Question

In the eqn. $\bigg \lgroup P + \frac{a}{V^{2}}\bigg \rgroup(V-b) = constant$, the unit of a is
(a) dyne × cm⁵
(b) dyne × cm⁴
(c) dyne/cm³
(d) dyne × cm²

Answer 1

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Answer 2

Answer:

B) dyne × cm⁴

Explanation:

Dimension of P = dimension of a/v²

Dyne/cm² = dimension of a /(cm³)²

Since we will add P and  a/v², thus both need to have same units.

Thus a/v²  must have unit of pressure

Unit of ‘P' (Pressure) = Unit of ‘a' / Unit of ‘V²' (Volume) (CGS System)

Unit of ‘a' = Unit of (P×V²)

= (g - cm^-1 - s^-2)× (cm^3)²

= g - cm^-1 - cm^6 - s^-2

= g - cm^5 - s^-2

= (g - cm - s^-2) × cm^4

Since, g-cm-s^-2 = Dyne

Thus, Unit of ‘a' = Dyne × cm⁴