Formulas for Molar Heat Capacity at Constant Pressure/Volume

[mneox]

Homework Statement

Just wanted to find some clarity regarding this subject. In my textbook, it states that Q = nCvdT for constant volume and Q = nCpdT for constant pressure.

However, one of the TA's in my classes were telling us how dU = nCpdT for constant pressure and dU = nCvdT for constant volume.

Which is right? I'm majorly confused right now.

Homework Equations

dQ = dU + dW

The Attempt at a Solution

No solution really needed, I just want some clarification as to which is right. I know that for constant volume processes, the work will be 0 and therefore dQ = dU which would mean they can BOTH equal nCvdT?

But what about nCpdT? That's what I'm confused about. Thanks for any help!

 

[ehild]

The internal energy of the gas increases by adding heat Q to it and/or doing positive work W on it: dU=Q+W. At constant volume, the work is zero, so Q=dU =n Cv dT. At constant pressure, the gas does work of PdV while taking heat on, so more heat is needed to rise its temperature. Cp is the heat which rises the temperature of 1mol gas by 1 K. At constant pressure dU=Q-PdV=nCp dT-PdV. As PV=nRT, dU=nCpdT-nRdT=n dT(Cp-R). But dU=n Cv dT, so Cp=Cv+R for an ideal gas.

ehild