Question

The compressibility of a substance is the reciprocal of

Answer 1

The correct answer to the question is bulk modulus of elasticity i.e the compressibility of a substance is the reciprocal of bulk modulus of elasticity.

Let v is the initial volume of a substance. Let the change in volume due to the applied pressure dp is dv.

Mathematically the bulk modulus of a substance is written as -

                           $\beta\ =\ \frac{normal\ stress}{volumetric\ strain}$

                                        $=\ -\frac{dp}{dv/v}$

                                        $=\ -v\frac{dp}{dv}$

Here, the negative sign is due to the fact that decrease in volume will yield negative result. The negative sign just changes the result  to positive.

The compressibility of a substance is defined as -

                           $k=\ -\frac{dv/v}{dp}$

                                      $=\ -[\frac{dv}{dp}] \frac{1}{v}$

Hence, we see that compressibility is the reciprocal of bulk modulus.