MOTIVE POWER OF HEAT. 185 



corresponding to the temperature t y is known. 

 For, by 30, equation (6), we have 



where dq is the quantity of heat absorbed, when 

 the volume is allowed to increase from v to v + dv\ 

 or the quantity evolved by the reverse operation. 

 Hence we deduce 



JH 



(8) 



Now, is constant, since the temperature 



remains unchanged ; and therefore we may at 

 once integrate the second number. By taking it 

 between the limits V and V, we thus find 



. ,. . 



where Q denotes the required amount of heat 

 evolved by the compression from Vto P'. This 

 expression may be modified by employing the equa- 

 tions P V = P' V = 2).v Q (1 + Et) ; and we thus 

 obtain 



EPV V EP'V . V 



Q = g 7 = log -- 



y 



* The Napierian logarithm of -~ is here understood. 



