Suppose N gas molecules with mass m live on a line, meaning they can only move l

Question

Suppose N gas molecules with mass m live on a line, meaning they can only move left or right. The gas molecules do not interact with one another, but are confined by walls to a region with length L . When the gas molecules reach the walls, they elastically collide and change direction. Assume the gas molecules are evenly distributed between the walls.Assuming an equation of state (i.e. gas law) of the form FL=NkT (where k is the Boltzmann constant), what is the relation between average kinetic energy and temperature for this gas?

Explanation / Answer

here,

Basically the average kinetic energy of a gas molecule is related in the following way:

W = 3kT/2

where W is average kinetic energy,

k is the boltzmann constant (=1.38*10^(-23) J/K or 8.617*10^(-5) eV/K)

T is temperature (K)

Another useful expression is

W = m*v^2 / 2

where m is the molecular mass
and v is the average molecular speed.

As an example.

Helium with m = 4.0026 (g/mol) at room temperature 308 (K) has an average kinetic energy of 0.04 eV or 6.3756*10^(-21) J and an average molecular speed of 1276 m/s.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.