Question

what is Molar specific heat?prove that
Cp-Cv=R​

Answer 1

Molar Specific Heat Capacity:

• It is the heat required to increase the temperature of one mole (unit mole) of any gas by 1 Kelvin.

To prove:

$C_{P}-C_{V} = R$

Proof:

From 1st Law of Thermodynamics:

• ∆Q at constant pressure.

$\Delta Q = \Delta U + W$

$\implies \: \mu C_{P}( \Delta T) = \mu C_{V} \Delta T + \Delta (PV)$

$\implies \: \mu C_{P}( \Delta T) = \mu C_{V} \Delta T + \mu R\Delta T$

$\implies \: C_{P} = C_{V}+R$

$\implies \: C_{P} - C_{V} = R$

[Hence Proved]