Question

how is force calculated for the small molecule of gas travelling in x direction​

Answer 1

Required Answer;-

If the molecule's velocity changes in the x-direction, its momentum changes from −mvx to +mvx. Thus, its change in momentum is Δmv = + mvx −(−mvx) = 2mvx. The force exerted on the molecule is given by F=ΔpΔt=2mvxΔt F = Δ p Δ t = 2 m v x Δ t .

Explain;-

We have developed macroscopic definitions of pressure and temperature. Pressure is the force divided by the area on which the force is exerted, and temperature is measured with a thermometer. We gain a better understanding of pressure and temperature from the kinetic theory of gases, which assumes that atoms and molecules are in continuous random motion.

an elastic collision of a gas molecule with the wall of a container, so that it exerts a force on the wall (by Newton’s third law). Because a huge number of molecules will collide with the wall in a short time, we observe an average force per unit area. These collisions are the source of pressure in a gas. As the number of molecules increases, the number of collisions and thus the pressure increase. Similarly, the gas pressure is higher if the average velocity of molecules is higher. The actual relationship is derived in the Making Connections feature below. The following relationship is found: \(PV=\frac{1}{3}Nm{\overline{v^2}}\\\), where P is the pressure (average force per unit area), V is the volume of gas in the container, N is the number of molecules in the container, m is the mass of a molecule, and \(\overline{v^2}\\\) is the average of the molecular speed squared.

What can we learn from this atomic and molecular version of the ideal gas law? We can derive a relationship between temperature and the average translational kinetic energy of molecules in a gas. Recall the previous expression of the ideal gas law: PV = NkT.

Equating the right-hand side of this equation with the right-hand side of \(PV=\frac{1}{3}Nm{\overline{v^2}}\\\) gives \(\frac{1}{3}Nm{\overline{v^2}}=NkT\\\).

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