data of your gas ( the NIST website at http://webbook.nist.gov/chemistry/fluid/ is a very good source ) or google for the term Compressibility Factor= p V/(R T) which is of course 1 for ideal gases but ≠1 for real gases.
A last comment concerning criticial temperature and pressure, just in case you don't know these :
If you have a gas at a temperature above its critical temperature then
the gas will occupy less and less volume as the pressure is increased
provided you keep the temperature constant by removing heat as you compress.
It will never
condense as the
pressure increases and we have no clear definition for when you would
stop calling it a gas and start calling it a liquid.