From  equation PV = nRT

 R = PV/nT = Pressure*Volume/(No. of moles*Temperature ) = Work done/(No. of moles*Temperature )

(i) Thus universal gas constant denotes the work done by (or on) a gas per mole per kelvin

(ii) Dimension : [ML²T­^-2q^-1]

(iii) Value : 8.31  = 1.98  = 0.8221

 Specific gas constant

When gas quantity is 1 gm, then gas constant used is known as specific gas constant. If M is the molecular weight and R is universal gas constant, so r = R/M

Since the value of M is distinct for different gases. Hence the magnitude of gas constant for 1 gram of a gas is distinct for different gases.

Boltzmann's constant

When 1 atom of gas is given account then the constant is known as Boltzman's constant.

For N atoms (6.023 × 10²³) gas constant = R

For 1 atom gas constant =   ;  Dimension : [ML²T^-2q^-1]

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