Stored Energy in a pressure vessel

[boka33]

Consider a problem where a tank holds compressed natural gas, compressed to approx. 250 times atmospheric conditions.

Now release the tank valve letting some of the gas out.

Assuming a small timestep, I can approximate the energy lost as 1/2 mv^2,

where m is the mass released during the timestep, and v is the (assumed constant for small timestep) velocity of exiting gas.

Can I equate this to the change in stored energy in the tank during this timestep with reasonable accuracy?

If so, can I model the stored energy as E = PV

where P is pressure in the tank and V is the volume.

Thanks a lot.

 

[mgb_phys]

Take a look at this thread https://www.physicsforums.com/showthread.php?t=192152

 

[boka33]

I think the difference is that I was assuming an isochoric process, since a tank of fixed volume held the process. Maybe this is not the case? Either way, it should be noted that in my case I am just looking for a valid approximation, so I do not wish to model a differential problem. I have been using timesteps.

So if isochoric is assumed

Work = PdV = 0

But I am looking at stored energy, not work done, this is where I am confused.