Why is Cv used instead of Cp for calculating the internal energy of a gas?

[freshjunior]

internal energy of a gas :(

Hi all! I have a problem with this equation ΔU=mCvΔT, where ΔU=change in internal energy, m=mass, Cv=specific heat of air/gas at constant volume,ΔT=change in temp. Although this expression is true for all processes which can be applied to a gas e.g polytropic, adiabatic, why is Cv used instead of Cp, which is specific heat of air/gas at constant pressure?

 

[Dadface]

Hello freshjunior,
If the volume is kept constant the gas is unable to expand and none of the energy input is used to do external work all of it being used to raise the internal energy.If the pressure is constant you need the same energy input as above to raise the internal energy but extra input is needed to account for the work done.
Cv for gases is similar to the specific heat capacities of liquids and solids.The expansion of liquids and solids is so small that usually we assume that the work done during expansion is negligible.Gases can expand a lot but this expansion can be prevented by holding the gas in a container of fixed volume

 

[freshjunior]

oic. Thanks alot!