Question

The dimensional formula for b is same as that for:
A.P
B.V
C.$P{V^2}$
D.RT

Answer 1

Hint: The dimensional formula of b is defined by the van der Waals equation. This equation states for a real gas. The dimensional formula for a is the same as for the values. Any physical quantity can be represented as the product for two or more fundamental quantities. The dimensions of a physical quantity are the powers to which the fundamental quantities are needed to be raised, in order to correctly represent the given quantity.

Complete step by step answer:
Here we see the volume correction given below:
As we know that ideal gas contains the value of \[PV = nRT\] . Real gas has the molecular volume cannot be ignored and now we assume that the volume is b for the moving gas molecules. A real gas contains the volume V, which has only available volume of \[\left( {V - nb} \right)\] and this can be an ideal gas volume.
Here, $P \propto \dfrac{n}{v}$
And ${P_i} = P + \dfrac{{a{n^2}}}{{{v^2}}}$
Here, n = number of moles and V = volume of the gas
Substituting the values of ideal volume and ideal pressure in the ideal equation is \[PV = nRT\] .
  $(P + \dfrac{a}{{{v^2}}})(V - b) = RT$
Here V is molar volume and T is the temperature of the given sample of gas. R is called molar gas constant. Here b will have the same dimensions as V.
 \[b = V\] .

Hence, option (B) is correct answer.

Note: Van der Waals equation fits pressure-volume-temperature data for a real gas better than the ideal gas equation does. The improved fit is obtained by introducing two parameters that must be determined experimentally for each gas. Van der Waals equation is particularly useful in our efforts.