Mr Searle, The Expansion of a Gas, etc. 245 



Suppose, now, that, as the gas enters the spiral tube, its state 

 is defined by p, v, t and that, on leaving, its state is defined by 

 p', v', t', and that each gramme of gas, as it passes through the 

 tube, absorbs H ergs of heat from the calorimeter. Suppose, 

 further, that the flow is very slow so that the conditions may be 

 treated as "steady" at each instant, and so that the kinetic energy 

 of the gas at the places where t and t' are measured may be 

 negligible. Then we have 



pv -p'v' + H= U'-U, 



or, by (8), H=R <Y -t)+U'- U. 



But, by (9), U' - U = T C v dt, 



J t 



and thus H=R(t'-t)+j G v dt, 



. t 



or, by (10), H=f t G p dt. 



Hence we see that, when the gas is perfect, the heat absorbed 

 by one gramme of gas is equal to the range of temperature 

 multiplied by the mean specific heat at constant pressure for 

 that range. Since, by (9), C v depends only upon the temperature, 

 it follows from (10) that G p depends only upon the temperature, 

 and thus it is not necessary to know the pressure of the gas 

 either before or after its passage through the spiral, or to take 

 any precautions to ensure that the fall of pressure of the gas on 

 passing through the spiral should be small. 



The text- books lay stress on the importance of ensuring that 

 this fall of pressure is very small ; this is illustrated by the 

 following extracts which refer to Regnault's experiments : (A) 1 " It 

 was further necessary to ascertain if the pressure of the gas was 

 the same at entering as at leaving the calorimeter. If that is not 

 the case, the gas will have expanded in the calorimeter, doing 

 work and absorbing heat and a consequent error will be intro- 

 duced-. Water manometers placed at the entrance and the exit 

 showed no more than 1mm. difference so that the error arising 

 from this cause was quite insensible." (B) a " Its pressure at entry 

 and emergence was shown by subsidiary experiments to differ by 

 not more than 1 mm. of water. Hence the pressure was practically 

 constant. We see then that a known weight of gas at constant 

 pressure was cooled in the calorimeter by an observed mean 

 amount." 



1 Preston, Theory of Heat, 2nd ed., p. 275. 



'-' There appears to be some confusion here. A gas necessarily expands when 

 its temperature rises and its pressure remains constant. 

 3 Poynting and Thomson, Heat, p. 70. 



