What is the relationship between Charles law and the kinetic theory of gases?

Question

Ellie Andrews · Accepted Answer

From the kinetic theory, one derives the pressure equation,

#p = (mnv^2)/2# where #m# is mass of a molecule, #n# is no. of molecules in unit volume, and #v# is rms speed.

Thus, #n = N/V# where, #N# is total number of gas molecules.

Therefore, one may write,

#pV = (mNv^2)/3#

Now, #(mv^2)/2 = E# where #E# is the kinetic energy of a molecule.

Thus, #pV = (2NE)/3#

Now from the kinetic interpretation of temperature,

#E = (3kT)/2# where #k# is the Boltzmann constant.

Thus, #pV = NkT#

Now since, #N# and #k# are constants, then for a fixed #p#,

#V/T =# constant

This is Charles' law from kinetic theory.

Mateo Aguilar · Answer

undefined Charles's law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature. This law is consistent with the kinetic theory of gases, which explains that gases consist of particles in constant, random motion. According to the kinetic theory of gases, an increase in temperature leads to an increase in the average kinetic energy of gas particles, causing them to move faster and collide with the container walls more frequently, thus increasing the volume. Therefore, Charles's law can be explained by the kinetic theory of gases, as it describes how the behavior of gas particles changes with temperature.