The bulk modulus of elasticity κ is a measure of the ability of a substance to withstand changes in volume when under compression on all sides. It is equal to the quotient of the applied pressure divided by the relative deformation (or volumetric strain).
[tex]\kappa=\dfrac{\Delta P}{\left(-\dfrac{\Delta V}{V}\right) } =-V\left(\dfrac{\Delta P}{\Delta V}\right) =-\dfrac{V_1(P_2-P_1)}{V_2-V_1}[/tex]
Negative sign shows the decrease in volume.
Solution:
Given:
[tex]P_1=15\text{ atm}\\P_2=30\text{ atm}\\V_1=1.23200\text{ L}\\V_2=1.23100\text{ L}[/tex]
Then,
[tex]\kappa=-\dfrac{(1.23200\text{ L})(30-15)\text{ atm}\times\dfrac{101.325\text{ kPa}}{1\text{ atm}} }{(1.23100-1.23200)\text{ L}}\\\\\kappa=+1.872\times10^6\text{ kPa}\\\kappa=1.872\text{ GPa}\quad\textsf{(ANSWER)}[/tex]
The coefficient of compressibility β is a reciprocal of bulk modulus of elasticity κ.
[tex]\beta=\dfrac{1}{\kappa}=\dfrac{1}{1.872\text{ GPa}}\\\\\beta=0.534\text{ GPa}^{-1}\quad\textsf{(ANSWER)}[/tex]
