Gas Leak (Effusion): Solving Differential Equation

  • Thread starter Thread starter moonman
  • Start date Start date
  • Tags Tags
    Effusion Gas
moonman
Messages
21
Reaction score
0
I'm working on a question where gas is leaking out of a container from a small pinhole. I have a differential equation dN/dt = (Constants)*N. I solved this to get an exponential. The exponent is that group of constants, which are A/2V*(kT/m)^1/2. Shouldn't the exponent have something to do with time? Because if they don't, the dimensions don't work out. Can anyone clear this up for me?
 
Physics news on Phys.org
dN/dt = C * N
yields
N = N0 * exp (C * t)
,where t is time

BTW, this is not "Advanced Physics" ;-)
 
You're right, that's not advanced physics, its simple DE. But that's not what I asked.
For that equation to make sense, the exponent should be dimensionless. C*t is not. That's the part I don't understand
 
N is a count ... dN/dt has units counts/sec ... C must have units 1/sec.
 
If A is area and V is volume (and yes, they are) then dimension of your constant is
m2/m3 * m/s = 1/s
and no problem.
I advise to use more precise formula
dN/dt = -1/4 n*<v>*A = -1/4 AN/V * sqrt[kT/(2*3.1416*m)]
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Kinetic Theory - A gas mixture effuses through a hole, find the pressure change
Replies
10
Views
2K
Gas effusing through hole, working out time dependence
Replies
1
Views
1K
Effusion of molecules into a Box through a hole
Replies
7
Views
3K
Effusion differential equation from Newtonian mechanics
Replies
4
Views
6K
What is the Equilibrium Temperature of Gas between Boxes?
Replies
4
Views
4K
How Long Does It Take for Pressure to Increase in a Punctured Container?
Replies
4
Views
2K
Effusion Gas Leakage: Estimating the Rate of Escape Through a Hole
Replies
2
Views
6K
Effusion of particles from one box to another - pressure calculation
Replies
5
Views
3K
Effusion and setting up the calculus problem
Replies
8
Views
2K
Solve these two coupled first-order differential equations and sketch the flow
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top