The equation (P+ a/V²) (V - b) = Constant. The units of a are

The correct answer is Option "dyne x cm⁴".

Step-by-Step Explanation:

To find the units of the constant $a$ in the given equation, we can use the principle of homogeneity of dimensions. According to this principle, physical quantities can be added or subtracted only if they have the same dimensions and units.

The given equation is:
$(P+\frac{a}{V^2})(V-b)=\text{Constant}$

Here:
- $P$ represents Pressure.
- $V$ represents Volume.

Since the term $\frac{a}{V^2}$ is added to pressure $P$, both terms must have the same units and dimensions.
Therefore:
$\text{Unit of}P=\text{Unit of}\frac{a}{V^2}$

Rearranging the equation to solve for the unit of $a$:
$\text{Unit of}a=\text{Unit of}P\times (\text{Unit of}V{)}^2$

Let us express the units in the CGS (Centimetre-Gram-Second) system, matching the options:
- The CGS unit of pressure $P$ is dyne/cm² (or dyne cm^-2).
- The CGS unit of volume $V$ is cm³.

Substituting these units into the relation:
$\text{Unit of}a=\left(\frac{\text{dyne}}{{\text{cm}}^2}\right)\times ({\text{cm}}^3{)}^2$

Simplifying the expression:
$\text{Unit of}a=\left(\frac{\text{dyne}}{{\text{cm}}^2}\right)\times {\text{cm}}^6$
$\text{Unit of}a=\text{dyne}\times {\text{cm}}^4$

Thus, the unit of $a$ is dyne x cm⁴.