Thermodynamics Particles in Water

[dcrisci]

Homework Statement

A column of water contains fine metal particles of radius 20 nm, which are in thermal equilibrium at 25°C. If there are 1000 such particles per unit volume at a given height h0 in the water column, how many particles would be found in the same volume 1.0 mm higher than h0? The density of the used metal is ρ = 20.0 g/cm3.

Homework Equations

$U = \frac{3}{2} nRT$
$N = N_0 e^{\frac{E}{kT}}$

The Attempt at a Solution

I am unsure of where to begin here, I just provided equations I though were necessary but am not exactly sure if they are the right ones. Any help to begin these problems would be awesome!

I was thinking of finding the internal energy of the water, and the difference in the gravitational potential energy of the particles 1mm higher, and then the total energy would be the sum of these two, which would be the value for E, then T = 298K N₀ is 1000?

 

[dcrisci]

I was thinking of finding the internal energy of the water, and the difference in the gravitational potential energy of the particles 1mm higher, and then the total energy would be the sum of these two, which would be the value for E, then T = 298K N₀ is 1000?

Just realized that the internal energy would be equal at both volumes of water (height h₀ and 1mm higher) so I could neglect this and only use the potential energy of the particles ie. E = mgh