For an ideal gas of classical non- interacting atoms in thermal equilibrium, the Cartesiancomponent of the velocity are statistically independent. In three dimensions, the probabilitydensity distribution of the velocity is:where σ² =kBTmP(Vx, Vy, Vz) = (2nо²)-³/² exp20²1. Show that the probability density of the velocity is normalized.2. Find an expression of the arithmetic average of the speed.3. Find and expression of the root-mean-square value of the speed.4. Estimate the standard deviation of the speed.

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For an ideal gas of classical non- interacting atoms in thermal equilibrium, the Cartesian component of the velocity are statistically independent. In three dimensions, the probability density distribution of the velocity is: where σ² = КВТ m P(Vx, Vy, Vz) = (2nо²)-³/² exp 20² 1. Show that the probability density of the velocity is normalized. 2. Find an expression of the arithmetic average of the speed. 3. Find and expression of the root - mean-square value of the speed. 4. Estimate the standard deviation of the speed.

For an ideal gas of classical non- interacting atoms in thermal equilibrium, the Cartesian component of the velocity are statistically independent. In three dimensions, the probability density distribution of the velocity is: where σ² = КВТ m P(Vx, Vy, Vz) = (2nо²)-³/² exp 20² 1. Show that the probability density of the velocity is normalized. 2. Find an expression of the arithmetic average of the speed. 3. Find and expression of the root - mean-square value of the speed. 4. Estimate the standard deviation of the speed.