Challenging Thermodynamics Problem

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«Challenging» Thermodynamics Problem

Homework Statement



Consider a cubical vessel of edge a, having a small hole in one of its walls. The total thermal resistance of the wall is [itex] \varphi [/itex] [itex] \mbox{At time} \ t=0 [/itex], it contains air at atmospheric pressure [itex] p_a [/itex] and temperature [itex] \theta_0 [/itex]The temperature of the surrounding is [itex] \theta_a ( > \theta_0 ) [/itex] Find the amount of gas in moles in the vessel at time t. Take [itex] C_v = \frac{5R}{2} [/itex]


Homework Equations



[tex] dQ=dW+dU [/tex]
[tex]dQ= \frac{i_{th}}{\varphi} [/tex]
[tex]
PV=nR \theta \mbox{ideal gas eqn} [/tex]

The Attempt at a Solution



I assumed pressure to be constant throughout the problem.
[tex] P=P_a [/tex]
Initially,
[tex] i_{th} = \frac{\theta_a - \theta_0}{\varphi} [/tex]
Now since volume and pressure both are constant,
PV=const.
or,
[itex]nRd\theta + R\theta dN = 0[/itex]

[itex] \frac{d\theta}{\theta} = -\frac{dn}{n} [/itex]

Now i try to apply first law, which gives,
[tex] \frac{\theta_a - \theta}{\varphi} dt = nC_vd\theta + \theta C_v n [/tex] where [itex] \theta\ is\ temperature \ at\ time \ t[/itex]
But since these rates are also varying, i have no idea how to continue. Specially if someone could throw light on the integration part.
Thanks for any assistance.
 
Last edited:

Answers and Replies

  • #2
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what level is this question?
 
  • #4
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Any1 got an idea?
 
  • #5
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Long time....if any1 knows a tactic for this do tell :cry:
 
  • #6
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Mabye you should try posting this in the Advanced Physics forum instead?
 

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