What is the difference between Cp and Cv for an ideal gas?

[sachi]

I'm just checking that it's okay to use Cv all the time as a heat capacity of an ideal gas, even when the volume's not constant. This is because the average energy per molecule is 3/2*Kb*T from kinetic theory, therefore the average energy per mole is equal to 3RT/2 = CvT etc.
I'm currently doing a calculation for a heat engine and I'm working out the change in internal energy at a constant volume and I need to make sure that we use Cv and not Cp as the heat capacity.
Also, what is the significance of Cp if it's not used? Is it just so that we can set gamma=Cp/Cv?

Thanks

 

[siddharth]

The heat capacity C of a substance is the amount of heat required to change its temperature by one degree.

So, in your thermodynamic processes, the value of the heat capacity depends on the path chosen.

That is why you have heat capacites at constant pressure(C_p) and constant volume(C_v) .

Now, for an ideal gas, the change in internal energy for any process depends on the temperature only and the relation is given by $\Delta U = nC_v \Delta T$.
That is why in most of the problems you are doing(which involves ideal gases), you are using C_v to calculate the change in internal energy.

Did that help?