Physics - Elasticity Question with Solution | TestHub

In the isothermal process

PV = constant

$\therefore \mathit{\text{P}}\text{d}\mathit{\text{V}}+\mathit{\text{V}}\text{d}\mathit{\text{P}}=0$or$\left(\frac{\text{d}\mathit{\text{P}}}{\text{d}\mathit{\text{V}}}\right)=-\left(\frac{\mathit{\text{P}}}{\mathit{\text{V}}}\right)$

$\therefore$Bulk modulus,$\mathit{\text{B}}=-\left(\frac{\text{d}\mathit{\text{P}}}{\text{d}\mathit{\text{V}}/\mathit{\text{V}}}\right)=-\left(\frac{\text{d}\mathit{\text{P}}}{\text{d}\mathit{\text{V}}}\right)\mathit{\text{V}}$

$\therefore \mathit{\text{B}}=-\left[\left(-\frac{\mathit{\text{P}}}{\mathit{\text{V}}}\right)\mathit{\text{V}}\right]=\mathit{\text{P}}$

$\therefore \mathit{ }\mathit{\text{B}}=\mathit{\text{P}}$

Note:Adiabatic bulk modulus is given by$B\mathit{ }= \gamma P$