Question

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. $\gamma =\frac{\alpha }{3}$

Answer 1

The correct option is B $\gamma =2\alpha$

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 $V=V_0(1+\gamma \Delta T)$

Since $V=A{l}_0=\left[A_0\right(1+2\alpha \Delta T\left)\right]l_0=V_0(1+2\alpha \Delta T)$

Hence $V_0(1+\gamma \Delta T)=V_0(1+2\alpha \Delta T)\Rightarrow \gamma =2\alpha$.