derive an epression for maxwells didribution law for molecules haring speed between and c+ dc - physics quenston
Answers
Answer:
The proper treatment is to average the squares of the velocities, and then take the square root of this value. The resulting quantity is known as the root mean square (RMS) velocity
vrms=∑ν2n−−−−−√(27.3.1)
where n is the number of molecules in the system. The formula relating the RMS velocity to the temperature and molar mass is surprisingly simple (derived below), considering the great complexity of the events it represents:
vrms=3RTM−−−−−√(27.3.2)
where
M is the molar mass in kg mol–1, and
R is gas constant.
Equation 27.3.2 can also be expressed as
vrms=3kbTm−−−−−√(27.3.3)
where
m is the molecular mass in kg
kb is Boltzmann constant and is just the “gas constant per molecule"
kb=RNa=R6.02×1023(27.3.4)
Equation 27.3.3 is just the per atom version of Equation 27.3.2 which is expressed in terms of per mol. Either equation will
Explanation:
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