Bridge From Macroscopic To Microscopic Physics
The Boltzmann constant, k, is a bridge between macroscopic and microscopic physics, since temperature (T) makes sense only in the macroscopic world, while the quantity kT gives a quantity of energy which is on the order of the average energy of a given atom in a substance with a temperature T.
Macroscopically, for an ideal gas, the product of pressure P and volume V is proportional to the product of amount of substance n (in moles) and absolute temperature T:
where R is the gas constant (8.314 4621(75) J K−1 mol−1). Introducing the Boltzmann constant transforms the ideal gas law into an equation about the microscopic properties of molecules,
where N is the number of molecules of gas (for 1 mole, n = 1 and N is equal to NA, the Avogadro constant). Thus, the left hand side of the equation is a macroscopic amount of pressure-volume work represented by the state of the bulk gas. The right hand side divides this energy into N units, one for each gas molecule, each of which represents an amount of energy equal to kT.
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