(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Tank contain an ideal gas. Known is type of gas, temperature of gas T, volume of tank V=const, pressure of gas in tank p1, and the temperature of surrounding air T (same as temperature of gas in the tank). That is state 1.

Tank has small valve that was not closed completly. Gas was leaking out very slowly, so that temperature in the tank was all of the time equal to T. After valve was closed, we noticed that pressure in tank is now p2<p1. So, new state of gas i T, V, and p2<p1.

So this is isotermic (T=const) change of gas state, but with mass m that is not constant.

We need to calculate amounth of heat (Q) exchanged in this process (heat given to the gas in the tank while leaking), change of inside energy (U2-U1) of gas in the tank, and work (W).

2. Relevant equations

3. The attempt at a solution

I have solved this example, but I'm not sure that it is correct. I have used formula for enthropy chanage and the formula for the second law:

dS = - R (dp/p)

dQ = T dS

From that we have:

dQ = - T R (dp/p)

Mass m is depending of pressure (T,V and R are constant for this problem) so I used state equatation:

m = (p V)/(R T)

Now, I got:

dQ = - V dp

Integration gives:

Q = - V (p2 - p1) = V (p1 - p2)

And that's it. I don't know is that correct. Also I don't know how to calculate (U2- U1) and W.

If anybody has stumbled to similar example , or knows solution to this one let me know.

Thanks.

Niksha.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: TERMODYNAMICS - gas leaking from container at T=const

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