Thermo: Deriving dh=Cp(dT) & du=Cv(dT)

[Anony-mouse]

Why does du/dT = Cv, and same for Cp?


Also, i don't understand how Cp/Cv = v, where v is the specific volume. It is derived from:
Cv + R = Cp, how is PV=nRT used to get from Cv + R = Cp to Cp/Cv = v? I know n is replaced by m/M to leave Pv=RT where R would equal R(universal gas const)/M, but how would you use that?


If anyone could please explain any of these things to me i would really appreciate it. This is for a 1st year mech eng undergraduate who has his thermo exam in just over 2 weeks!. cheers.

 

[Mapes]

You have to put energy into a system to raise its temperature. Cv is the amount of energy you have to put it to raise its temperature by one degree at constant volume.

Cp is higher, because the system is allowed to expand, which does work on the surroundings. So you have to put in more energy to get the one degree increase in temperature.

It's good that you don't understand Cp/Cv = v, because it's not true.

 

[stewartcs]

Also, i don't understand how Cp/Cv = v, where v is the specific volume. It is derived from:
Cv + R = Cp, how is PV=nRT used to get from Cv + R = Cp to Cp/Cv = v? I know n is replaced by m/M to leave Pv=RT where R would equal R(universal gas const)/M, but how would you use that?

Cp/Cv is equal to the specific heat ratio, not specific volume.

CS