Question

In Van der Waals equation `["P" + "a"/"V"^2]` [V - b] = RT ; P is pressure, V volume, R is universal gas constant and T is temperature.

The ratio of constants `"a"/"b"` is dimensionally equal to:

विकल्प

• `"P"/"V"`

• `"V"/"P"`

• PV

• PV³

Answer 1

PV

Explanation:

`["P"+"a"/"V"2] ["V"-"b"]` = RT

Physical quantities with the same dimensions can only be added or removed according to the Dimensional Homogeneity principle.

Thus, Dimensions of P and  `"a"/"V"^2` and dimensions of V and b must be same

∴ [P] = `["a"/"V"^2]` ⇒ [a] = [PV²]          ...(1)

[V] = [b]

Thus, Ratio of `"a"/"b" = ["PV"^2]/["V"]`

= [PV]