[danago]

Hey. Here is a question i was given:

Consider a process that takes steam from an initial state (P = 1 bar and T = 400°C) to a final state (P = 0.5 bar and T = 200°C).  Evaluate the change in internal energy for the steam using (a) the steam tables and (b) ideal gas heat capacity.

I managed to get the correct answer, but i want to just confirm that i used the correct reasoning (for part b).

Since internal energy is a state property, the change in internal energy will not depend on how the system goes from state 1 to state 2, so i created a hypothetical situation where the gas remains at constant volume while lowering in temperature and pressure. Since the volume doesnt change, i can calculate the change in internal energy by using c_v.

Is my reasoning correct, or did i just get lucky when solving this?

Thanks,
Dan.

[aldoxime_amine]

The change in internal energy is a function of only Cv and the change in temperature, and of course the amount of gas. It does not depend on the process. Had the process been adiabatic also, your answer wouldn't have changed.

In fact you can try proving that (not very difficult), that the change in internal energy of a given amount of ideal gas is given by
dU=nC_vdT

[danago]

But in using c_v to find the change of internal energy, dont i need to be talking about a constant volume process?

[aldoxime_amine]

NO 

Are you aware of the degree of freedom of a gas?

[danago]

I dont formally know what it is, but is it related to the number of ways in which the molecules can store energy, such as through rotation, ttranslation and vibration?

[aldoxime_amine]

Yes that is correct.

Sorry for replying very late. 

Whatever you need can be found here---> http://en.wikipedia.org/wiki/Specific_heat_capacity

Sorry for not being very topic specific. That topic is very huge, but you will find what you will need there, including the answer to your question.