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