Question

Drive the relation of ideal gas equation Cp-Cv=R proof

Answer 1

It is Mayer's equation.

Derivation:

ΔU = ΔQ + ΔW ΔU = Cv ΔT (At pressure is constant)

ΔQ = Cp ΔT (At pressure is constant)

ΔW = -P ΔV (Negative since the calculation been complete)

Pv = RT (1 mole of gas)

Because of pressure is constant, R is also constant

Change in V will make change in T

PΔV = R ΔT

Cv ΔT = CpΔT - RΔT

Divided by ΔT

Cv = Cp - R

Cp - Cv = R