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Mayer's Formula is given by: Cp – Cv = R
But is the relation remains same for two mole of ideal gas, or is it
Cp - Cv = 2R

As, far as i know the number of moles are cancelled out in the derivation.

∆H = ∆U + nR∆T
nCp∆T = nCv∆T +nR∆T
Cp - Cv = R (remains same)

(∆H is enthalpy change, ∆U is internal energy change, n is no of moles, R is gas constant and ∆T is change in temperature, Cp is molar specific heat capacity of an ideal gas at constant pressure, Cv is molar specific heat capacity of an ideal gas at constant volume )

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Note that dimension of $R, C_p, C_V$ is $\pu{J K-1 mol-1}$ and not $\pu{J K-1}$.

Molar ($\pu{J K-1 mol-1}$) and specific ($\pu{J K-1 kg-1}$) heat capacities are intensive properties, independent on scaling (amount of gas).

Heat capacities ($\pu{J K-1}$) are extensive properties, proportional to scaling (amount of gas).

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