Numerical value R :
Consider one mole of a gas at STP, then
R = \(\frac{P_0V_0}{T}\)
Standard pressure
P0 = 0.76 m of Hg column
= 0.76 × 13.6 × 103 × 9.8 N/m2
Standard temperature = T0 = 273.15K
Volume of one mole of gas at
= 22.4 × 10-3m3
R = \(\frac{0.76\times13.6\times10^3\times9.8\times22.4\times10^{-3}}{273.15}\)
= 8.31 J mol-1K-1
In the C.G.S. system,
R = \(\frac{8.31}{4.2}\) cal mol-1°C-1
= 1.98 cal mol-1°C-1
Numerical value of kB:
We know that,
kB = \(\frac{R}{NA}\)
kB = \(\frac{8.31\,J\,mole^{-1}K^{-1}}{6.02\times10^{23}mole^{-1}}\)
=1.38 × 10-23 J/K.