Question

What is the dimensional formula for compressibility?

Answer 1

Hint: The compressibility is defined as the reciprocal of the bulk modulus
The compressibility is a thermodynamic quantity
Compressibility is dependent on particle shape, particle density, particle hardness, chemical composition, and, to a degree, particle size.

Complete answer:
The compressibility is reciprocal of the bulk modulus, it can be written s matha medically as follows,
$K = \dfrac{1}{B}$
Where,
$K$ is the compressibility
$B$ is the bulk modulus of the substance.
Bulk modules are defined as the ratio of the pressure and relative volume change is generated due to the applied pressure.
We can write this mathematically as follows,
$\left[ {{M^{ - 1}}{L^1}{T^2}} \right]$
Where \[P\] is the pressure applied on the liquid body
$V$ is the Volume of the liquid
$\Delta v$ is the change in volume due to the applied force.
The dimensional formula of the bulk modulus is the same as the dimensional formula of the pressure. So it has the same unit of pressure.
So we can write the dimensional formula for the bulk modulus is the same as pressure, and it can be written as,
$\left[ {{M^1}{L^{ - 1}}{T^{ - 2}}} \right]$
We know that the compressibility is reciprocal of the bulk modulus
Hence we can write the dimensional equation for the compressibility is as follows,
$\left[ {{M^{ - 1}}{L^1}{T^2}} \right]$
Finally, the dimensional formula of the compressibility can be written as $\left[ {{M^{ - 1}}{L^1}{T^2}} \right]$.


Note: Bulk modulus having the same unit and dimensions of the pressure
We know that the Compressibility is the reciprocal of the bulk modulus
Compressibility is the change in the volume of the substance.