How to Convert Dimension of $R$ constant of Air (J/Kg.K)?

Example) (P=nRT/V) in this equation P=nRT/V, The final dimension is achieved should be a function of pressure, But I can not understand this dimension in final (mol.J/Kg.Liter).

when use in R Constant of Air or other gas with this demansion (J/Kg.K), I encounter to problem.

According to your description, you must try to use $$PV=mR_{air}T$$ where m is air mass with unit kg and $R_{air}$ is air gas constant with unit of J/kg-K. Air gas constant $R_{air}=R/MW_{air}$ where R is universal gas constant and $MW_{air}$ is air molecular weight with unit kg/kmole or g/mole.

First of all, here is a list of gas constant (R) values in different useful units. Also, I do not understand why there is a mass unit (kg) in your cidted unit (maybe just a typo).

Now assuming your question is about how the unit of R you cited here results in a unit of pressure, consider the following:

$$P=\frac{nRT}{V}, \mathrm{with}\ [R]=\frac{J}{K\ mol}.$$

So then units of P are

$$[P]=\frac{J}{m^3}=\frac{N\ m}{m^3}=\frac{N}{m^2},$$

which is precisely the units of pressure.

• Thanks, but R is here Specific R that for Air is 286.9 J/Kg.K. so we have: P=nRT/V that P=(mol)×J/(Kg.K)×(K)/m^3 ).
– EMHA
Dec 10, 2016 at 6:04