Solve Tough Thermo Problem: Find Final Pressure of Helium

[ashy]

Homework Statement

Gaseous helium is contained in a rigid container with a volume of V=0.5 m³, and is initially at a pressure of 500 kPa. Agitation by a stirrer transfers 250 kJ of work to the gas in an adiabatic process. C_v for the gas is constant and equal to 12.46 kJ/kmol*K. What is the final pressure of the gas?
So
At state 1: V=0.5 m³, P=500 kPa,
Process 1->2: W=-250kJ
At state 2: V=0.5 m³, P=?

c_v=12.46kJ/kmol*K

Homework Equations

Energy balance for the process:
Q-W=deltaU+deltaKE+deltaPE
Q=deltaPE=deltaKE=0 so
-W=deltaU, W=-250kJ so
250kJ=deltaU.

The Attempt at a Solution

This is what I have:
250kJ=deltaU=n*deltau where u=U/n and n is the number of moles of helium.
c_v=du/dT so
deltau=c_v*deltaT and
250 kJ=n*c_v*deltaT

I don't really know where to go with this problem to find anything to do with the pressure, the equation seems underdetermined. Help?[/B]

 

[gezibash]

Has mass been given? Or is the given volume specific as in m³/kg?

 

[ashy]

No, no mass is given and the the volume given is not specific, it is just the volume of the tank.

 

[gezibash]

What about the number of moles? It's impossible to predict the temperatures without the mass or moles therefore you won't be able to predict the final pressure.

 

[ashy]

no, the data given is the only available data. this is why I thought it was underdetermined. Can it even be done?

 

[gneill]

You may want to throw the ideal gas law, PV = nRT, into your set of Relevant Equations. Note that ##C_v## is specified in terms of moles, and n in the ideal gas law is moles. Set up a ratio and ponder on what you know about the various variables:

$$\frac{P V}{P_o V_o} = \frac{n R T }{n R T_o}$$

 

[rude man]

This problem is unsolvable unless either the mass, no. of moles or initial temperature are given.

You could proceed assuming initial temperature = room temperature ~ 293K.

 

[gneill]

I think it may be doable. Just assume that the number of moles is n and see where things go using the ideal gas law and C_v to find the change in temperature given the change in heat. I think that the n will cancel out along the way.

 

[rude man]

I think it may be doable. Just assume that the number of moles is n and see where things go using the ideal gas law and C_v to find the change in temperature given the change in heat. I think that the n will cancel out along the way.

Send me a PM on how?
rude man

 

[rude man]

gneill is right. It is solvable.

 

[gneill]

Send me a PM on how?

Done. Check your mail (inbox).

 

[gneill]

@ashy : Did you resolve your difficulty?