# Thermodynamics identifying an ideal gas

I'm pretty confused. So I've been told that the equation of state for n moles of some type of gas is P(V-b) = nRT. That's not quite like an ideal gas. But then the relations $C_p - C_v = R$, and $\gamma = \frac{C_p}{C_v} = 5/3$ hold of the gas, and at the very least the last equation is definitely for ideal gases.

So if a gas has these properties, and only one mol is considered, is it fair to assume it is an ideal gas? Using the above relations gave me $C_v = \frac{3}{2} R$, which again is for ideal gases.

The gas you describe is is a gas with no interactions, but with molecules of finite volume. Having molecules of finite volume reduces the space avaliable for molecules to move around, hence the $V-b$ factor instead of just $V$ for an ideal gas.
The heat capacities of this gas behave the same as for an ideal gas. The PVT behavior is not. So, what is the problem? Note that, for this gas, even though $C_v$, $C_p$, and U are functions only of temperature, like an ideal gas, H is a function not only of temperature but also of pressure p: $dH=C_pdT+bdP$.