Question

Value of the universal gas constant $R$ is the same for all gases. What is its physical significance?

Answer 1

The universal gas constant: $R=\frac{PV}{nT}$

Its unit is obtained from expression,

$R=\frac{Pressure\ast volume}{no.ofmoles\ast temperature}$

Pressure $=\frac{force}{area}=\frac{force}{lengt{h}^2}=force.lengt{h}^{-2}$

Volume $=lengt{h}^3$

So,

$R=\frac{force.lengt{h}^{-2}\times lengt{h}^3}{no.ofmoles\times kelvin}$

$R=\frac{force\times length}{no.ofmoles\times kelvin}$

Thus, the unit of $R$ is work per mole per Kelvin ($work=force\times length$).

Hence, $R$ is the amount of Work done per mole per Kelvin.