Ask Me Help Desk - Proof of Cp-Cv=R

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.