Under what conditions do the gas laws deviate and give best results?

Answer 1

The ideal gas equation is derived for non-interacting, classical particles. Particles don't interact when they are far away, so it applies best to very low density gases. But it's a very good approximation in a wide range of circumstances, eg air at room temperature, the hydrogen in stars and nebulae etc.

In general, we express classical deviations from ideal gas behaviour using the virial coefficients Bn:

p/(k_B*T) = n + B1(T)*n^2 + B2(T)*n^3...

where n is the particle density of the gas, p is the pressure, k_B is Boltzmann's constant and T is the temperature. Ideal gas behaviour is when all the terms on the right hand side apart from n are very small. If the density is still fairly low though, we only need to worry about B1. It turns out that at a certain temperature, called the Boyle temperature, B1=0 and so the gas behaves ideally at higher densities. If T is higher than this B1 is positive and if T is lower than B1 is negative.

We might also need to worry about quantum mechanical effects. These become significant if the de Broglie wavlength of the particle approaches the inter-particle spacing. Basically this means light particles at very low temperature, for instance superfluid helium.