202 THE i/eCHANISM OF LIFE 



a region of 286° to a region at 293°, and entropy will decrease 



by the amount . At the same time Q units of heat will enter 



^ 288 



a region at a temperature of 293°, and entropy will increase by 



the amount — . Therefore the total change is 1- — , and 



293 ^ 288 293 



obviously this expression is negative. Now we get the result 



that when, by reason of the reversal of the direction of motion 



of all the molecules of the gas, the latter segregates into regions 



at different temperatures entropy decreases. 



We have now obtained a result of considerable interest. It 

 has been shown that it is theoretically possible that a ga^ origi- 

 nally at an uniform temperature can, of itself, separate into two 

 equal portions, one of which is at a higher temperature than is 

 the other. Heat can flow of itself from a region of lower to a 

 region of higher temperature. A gas which in virtue of its 

 temperature alone possesses no available energy can pass, of 

 itself, into a condition in which it does possess available energy. 

 A system can, of itself, decrease its entropy. All this is very 

 surprising, for these statements mean the same thing that is 

 expressed by saying that water can, of itself, flow uphill ! 



They mean that we can state the second law of thermo- 

 dynamics as follows : The entropy of the universe may tend to 

 a maximum or a minimum. 



But we must consider the probability of this reversal of the 

 sign of the second law of thermo-dynamics, for our results merely 

 give a theoretical possibility. The condition that it may occur 

 in such a case as we have investigated above is that at the same 

 moment all the molecules of the gas are arranged in pairs, and 

 the members of each pair are approaching each other end on and 

 with the same velocities. Now this condition is only one of an 

 incredibly great number that may exist in the gas, and the 

 probability that it may exist is the ratio, unity to a very large 

 numerical value. Perhaps the reader will best appreciate what 

 is this probability if we put it in Boltzmann's own way. In order 

 that we may observe this reversal of the second law in a decilitre 

 of gas, we might have to wait for a number of centuries repre- 

 sented by unity followed by 10,000 millions of zeros ! It is as 

 probable that it may occur as it is probable that every house in 

 London may catch fire accidentally and independently of all the 

 others on the same day, or that every grown-up person in London 



