First, let the temperature T and T* and gas constant as R and R* in kelvin scale and G scale respectively.
Formula for ideal gas is
PV=nRT which is further equal to nR*T* i.e. RT = R*T*
Given value of magnitude of ideal gas constant is 1.00 [tex]JG^{-1}mol^{-1}[/tex]
From the formula, T* = [tex]\frac{R}{R*}\times T[/tex] (value of gas constant is [tex]8.314 JK^{-1}mol^{-1}[/tex]
T* = [tex]\frac{8.314 JK^{-1}mol^{-1}}{1.00 JG^{-1}mol^{-1}}\times T[/tex]
T*= [tex]8.314\times T[/tex]
Thus, the temperature scale for which the ideal gas constant is 1.00 [tex]JG^{-1}mol^{-1}[/tex] is [tex]8.314\times T[/tex]