How Is Work and Heat Transfer Calculated in a Polytropic Process for Helium Gas?

[dillonmhudson]

Helium gas initially at 2 bar, 200K undergoes a polytropic process, with n=k, to a final pressure of 14 bar. Determine the work and heat transfer for the process, each in kJ per kg of helium. Assume ideal gas behavior.

Ok so I have the following:
P1=200kPa
T1=200K
R_He=2.0769kJ/kg*K
Cp=5.1926
Cv=3.1156
k=Cp/Cv=1.6666

P2=1400kPa

I know that
PV^k=const

My trouble is in finding either the mass or the volume of the helium.

Thanks for any help.

 

[Andrew Mason]

Helium gas initially at 2 bar, 200K undergoes a polytropic process, with n=k, to a final pressure of 14 bar. Determine the work and heat transfer for the process, each in kJ per kg of helium. Assume ideal gas behavior.

Ok so I have the following:
P1=200kPa
T1=200K
R_He=2.0769kJ/kg*K
Cp=5.1926
Cv=3.1156
k=Cp/Cv=1.6666

P2=1400kPa

I know that
PV^k=const

My trouble is in finding either the mass or the volume of the helium.

Thanks for any help.

You do not need to know the mass or volume. You only need to know the proportional change in volume. From that you can determine the change in temperature.

Use the fact that $P_iV_i^k = P_fV_f^k$ to find the relative change in volume. Then use the ideal gas law to determine the change in temperature. That will enable you to find the change in internal energy.

Since k = Cp/Cv, what kind of process is this? What does that tell you about the heat transferred during the process?

Apply the first law of thermodynamics to determine the work from the change in internal energy and the heat flow.

AM

 

[dillonmhudson]

Since k = Cp/Cv, what kind of process is this? What does that tell you about the heat transferred during the process?

Are you asking me or are you getting me to think?
It is a polytropic process. I'm not sure what you are getting at.

Can you help me solve for the difference/proportional increase in the volume? Not really sure how to do that either.

Thanks.

 

[dillonmhudson]

Nevermind, I got it.