200 THE MECHANISM OF LIFE 



is one case which is of particular interest to us, that of two 

 molecules moving end on with the same velocity (Case 4), and 

 at any moment a certain very small fraction of all the pairs of 

 molecules must collide in such a way. It is possible that all, 

 or |, or J, or T ^, and so on, of the total number may collide 

 end on, but it is much more probable that y^ will collide end 

 on than will }, and so on. 



It is possible, we say, that all the molecules will at the same 

 moment collide in pairs, and end on, as in Case 4, Fig. 50, and 

 the probability that this sort of encounter may simultaneously 

 occur throughout the whole volume of gas can be calculated. 

 Now, though possible, the chance of this occurrence is almost 

 incredibly small; small as it is, however, we must consider it in 

 speculative reasoning. 



Imagine now our decilitre of hydrogen enclosed in a box 

 divided into two equal parts by a partition, and imagine the walls 

 of the box and the partition to be made of some material abso- 

 lutely impermeable to heat. Let there be a hole in the partition 

 closed by a valve which is also a non-conductor of heat. Let 

 the gas in the right-hand side have a temperature of 20 C., and 

 that on the left-hand side a temperature of 10 C. 



In such a case the system contains available energy. There is 

 the same mass of gas in either division, but that on the right has 

 a temperature of 20 C., and so its pressure is higher than the gas 

 in the other division. If the valve is now opened the gas at 

 high pressure will rush through the aperture, and it can do work 

 (say, by turning a small propeller) while the pressure is being 

 equalised. But when the latter condition has been attained 

 the system, in itself, can do no more work. Its total energy is 

 still the same, but there is no difference in intensity, and so no 

 transformation (with regard to pressure change) can occur.* 



Consider, also, what happens while the temperatures and 

 pressures are being equalised. The gas in the right-hand division 

 is at a temperature 20 C., and contains a certain quantity of 

 heat, Q'. After the transformation has occurred, the whole mass 

 of gas attains the average temperature 15 C., because Q units 

 of heat have now flowed from a region originally at 20 C. to a 

 region originally at 10 C. Now replace ordinary temperatures 

 by absolute ones that is, add 273 C. to each of the former; 



* For simplicity we neglect here the conditions under which the trans- 

 formation must occur to render the calculation that follows applicable. 



