Spherical thermodynamical chamber

[RingNebula57]

Homework Statement

In a spherical chamber with volume V , which contains a gas with pressure p1, there is a surface that has a much more low temperature than the other surface temperature of the sphere surface( which is kept constant). Because of that the particles that hit the coresponding surface S will condensate on it. We know: molar mass, universal gas constant, and neglate the liquid formation from condensation.

After how much time will the gas have another pressure, let's call it p2?

Homework Equations

at solution

The Attempt at a Solution

The number of molecules that hit the cold surface in a time interval dt is:

dN = n * dV , where dV= v * dt * S, v= root mean square velocity ; n= molcule volumetric concentration ( m^-3)

For that dt we can keep n constant so : n=N/V => dN/N= v* dt* S / V, and here is my problem...

I can't integrate this because I would say that the intitial number of molecules is 0. Any ideas?

Thank you[/B]

 

[DEvens]

You nearly have it. But why do you think that the number of molecules at t=0 is zero?

Really what you want to do is write a differential equation for the pressure as a function of time, P(t) . Use the ideal gas law, and the pressure at t=0, P(0). It should look something like so.

$\frac{dP(t)}{dt} = - \text{const} P(t)$

And you should be able to solve that pretty easily. So can you work out what "const" should be here?

 

[RingNebula57]

I'm stuck at something...

from ideal gas equation:

dp/dt * V = dN/dt * m/M * R*T ; m-molecule mass; M=molar mass

What is dN/dt? dN/dt = -N * v * S / V ?

 

[RingNebula57]

yes, I think that's the answer:

so: N = p*V/R*T => dN/dt = - p * v * S/ R * T => const = v*S*m*v / M*V