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Determine the numerical values of R and kB.

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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.

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