The highest building in Montreal is the ‘1 square building’, with a height of 203m. The atmospheric pressure in the streets of Montreal is P1 = 9.9 x 104 Pa. Suppose air density is constant : ρair = 1,2 kg/m3 and g = 9.8 m/s2. Suppose the rooftop temperature to be T = 298K, and the air composition is 100% N2 molecules. d. How would you find the probability for a molecule picked randomly to have a speed in the range vrms and vrms+5.0 m/s. (No calculations needed) e. Find the ratio between the most probable speed (vmp) and the mean speed (vmean). The collision cross-section of N2 molecules is 0.43 nm2. f. Find the collision frequency. Is it in the order of magnitude that you were expecting?

The highest building in Montreal is the ‘1 square building’, with a height of 203m. The atmospheric pressure in the streets of Montreal is P1 = 9.9 x 104 Pa. Suppose air density is constant : ρair = 1,2 kg/m3 and g = 9.8 m/s2. Suppose the rooftop temperature to be T = 298K, and the air composition is 100% N2 molecules. d. How would you find the probability for a molecule picked randomly to have a speed in the range vrms and vrms+5.0 m/s. (No calculations needed) e. Find the ratio between the most probable speed (vmp) and the mean speed (vmean). The collision cross-section of N2 molecules is 0.43 nm2. f. Find the collision frequency. Is it in the order of magnitude that you were expecting?

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter13: Temperature, Kinetic Theory, And The Gas Laws

Section: Chapter Questions

Problem 38PE: (a) In the deep space between galaxies, me density of atoms is as low as 106atoms/m3, and me...

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Concept explainers

Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell established the context for the distribution of molecular velocities for random molecules moving in a closed environment. This theory was generalized in 1871 by German physicist Ludwig Boltzmann. He improvised the theory to express the distribution of energy levels among different molecules.

Question

The highest building in Montreal is the ‘1 square building’, with a height of 203m.

The atmospheric pressure in the streets of Montreal is P₁ = 9.9 x 10⁴Pa.

Suppose air density is constant : ρ_air= 1,2 kg/m³ and g = 9.8 m/s².

Suppose the rooftop temperature to be T = 298K, and the air composition is 100% N₂ molecules.

d. How would you find the probability for a molecule picked randomly to have a speed in the range v_rms and v_rms+5.0 m/s. (No calculations needed)

e. Find the ratio between the most probable speed (v_mp) and the mean speed (v_mean).

The collision cross-section of N₂ molecules is 0.43 nm².

f. Find the collision frequency. Is it in the order of magnitude that you were expecting?

Now, consider Earth's atmosphere as 80% N₂ and 20% O₂. (No calculations needed)

g. Explain if larger, smaller, or equal to the previous situation:

- Ratio v_mp/v_mean

- The rms speed v_rms

- Probability to find a molecule at a speed between v_rms and v_rms+5.0 m/s.

- Collision frequency.

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