Question

Consider n = 10^-7 mol of neon gas adsorbed to a cold nickel plate of area A = 10 cm^2, held at T = 10 K. Assuming that the gas moves freely on the plate, and undergoes elastic collisions with the edge of the plate. Determine the average force 2 per unit length on the plate edge due to these collisions. To solve this problem, you must derive the equation of state for an ideal gas in two dimensions.

Answer 1

Assuming that the molecules and atoms of the gas are point masses with no significant volume and undergo elastic collisions,

For a 2 dimensional case,

The number of accessible states of a gas varies like

-(1)

where N is the number of atoms and depends only on the energy of the gas.

Now,the mean force conjugate to the external parameter x_a,

Where

For an ideal gas in 2D, since

If we apply this on eqn -1,

For one mole,

.

This is the equation of state of an ideal gas in 2D.

Here tau is the force per unit length of plate.

In the case mentioned above,

n = 10^-7

T = 10 K

A = 10 cm² = 0.001 m²

R = 8.3145 J/mol K