360 M. CLAPEYKON ON THE MOTIVE POWER OF HEAT. 



This equation shows also that when a gas varies in volume ioithout 

 change of temperature, the quantities of heat absorbed or disengaged by 

 this gas are in arithmetical progression, if the increments or reductions 

 of volume are in geometrical progression. M. Carnot enunciates this 

 result in the work already cited. 



The equation 



Q - Q' = R C log (^) 



expresses a more general law; it includes all the circumstances by 

 which the phaenomenon can be affected, such as the pressure, the 

 volume, and the temperature. 

 In fact, since 



we have 



261+ to 267 + <' 



Q _ Q' = ^^/_±_^ C log 



This equation exhibits the influence of the pressure; it shows that 

 equal volumes of all the gases, taken at the same temperature, being com- 

 pressed or expanded by the same fraction of their volume, disengage or 

 absorb quantities of heat proportionate to the pressure. 



This result explains why the sudden entrance of the air into the va- 

 cuum of the air-pump does not disengage a sensible quantity of heat. 

 The vacuum of the air-pump is nothing but a volume of gas v, of 

 which the pressure p is very small ; if atmospheric air be admitted, its 

 pressure p will suddenly become equal to the pressure of p' of the at- 

 mosphere, its volume v will be reduced to v', and the expression of the 

 heat disengaged will be 



C P" log -1^ = C -P^ logPi 

 267 + t ^ v 267 + t ^ p- 



The heat disengaged by the reentrance of atmospheric air into the 

 vacuum will therefore be what this expression becomes when p is there 



made very small ; it is then found that log £- becomes very great, 



P 



but the product of » by log £- is not the less small on that account ; 



P 

 in fact we have 



p\ogP-=p log pi ~ plogp = p (log p' — log p), 

 P 

 a quantity which converges towards zero when jo diminishes. 



The quantity of heat disengaged will therefore be small in propor- 

 tion to the feebleness of pressure in the recipient, and it will be re- 

 duced to zero Avhen the vacuum is perfect. 



