Question:

$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be:

Updated On: Mar 19, 2025
  • Bulk modulus
  • Compressibility
  • Modulus of rigidity
  • Energy density
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The Correct Option is B

Solution and Explanation

The correct option is (B): Compressibility
\([b]=[V]\)
\([\frac{a}{b^{2}}]=[P]\)
\(∴[\frac{b^{2}}{a}]= \frac{1}{[P]} = \frac{1}{[B]} = [K]\)
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Concepts Used:

Units and Measurement

Unit:

A unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by the society and in terms of which other quantities of similar nature may be measured.

Measurement:

The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.

Read More: Fundamental and Derived Units of Measurement

System of Units:

  1. CGS system
  2. FPS system
  3. MKS system
  4. SI units

Types of Units:

Fundamental Units -

The units defined for the fundamental quantities are called fundamental units.

Derived Units -

The units of all other physical quantities which are derived from the fundamental units are called the derived units.