Helium Cylinder Charging: Thermodynamics Help

[Perses]

Hello; I'm having a bit of difficulty with a problem here;

Compressed helium, supplied through a throttle at a pressure of 10 bar and a temperature of 350K, is used to charge a 5 litre gas cylinder. Initially the cylinder contains helium at pressure of 2 bar and a temperature of 290K. Given that the heat loss from the cylinder is negligible during this process, calculate how many mol of helium are added to the contents of the cylinder. refer to;
W + Q = (delta)Ub - (delta)M(ha) + (delta)Mg(zb-za) - 1/2(delta)M(Ca)^2
Where W is the shaft work, Q the heat input between points a and b, Ca is the speed at a and ha is the enthalpy per kg at a.

Any help would be greatly appreciated! thank you

 

[Andrew Mason]

Hello; I'm having a bit of difficulty with a problem here;
Compressed helium, supplied through a throttle at a pressure of 10 bar and a temperature of 350K, is used to charge a 5 litre gas cylinder. Initially the cylinder contains helium at pressure of 2 bar and a temperature of 290K. Given that the heat loss from the cylinder is negligible during this process, calculate how many mol of helium are added to the contents of the cylinder. refer to;
W + Q = (delta)Ub - (delta)M(ha) + (delta)Mg(zb-za) - 1/2(delta)M(Ca)^2
Where W is the shaft work, Q the heat input between points a and b, Ca is the speed at a and ha is the enthalpy per kg at a.
Any help would be greatly appreciated! thank you

You should explain all the terms. zb-za appears to be a height difference. Are we to assume that the height difference is 0?

You should show what you have done so far. What is the condition for the flow to stop? Is there any work done? What does the left side amount to?

AM

 

[Perses]

(delta)Mg(zb-za) is supposed to be the potential energy component of the system. And (delta)Ub is the increase in internal energy of the gas in the fixed volume

What i thought is that i could let W and Q go to zero and that the system stops flowing when the pressure in the cylinder equals the pressure coming into the system, so 10bar or 1MPa. so

W + Q = 0 = (delta)Ub - (delta)M(ha) + (delta)Mg(zb-za) - 1/2(delta)M(ca)^2
where;
zb = za; so zb -za =0
and ha = ua +vP, then (delta)M(ha) = Ha = Ua + VPa <-- does that make sense?

0 = ((delta)Ub-Ua) + V(delta)Pa - 1/2(delta)M(ca)^2

Now I'm stuck; i don't really know what to do from here.