134- HEAT. 



collision is finished as it was before it began. We know that the 

 energy of translation does not in reality always remain constant, for 

 a glowing gas, when cooling, loses some of its energy of translation, 

 and loses it in part by radiation. This implies that in some cases some 

 of the energy of motion is converted into vibratory energy of the mole- 

 cules and atoms in the collision, and is then radiated out. In other 

 cases the collisions may convert energy of vibration into energy of trans- 

 lation, for radiant energy is also being absorbed from surrounding bodies 

 to some extent. When, therefore, the temperature is maintained con- 

 stant we must suppose that there is a balance between loss and gain, 

 and that the mean kinetic energy of the whole group remains the same, 

 even though it may change for individual pairs of colliding molecules. 



The assumptions that the time occupied in collision is very small, and 

 that the number of molecules in even a small space is very large, taken 

 together, imply that the dimensions of the molecules are exceedingly 

 small compared with their distance apart. 



The most characteristic features of a gas are its diffusibility through- 

 out any vessel in which it is contained, however the volume of the vessel 

 may be increased, and the uniformity of the pressure which it exerts over 

 the containing-walls in accordance with Boyle's Law. On our theory, the 

 diffusion is due to the rushing of the molecules into any space open to 

 them, while the pressure on the containing-walls is due to the can- 

 nonade of the molecules against them. Each molecule as it comes up 

 against the walls rebounds, and imparts momentum to the walls equal 

 and opposite to that which it receives. Though on an area comparable 

 with the dimensions of a molecule the cannonade in a very small time 

 may vary, on any sensible area an enormous number of impacts will 

 occur in any sensible time, and the average will be practically constant 

 If some molecules lose energy in the collision, others gain, and on the 

 average we must suppose the loss and gain equal. Hence the average 

 momentum imparted per second (that is, the pressure exerted) will be 

 the same everywhere. We can see, too, in a general way how Boyle's 

 Law is explained, for doubling the number of molecules in a space 

 doubles the number colliding in a given time against the containing- 

 walls, and so doubles the momentum imparted per second. In other- 

 words, the pressure is proportional to the density. 



The Mean Value of the Square of the Velocity of Trans- 

 lation. Knowing the pressure and the density of a gas, it is possible 

 to calculate the mean value of the squares of the velocities with which 

 the molecules are moving. 



If we follow any one molecule in imagination, its velocity will be 

 continually changing through collisions ; but if we consider a large 

 number of molecules, say those in a cubic centimetre, we may safely 

 assume that, so long as the conditions exhibited by the whole are the 

 same, the velocities are distributed in such a manner that a definite 

 and constant fraction of the whole will be moving with a given velocity 

 or with a velocity within narrow given limits, though the individuals 

 may be continually changing. This assumption * is justified by our 



* More advanced theory than we can give here shows how the velocities of the 

 molecules must be distributed in order that the collisions may not affect that 

 distribution. We may refer the reader to O. E. Meyer's Kinetic Theory of Giises, 

 from which much of the theory given in the text is derived. 



