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The S.I. unit of compressibility is?
A. $\dfrac{{{m^2}}}{N}$
B. $N{m^2}$
C. $\dfrac{N}{{{m^2}}}$
D. $\dfrac{{kg}}{{{m^3}}}$

Last updated date: 16th Jul 2024
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Hint:Let us understand the unit first. A unit of measurement is a definite magnitude of a quantity that is used as a norm for measuring the same kind of quantity. It is described and accepted by convention or by law.

Complete answer:
In order to answer this question first we should get some idea about the compressibility. The compressibility (also known as the coefficient of compressibility or, if the temperature is kept constant, isothermal compressibility) is a measure of a fluid or solid relative volume change in response to a pressure (or mean stress) change in thermodynamics and fluid mechanics.

The compressibility $\kappa $(denoted $\beta $in some fields) can be expressed in its simplest form as
$\kappa = - \dfrac{1}{V}\dfrac{{\partial V}}{{\partial p}}$
where $V$ stands for volume and \[p\] stands for pressure. In the (usual) case where a rise in pressure causes a reduction in volume, the option to describe compressibility as the negative of the fraction renders compressibility positive. The isothermal bulk modulus is the inverse of compressibility at a fixed temperature.

When we discuss compressibility, we usually refer to it as the opposite or reciprocal of the bulk modulus of elasticity. So, when we talk about compressibility units, we're talking about mutual pressure units. The SI unit of compressibility is given as $\dfrac{{{m^2}}}{N}$.

Hence, the correct answer is option A.

Note: The compressibility factor (Z) is a thermodynamic property that can be used to change the ideal gas law to account for real-world conduct.The ideal gas law, also known as the general gas equation is an equation of state of a hypothetical ideal gas. Although the ideal gas law has several limitations, it is a good approximation of the behaviour of many gases under many conditions.