CBSE Class 11-science Answered

Mayer 's formula gives the relationship between molar specific heat of a gas at constant volume and pressure.

By using 1st law of thermodynamics,

dQ=dU + pdv

If specific heat of a gas at constant volume

C_v = (dQ / dT)_v

C_v = dU / dT ...................(1^st)

If specific heat capacity at constant pressure

C_p = (dQ / dT)_p

C_p = dU + Pdv / dT

C_p = dU / dT + P(dV / dT)

C_{p =} C_v + Pdv / dT (using 1^st) ........................(2)

By applying ideal gas equation for 1 mole

PV = nRT

PV = (1)RT

PV = RT

P dv / dt = R dT / dt

Pdv = RdT

P(dv / dT) =R

Putting dis value in eqⁿ 2nd we get,

C_p - C_v = R   [Mayer's relation]