296 HEAT. 



and dividing 



T ,_288_288 

 ~ ' 



a fall of 70. 



Decrease of Temperature Upwards with the Atmosphere in Convedivt 

 Equilibrium. As already pointed out (p. 216), the limiting condition 

 of equilibrium for the atmosphere is one of " convective " equilibrium, 

 i.e. one in which the temperature decreases upwards in such a way that 

 a mass of air in ascending will expand and cool in doing work so as 

 always to be at the temperature of its surroundings. Such expansion is 

 adiabatic. Hence the temperature and pressure should be connected in 

 this condition in air in which there is no condensation by the equation 



Let us apply this to find the decrease per 100 feet rise from the sur- 

 face, which we will suppose to be at 0. 

 Taking logarithms we have 



(y - 1) log p = log A + y log T 

 whence -l = 



or 



7 P 

 If dp is the decrease due to a rise of 100 feet, 



dp = 100 

 p "26000 



since 26,000 feet is the height of the homogeneous atmosphere. 



T = 273 



41 100 



X 



1-41 26000x273 

 = 3 



Or, when the atmosphere is just in equilibrium, the temperature 

 decreases by about '3 per 100 feet rise, when the mean is about C. 

 With a more rapid decrease there will be circulation. 



The Internal Energy taken up by a Gas in Expanding. We 



have already mentioned (chap, viii.) Mayer's assumption that a gas in 

 expanding does no work against internal forces, and have described the 

 experiment, first made by Gay Lussac and later made by Joule, to test 

 the truth of the assumption. In Joule's experiment air was compressed 

 in one vessel to a pressure of 22 atmospheres, and was then allowed to 

 expand into another equal vessel previously empty, so that no energy was 

 given to or taken from the air by external work. If in mere expansion 

 the gas had done work against its own cohesion, it would have drawn on 

 its own heat for the supply, and the temperature would have fallen. 



