VAPOR-DENSITIES. 381 



work done by the conversion of a unit of N 2 4 into N0 2 under 

 constant pressure is a 2 t. Therefore, the ratio of the heat absorbed 

 to the external work done by the conversion of N 2 4 into NO 2 is 

 7l81-i-, or 23 at the temperature of 40 centigrade. Let us next 

 consider how much more rapidly this vapor expands with increase 

 of temperature at constant pressure than air. From the necessary 

 relation 



kmt 



v = ^r\> 

 pD 



where m denotes the weight of the vapor, and k a constant, we obtain 



(dv\ _v__v^(dG\ 

 \dt) p ~t BVcEf/,' 



where the suffix p indicates that the differential coefficients are for 

 constant pressure. The last term of this expression evidently denotes 

 the part of the expansion which is due to the conversion of N 2 O 4 

 into NO 2 , and the preceding term the expansion which would take 

 place if there were no such conversion, and which is identical with 

 the expansion of the same volume of air under the same circum- 

 stances. The ratio of the two terms is T^l^rr ) , the numerical 



D \ at /p 



value of which for the temperature of 40 is 2 '42, as may be found 

 by differentiating equation (10), or, with less precision, from the 

 numbers in the third column of Table I. Let us now suppose that 

 equal volumes of peroxide of nitrogen and of air at the temperature 

 of 40 and the pressure of one atmosphere receive equal infinitesimal 

 increments of temperature under constant pressure. The heat ab- 

 sorbed by the peroxide of nitrogen on account of the conversion of 

 N 2 O 4 into NO 2 is 23 times the external work due to the same cause, 

 and this work is 2'42 times the external work done by the expansion 

 of the air. But the heat absorbed by the air in expanding under 

 constant pressure is well known to be 3'5 times the work done. 

 Therefore the heat absorbed on account of the conversion of N 2 O 4 

 into NO 2 is (23 X 2*42 -7- 3*5 = ) 15'9 times the heat absorbed by the air. 

 To obtain the whole heat absorbed by the vapor we must add that 

 which would be required if no conversion took place. At 40 the 

 vapor of peroxide of nitrogen contains about 54 molecules of N 2 O 4 

 to 46 of NO 2 , as may easily be calculated from its density. The 

 specific heat for constant pressure of a mixture in such proportions 

 of gases of such molecular formulae, if no chemical action could take 

 place, would be about twice that of the same volume of air. Adding 

 this to the heat absorbed by the chemical action we obtain the final 

 result, that at 40 and the pressure of the atmosphere the specific 



