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Let v be the speed, in meters per second, of an oxygen molecule, and let p(v) be the density function of the speed distribution of oxygen molecules at room temperature. Maxwell showed that p(v)= av^(2)e^(-(mv^(2))/(2kT) where k= 1.4 x 10 ^(-23) is the Boltzmann constant, T is the temperature in Kelvin (at room temperature, T = 293), and m= 5 x 10^(-26) is the mass of the oxygen molecule in kilograms.

a) Find the value of a

b)estimate the median and the mean speed. Find the maximum of p(v).

c) How do your answers in part (b) for the mean and maximum of p(v) change as T changes?

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