Question

A liquid of bulk modulus $B$ and coefficient of volume expansion $\gamma$ is enclosed in a cylinder fitted with a frictionless piston of cross-sectional area $A$. If the temperature of the liquid increases by $T$ degree, the weight that should be placed on the piston to restore the liquid level is :
( neglect the expansion of the cylinder)

• A. $\frac{\gamma ABT}{3}$
• B. $\frac{\gamma AT}{B}$
• C. $\frac{\gamma BT}{A}$
• D. $\gamma ABT$

Answer 1

Answer: (D)

$\gamma ABT$

Change in volume of the liquid due to increase in temperature = $V_0\gamma \Delta T$

$⟹$ Strain produced =$\frac{\Delta V}{V_0}=\gamma T$

Also $B=\frac{P}{strain}=\frac{P}{\gamma T}$

$⟹P=B\gamma T=\frac{W}{A}$

$⟹W=\gamma ABT$