Question

Derive mayers relation for moler specific heats

Answer 1

Answer:

we derived Mayer's law in thermodynamics. Mayer's formula is Cp - Cv = R. Here Cp is molar specific heat capacity of an ideal gas at constant pressure, Cv is its molar specific heat at constant volume and R is the gas constant.

Answer 2

Explanation:

Consider one mole of an ideal gas. Let dQ be the amount of heat is given to the system to raise the temperature by dT,

and change in internal energy be dV.

Then, from first law of Thermodynamics, dQ = dU + PdV …(1)

If heat is supplied to one mole at constant volume, i.e., V = constant, then, dV = 0 From equation (2),

dQ = dU …(3)

Molar specific heat (CV ) at constant volume, From equation (4),

dQ = dU = Cv dT …(5)

If one mole of gas is supplied heat at constant pressure, i.e., from equation (3)

of molar specific heat Cp at constant pressure,

The above expression is called Mayer’s relation where R = 8.31 J.mol-1 K-1.