186 Dr. Schroeder van der Kolk on Gases. 



The numbers of the last column show by how much the gases 

 deviate from Mayer's assumption. From these numbers the for- 

 mula may be calculated which gives the quantity of heat which 

 must be imparted to, or taken from a gas, if, while it retains a 

 constant temperature, it is to expand from a higher to a lower 

 pressure without performing any external work. We can always 

 imagine here a globe filled with gas, which is put in connexion 

 with an exhausted globe. Let us calculate the formula for air 

 at 5°. At this temperarure let c, d, and c" denote the specific 

 heats under constant volume for the pressures 0*76, 1, and 2 

 metres; we have then, at 5°, 



Pressure . 



0-7626 



c, 



0-7600 



c +0-000050, 



1-0035 



*', 



1-0000 



c' +0000117, 



2-0070 



c", 



2-0000 



c" + 0-000384. 



Different values of c are given, as it is not to be presupposed 

 that c is independent of the pressure. Yet in calculating the 

 formula this has no influence. 



The numbers in the last column show how much more heat is 

 contained in a kilogramme of air at 5° and the pressure given, 

 than in one at 4° and the corresponding pressures 0'76, 1, and 

 2 metres. 



From this the three following differential quotients of the in- 

 ternal work w may be deduced : — 



hdw_ 3 x 0-0003 84 _ 

 AtZ ' ~dh ~ -00070 _ U11U ' 



*>, £ =-0-03,, 



atO m -76 ~- =-0-014. 



dh 



The increase of pressure dh is not given in metres, but in parts 

 of the existing pressure. In this way the constants of the fol- 

 lowing formulae were calculated, 



7 dw /3 



fl-TT =Ct 



dh y — h 



and they gave 



« = 0-798; /3 = 9-535; 7 =12-5. 



