Juliuskingsley00idn
Answered

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A rigid steel container is partially filled with a liquid at 15 atm. The volume of the liquid is 1.23200 L. At a pressure of 30 atm, the volume of the liquid is 1.23100 L. Find the average bulk modulus of elasticity of the liquid over that given range of pressure if the temperature after compression is allowed to return to its initial value. What is the coefficient of compressibility (β)?​

Sagot :

Kharmsorzidn

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]

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