68 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



number. A word further in this connection may, however, be 

 helpful. In reversible processes we have the well-known relation 

 dQ=TdS. To simplify matters, let us suppose heat dQ supplied 

 while volume is kept constant, then dQ = c v dT= TdS or 



(30) 



Here Entropy S has the same dimensions as c v ; now in the 

 relation dQ = c v dT if we regard c v as an abstract number then, 

 in order that the equation shall be homogeneous the factor (dT) 

 must represent heat energy like dQ, and this is sometimes done; 



x7T T 



in such case (if T retains its ordinary meaning) the quotient -= 



in Eq. (30) is no longer a mere ratio or abstract number, but a 

 quotient of the dimensions of energy divided by temperature. 



On the other hand, if c v=jf be regarded as of the dimensions 

 of the quotient of energy divided by temperature, then we may 



7/T-l 



consider -= in (30) as an abstract number or ratio and dS of the 



same dimensions as C v . When an absolute system of units is 

 employed, which possesses as one of its features the expression of 

 temperature in units of energy, then k, S and c v will all be mere 

 ratios or abstract numbers. 1 



i See C. V. BURTON'S article in Philosophical Transactions, Vol. 23-24, 1887. 



