Appendix. Some definite integrals

Maxwell-Boltzmann statistics. For this purpose use equation (12 88) to show that the nximber of translational energy states per molecule, whose energy is such that is not insignificant, is much larger 

Show that the number of molecules which cross a plane of unit area in a gas in unit time, and which have a component of velocity normal to this plane greater than a value is given by 

Show also that the number crossing imit area in imit time whose total kinetic energy exceeds the value is given by 

Note that if no lower limit is given to or to c, the above expressions both reduce to NlkT p 

Consider the molecules which cross a given plane in a gas in unit time. Show that their mean kinetic energy in the direction normal to this plane is kT, and also that their mean total kinetic energy is 2I(T. Why is this larger than the value ikT, which is the mean kinetic energy of all molecules in the gas  

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Appendix B also lists some functions integrated for specific limits these are called definite integrals. Perhaps the most important of these functions, which we will use extensively in later chapters, is f(x) = exp(-x2/2a2) (Figure 2.3). This function is called a Gaussian. The constant a adjusts the width of the curve (/(x) is very small if x a) and is called the standard deviation. 

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