Correct Answer - Option 1 : dyne × cm

^{4}
__Concept:__

Real Gas: It will obey the gas rule only at high temperature and low pressure.

- The molecules are not having a negligible volume.
- They can be repulsive and attractive between the molecules.
- It obeys Van der Waals equation: \(\left( {P + \frac{a}{{{V^2}}}} \right)\left( {v - b} \right) = RT\)

Where P = pressure, V = volume, R = universal gas constant and T = temperarure.

__Explanation:__

\(⇒ \left( {P + \frac{a}{{{V^2}}}} \right)\left( {v - b} \right) = RT\)

As pressure can be added only to pressure, therefore, a/v2 represents pressure P i.e.,

\(⇒ \frac{a}{V^2}=P\) or,

⇒ a = PV2

\(\implies a = \frac{Force}{Area} ×( Volume)^2\) (Pressure is Force by area)

Now, the Cgs unit of Force is dyne, of volume is cm ^{3} and area is cm ^{2} .

So, the value of a is

\(\implies unit \ of \ a = \frac{dyne}{cm^2} ×(cm^3)^2\)

\(\implies unit \ of \ a = \frac{dyne}{cm^2} ×(cm^6)\)

⇒ unit of a = Dyne Cm ^{(6 - 2) }= Dyne × cm4

**So, the correct option is dyne × cm4**