Why does Cp have J/K·mol but Cv = Cp - R gives J/K?

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jimmy42
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I have the equation for heat capacity for constant volume and pressure.

Cv = Cp -R

So for Cp I have the units J/k and for R the units are J/k mol. So my question is related to that mol. Is it right that I need to get rid of that mol? if so how? Does it involve Avogadro's Constant? Or do I have the wrong units for Cp?

Thanks.
 
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The units for cp is kJ/kgK which can be rewritten as kJ/kmol*k. Although I know that R to be the gas constant and not the universal gas constant.
 
I have

Where Q is the energy as heat and dT is the change in temp in Kelvin.

Cp = Q/dT

Cp = 100J / 2K

Cp = 50 J/K

So, is that not right? R = molar gas constant.