2.3.6 Equation of State: One more relation is needed to close the system of equations. For this, we can use the thermodynamic equation of state relating p to p=Cp (2.35) where C is a constant and y is the ratio of specific heats Cp/Cy. The term VP is therefore given by n: Vp р = Y For isothermal compression, we have Vn n (2.36) Vp=V(nKT)=KTVn (2.37) so that, clearly, y = 1. For adiabatic compression, KT will also change, giving y a value larger than one. If N is the number of degrees of freedom, y is given by y = (2+N)/N (2.38) The validity of the equation of state requires that heat flow be trivial; that is, that thermal conductivity be low. Again, this is more likely to be true in directions perpendicular to B than parallel to it. Fortunately, most basic phenomena can be described suitably by the simple assumption of Eq. (2.35).