512 Prof. W. MeF. Orr on Clausius?’ 
the definition of “reversibility.” The definition which is 
used by Planck appears in fact to be this, that a process 
is “‘ reversible ” (“reversibel”’) if it is possible to pass the 
system back from the final state to the initial without inter- 
changing heat with external bodies. 
Planck conceives of the Entropy of a Gas when rushing 
into a vacuum. 
. Planck proceeds :—“It must not be supposed that the 
oss of a gas has a meaning only for states of equilibrium. 
We may assume each sufficiently small particle, even of a gas 
in turmoil, to be homogeneous and at a definite temperature, 
and must, therefore, according to (52)”’—(the equation in § 2 
above by which the entr opy ofa gas is defined) —“assign to ita 
definite value of the entropy. .... A summation extendin 
over all the particles of the mass—within which the values of 
v and @ may vary from particle to particle—gives the entropy 
of the whole mass of the gas in the particular state. The 
proposition still holds, that the entropy of the whole gas 
must continually increase during any process which does not 
give rise to changes in other bodies, e.g. When a gas flows 
from a vessel into a vacuum ” 
Bertrand’s Objection. The terms “ Temperature,” “ Pres- 
sure, “ Entrop i meaningless im many irreversible 
Batis -ips 
This view is in direct opposition to that held by Ber- 
eae) who objected + that 1 in many irreversible processes such 
terms as “ temperature,” ‘“ pressure,” “ entropy,” have no 
definite meaning. ‘‘ What,” he asked, “is the pressure of a 
gas when it is rushing in a state of tumult into a vacuum ? 
Tt is neither the same at each point nor the same in all 
directions... .”’ He consequently regarded such discussions 
as for the most part meaningless and futile. 
Ordinary dejimtions of “ Temperature” refer only to states 
of equilibrium. 
8. The defining of “temperature,” and of “equality of 
temperature,” presents indeed a great fundamental difficulty 
in the Theory of Heat ; the proper elucidation of this matter 
is one of the most formidable tasks with which the writer of 
a treatise on Thermodynamics is confronted, and one to 
which a chapter, rather than as is usual merely a few lines, 
* Oge’s translation, Art. 127. 
T Thermod lynamique, Chap. XII, 
