The following questions pertain to the magnitude of the x-component of the speed(absolute value of the velocity) cx=|vx| of atoms in a gas, whose probability distriubution has the form P(cx)= ae^-bc2/x.

A. Write down the integral you would need to evaluate in order to calculate the avg value of c^2/x.

B. Evaluate the above integral in terms of the constants a and b.

C. Express b in terms of the mass m of each atom and the temperature T of the gas( and other constants), given that the Boltsmann factor in P(cx) pertains to the x- component of the kinetic energy of each atom in the gas.

D. How should the value of a differ from that in Eq - P(vx)dvx= sq root. m/2pikbT e^-mv2/x/2kbT dvx given that speed cx includes both the corresponding positive and negative velocities, and so the probability of observing a speed cx is twice that of observing the corresponding velocity vx?

E. Use the above results to express the avg value of c2/x in terms of m and kbT, and then show that the avg kinetic energy in the x-direction =1/2m has the expected value.