Ludwig+Boltzmann+3

Boltzmann Distribution



  The Boltzmann probability distribution function is commonly used in statistical mechanics in order to determine the speeds of molecules. The reason statistics is used in order to do this is a direct result of the infinitesimal size of atoms and molecules. If a computer were to keep track of a sample of an ideal gas the size of a grain of salt at room temperature and pressure, it would need to dynamically account for the position and velocity vectors for a number of molecules on the order of 1015. This is too many operations for most modern computers to handle adequately. Other problems occur of course which stem from quantum mechanics and our increasing inability to precisely know the exact positions and velocities of particles the smaller the scale we choose to examine. We are forced therefore to concern ourselves with large populations of molecules. We are interested in determining a statistical representation which will accurately predict the velocities of particles in a given sample of matter. In this case, we restrict ourselves to an ideal or hard-sphere gas in which there are no intermolecular interactions. To begin, we examine the number of collisions which a sample of gas exerts on a planar boundary surface, in this case orientated arbitrarily perpendicular to the x-axis.

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