Gas effusing through hole, working out time dependence

  • #1
Homework Statement:
Consider instead a thermally insulated container of volume V with a
small hole of area A, containing a gas with molecular mass m. At time t = 0, the density is ##n_0## and temperature is ##T_0##. As gas effuses out through a small hole, both density and temperature inside the container will drop. Work out their time dependence, n(t) and T(t) in terms of the quantities given above.
Relevant Equations:
##N_L = \frac{1}{4} n A <u> = \frac{1}{4} \frac{N_0}{v} A \sqrt{\frac{8kT}{\pi m}}##
Consider instead a thermally insulated container of volume V with a
small hole of area A, containing a gas with molecular mass m. At time t = 0, the density is ##n_0## and temperature is ##T_0##. As gas effuses out through a small hole, both density and temperature inside the container will drop. Work out their time dependence, n(t) and T(t) in terms of the quantities given above.

I know that ##N_L = \frac{1}{4} n A <u> = \frac{1}{4} \frac{N_0}{v} A \sqrt{\frac{8kT}{\pi m}}##, but not sure how to use this to find n(t) and T(t). I think I need to find the flux of the energy to know if the temperature is decreasing and then find n and t from that but not sure exactly how to do this. Any help greatly appreciated.
 

Answers and Replies

  • #2
21,417
4,822
This can be solved using the open-system (control volume) version of the 1st law. Are you familiar with that?
 

Related Threads on Gas effusing through hole, working out time dependence

  • Last Post
Replies
2
Views
2K
Replies
7
Views
2K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
0
Views
4K
Replies
0
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
808
Top