Boltzmann's Equipartition Hypothesis. 



749 



consideration of that of a particular gas. Taking the case 

 of nitrogen, its molecule has five degrees of freedom, — three 

 due to its translational motion and two due to rotation of its 

 axis. In an adiabatic expansion energy is taken from both 

 the translational and the rotational motions to do work. But 

 work is only done by the pressure resulting from the trans- 

 lational motion of the molecules; before rotational energy 

 can do work it must first be transformed into translational 

 molecular energy. Such a process takes time. Theoretically 

 we may imagine an ideal case in which the expansion is so 

 rapid that during expansion the rotational energy is virtually 

 locked up. In such a case the gas would behave as a gas 

 having only the three degrees of freedom due to its trans- 

 lational motion. The equation to its expansion curve, which 

 would still be an adiabatic but irreversible, would then 

 become pv l ' 6 = const., the same as that for mercury gas. 

 Such an ideal case cannot be reached ; but there are cases of 

 very rapid expansion in which we may expect the actual 

 expansion line to lie between the two curves pv 1 ' 4 — const, 

 and pv 1,6 = const., such as ab of fig. 1. If after expansion 



Fkr. 1. 





l/OL UM£ 



to b the volume be kept constant, the rotational energy 

 which was not available will show itself in a rise of pressure 

 to some point c above the upper curve. 



Two experiments show that in nozzles the actual expansion 

 curve ab falls below the reversible adiabatic (pv l '* = const.). 

 (1) Measurement of pressure or temperature at a chosen 

 volume gives values lower than those corresponding to the 

 curve pr 1 ' 4 = const. (2) Measurement of discharges gives 

 values greater than is possible with reversible expansion. 



