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States Of Matter

Question
CBSEENCH11005915

Derive the dimensions of the gas constant. 
Or
What do you mean by the nature of universal consant R?

Solution

The ideal gas equation is
              PV = nRT
     or space space straight R space equals space PV over nT
space space space space space space equals space fraction numerator Pressure space cross times space Volume over denominator No. space of space moles space cross times space Temperature left parenthesis straight K right parenthesis end fraction

space space space space space space equals space Force over Area cross times space fraction numerator Area space cross times space Length over denominator No. space of space moles space cross times space Temperature space left parenthesis straight K right parenthesis end fraction

space space space space space space space equals space fraction numerator Force space cross times space Length over denominator No. space of space moles space cross times space Temperature space left parenthesis straight K right parenthesis end fraction

space space space space space space space space equals space fraction numerator Energy space left parenthesis or space Work right parenthesis over denominator No. space of space moles space cross times space Temperature space left parenthesis straight K right parenthesis end fraction
therefore R represents energy or work done per degree per mole.