CHI-MIKE
Jan 25, 2010, 01:22 AM
I want to know how to prove Cp-Cv=R
Unknown008
Jan 25, 2010, 08:55 AM
I don't know if you'll understand, but I'll try.
PV = RT\ (for\ one\ mole\ of\ gas)
P\Delta V = R\Delta T... 1
Law of conservation of energy;
\Delta Q = \Delta U + \Delta W
\Delta U = Q_1
\Delta W = P\Delta V
Hence,
\Delta Q = Q_1+ P\Delta V... 2
From 1 and 2;
Q_2 = Q_1+ R\Delta T
Where Q1 is the energy involved during isovolumetric change.
And let's call delta Q, Q2, where this is the energy involved during isobarric change.
The respective formulae are:
Q_1 = c_v \Delta T
Q_2 = c_p \Delta T
c_p \Delta T = c_v \Delta T+ R\Delta T
Remove the delta T;
c_p = c_v + R
c_p - c_v = R
There you are. I don't quite get it myself, but this is what my teacher gave me.