Equation of state for ideal gases at very low temperatures

Equation of State for Ideal Gases at Very Low Temperatures.—If, as we have done throughout, we denote the negative energy content of the system by U, the formulae of the previous section show that at the absolute zero 

Therefore, if we partially differentiate equation (I486) with respect to V, it follows that 

If our theory is strictly correct, equation (148) is obviously of a fundamental character, for it has to apply in place of the equation of state hitherto generally assumed for ideal gases, 

But even if our formulae describe the phenomenon of the degeneration of gases to a first approximation only, equation (148) may serve, at any rate, for preliminary exploration. 

For regions of temperature in which T is large compared with f v we have 

---