Does mayer's equation change for two mole of ideal gases or is it remains same for any number of moles [duplicate]








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[Relation between constant-pressure and constant-volume heat capacities: Cp - Cv = nR](/questions/59618/relation-between-constant-pressure-and-constant-volume-heat-capacities-cp-cv)

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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 )




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


[Molar](https://en.wikipedia.org/wiki/Molar_heat_capacity) ($\pu{J K-1 mol-1}$) and [specific](https://en.wikipedia.org/wiki/Specific_heat_capacity) ($\pu{J K-1 kg-1}$) heat capacities are [intensive properties](https://en.wikipedia.org/wiki/Intensive_and_extensive_properties), independent on scaling (amount of gas).


[Heat capacities](https://en.wikipedia.org/wiki/Heat_capacity) ($\pu{J K-1}$) are [extensive properties](https://en.wikipedia.org/wiki/Intensive_and_extensive_properties), proportional to scaling (amount of gas).


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