1
$\begingroup$

Suppose there is air of mass m1 in an insulated tank at temperature T1 and pressure P1.

0.25m1 of air is released through a valve attached to the tank. Find the final temperature, T2 and pressure P2?

I know its a transient state process and has to use control volume equations. But am having my doubts on how to solve it.

Edit : Equation that I used : enter image description here

subscripts meaning- e-exit i-inlet 1-initial state of CV 2-final state of CV

I dont know how to calculate the enthalpy of air.

Improve this question
$\endgroup$
4
  • $\begingroup$ Can you give us some idea of how you have attempted to solve this problem so far? How about writing down some of the key equations governing the system? $\endgroup$
    – tok3rat0r
    Commented Jun 18, 2015 at 13:34
  • $\begingroup$ I tried to use the first law equation for control volume undergoing a transient process. $\endgroup$
    – karthikeyan
    Commented Jun 18, 2015 at 13:36
  • $\begingroup$ @tok3rat0r No it is not a repeat. PV^γ=Constant is for control mass. Here the problem that I am asking deals with control volume. $\endgroup$
    – karthikeyan
    Commented Jun 18, 2015 at 13:41
  • $\begingroup$ Ah, you're right: i saw 'insulated tank' and immediately thought of an adiabatic process. Comment deleted. $\endgroup$
    – tok3rat0r
    Commented Jun 18, 2015 at 13:52

1 Answer 1

Reset to default
1
$\begingroup$

You can use your old friend $PV^\gamma=k$ for the expansion. Imagine putting a divider sheet across the tank, with $0.75m_1$ on the side away from the outlet and $0.25m_1$ on the side toward the outlet. As the gas is released, the sheet moves until it is against the wall with the outlet. If the divider is massless, the pressure is the same on both sides, and no work is done. You are expanding the volume from $3/4$ of the tank to all of it.

Improve this answer
$\endgroup$
3
  • $\begingroup$ As I have earlier mentioned in the comment, PV^γ=k works for control mass undergoing reversible process. And the system is well defined homogeneously at all points in the control mass. But the question that I have put forth involves control volume and a transient process. $\endgroup$
    – karthikeyan
    Commented Jun 18, 2015 at 14:42
  • 1
    $\begingroup$ My divider changed it to a control mass. The mass in the volume away from the vent is constant. The process inside the tank is reversible-you could make the divider a piston and recompress the control mass. The escape out the vent is irreversible, but we are not concerned with that gas. $\endgroup$
    – Ross Millikan
    Commented Jun 18, 2015 at 14:48
  • $\begingroup$ Nice thinking. Couldn't get it before. This involves a intuitive model and simpler math. Thanks $\endgroup$
    – karthikeyan
    Commented Jun 18, 2015 at 17:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.