Q. The figure shows a glass tube (linear co-efficient of expansion is $\alpha$) completely filled with a liquid of volume expansion co-efficient $\gamma.$ On heating length of the liquid column does not change. Choose the correct relation between $\gamma$ and $\alpha$
A) $\gamma = \alpha$
B) $\gamma = 2\alpha$
C) $\gamma = 3\alpha$
D) $\gamma = \frac{\alpha}{3}$
Explanation
(b) When length of the liquid column remains constant, then the level of liquid moves down with respect to the container, thus $\gamma$ must be less than $3\alpha$
Now we can write $V = V_{0}(1 + \gamma\mathrm{\Delta}T)$
Since $V = Al_{0} = \left\lbrack A_{0}(1 + 2\alpha\mathrm{\Delta}T) \right\rbrack l_{0} = V_{0}(1 + 2\alpha\mathrm{\Delta}T)$
Hence $V_{0}(1 + \gamma\mathrm{\Delta}T) = V_{0}(1 + 2\alpha\mathrm{\Delta}T) \Rightarrow \gamma = 2\alpha$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.