44 



HEAT. 



three-way tap, by which M could either be brought into communication 

 with M' or with the pipe P opening downwards. E,' was a simple tap 

 allowing M' to be brought into communication with the pipe P' opening 

 downwards ; p was a branch tube, put into communication with a 

 drying apparatus and pump before the commencement of measurements, 

 so that A could be filled with air thoroughly dried. A was then 

 surrounded by melting ice, mercury was poured into the manometer till 

 it rose to a in both limbs, p was sealed up, and the barometric height was 

 read, and the temperature of the water-bath observed. 



A was next exposed to the steam from the boiler, some of the air 

 being pushed in consequence into M, driving the mercury down that 

 tube and up M'. The tap E.' was turned, to allow mercury to run out of 

 the manometer, until the levels were again the same in M and M', say 

 at p. The barometric height and the temperature of the water-bath 

 were again observed. For simplicity, we may suppose them the same 



as before. The air in the bulb 

 and the part of the stem exposed 

 to the steam has, in rising from 

 to the boiling-point, filled the 

 increase of volume in these, and 

 also the volume of the manometer 

 a tube between a and (3. The various 

 volumes being gauged, it is easy 

 to find the expansion of the air. 

 V' For if Y is the volume of the bulb 

 and the part of the stem exposed 

 to change of temperature, K its mean 

 co-efficient of expansion, v the volume 



Furnace 



of M between a and (3, T the boiling- 

 point, t the temperature of the 

 bath, a the co-efficient of expansion 

 of air, assumed to be constant in 

 other words, we use the gas scale of 

 temperature to be described here- 



after the volume V of air at has expanded to fill V(l + *T) at T, and 

 v at t, at the same pressure. But if the air contained in v were also at 



FIG. 36. Regnault's Expansion of Gas 

 at Constant Pressure. 



- 

 1 + at 



and the total volume at T would be 



T, its volume would be v 



But the increased volume of air, all at T, may also be expressed by 



V(l + aT). 

 Equating these, we have 



which determines a. 



In practice, the variations of barometer and of temperature of water- 

 bath were allowed for, and the equation was slightly more complicated. 



Increase of Pressure with Constant Volume. Nearly the same 

 form of apparatus was used by Regnault to determine the co-efficient of 



