The probability density function for the x component of the velocity of a molecule of an ideal gas is proportional to e−mv2/(2kT ) where v is the x component of the velocity, m is the mass of the molecule, T is the temperature of the gas and k is the Boltzmann constant. By comparing this with (8.1), find the mean and standard deviation of v, and write the probability density function f(v).

The probability density function for the x component of the velocity of a molecule of an ideal gas is proportional to e−mv2/(2kT ) where v is the x component of the velocity, m is the mass of the molecule, T is the temperature of the gas and k is the Boltzmann constant. By comparing this with (8.1), find the mean and standard deviation of v, and write the probability density function f(v).

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Question

The probability density function for the x component of the velocity of a molecule of an ideal gas is proportional to e^{−mv2/(2kT )} where v is the x component of the velocity, m is the mass of the molecule, T is the temperature of the gas and k is the Boltzmann constant. By comparing this with (8.1), find the mean and standard deviation of v, and write the probability density function f(v).

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