Question

In the formula , p = (nRT)/(V-b) e ^(a)/(RTV) find the dimensions of a and b, where p = pressure , n= number of moles , T = temperture , V = volume and E = universal gas constant .

Answer 1

The dimensions of a and b are:

• Given formula, $p=\frac{nRT}{V-b} * e^{a/RTV}$

• For a equation to be valid, one must check whether it is dimensionally correct.

• For addition and subtraction operation, dimensions of the variables must be same.

        Hence, dimension of b = dimension of V = $[L^3]$

• Exponential term's are dimension less.

        Hence, dimension of a = dimension of (RTV) = [RTV]=$[\frac{PV}{nT} *T*V]$ = $[\frac{PV^2}{n} ]$

        Dimension of a = $[ML^{-1}T^{-2}]* [L^6]$ = $[ML^5T^{-2}]$

• Note that n is dimensionless.
• Hence, dimension of a = $[ML^5T^{-2}]$ and dimension of b= $[L^3]$