Dimensional Analysis

Step 1: Identifying the Dimensions of Given Quantities
- The equation given is:

%5Cleft(%20P%20%2B%20%5Cfrac%7Ba%7D%7BV%5E2%7D%20%5Cright)%20(V%20-%20b)%20%3D%20RT.

- The dimensions of pressure

P

are:

%5BP%5D%20%3D%20ML%5E%7B-1%7D%20T%5E%7B-2%7D.

- The dimensions of volume

V

are:

%5BV%5D%20%3D%20L%5E3.

Step 2: Finding Dimensions of $a$
Since

P%20%2B%20%5Cfrac%7Ba%7D%7BV%5E2%7D

must have the same dimensions as

P

, we equate:

%5Cfrac%7Ba%7D%7BV%5E2%7D%20%3D%20P.

Rearranging for

a

a%20%3D%20P%20%5Ccdot%20V%5E2.

Substituting dimensions:

%5Ba%5D%20%3D%20(ML%5E%7B-1%7D%20T%5E%7B-2%7D)%20%5Ccdot%20(L%5E6).

%5Ba%5D%20%3D%20ML%5E5%20T%5E%7B-2%7D.

Step 3: Conclusion
Thus, the correct dimensional formula for

a

is:

%5Cmathbf%7BML%5E5%20T%5E%7B-2%7D%7D.

Chapter Questions
1 MCQs