Question

The figure shows a glass tube (linear coefficient of expansion is $\sigma$) completely filled with a liquid of volume expansion coefficient $\gamma$. On heating, length of the liquid column does not change. Choose the correct relation between $\gamma$ and $\sigma$.

• A. $\gamma =\alpha$
• B. $\gamma =2\alpha$
• C. $\gamma =3\alpha$
• D. $\gamma =\alpha /3$

Answer 1

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

When length of liquid coloumn remains constant,

then the level of liquid moves down w.r.t container

thus $\gamma =3\alpha$

Now, $V=V_o(1+{\gamma }^{\Delta T})$

Since, $V=A{l}_o=\left[A_o\right(1+2\alpha \Delta T\left)\right]10=V_o(1+2\alpha \Delta t)$

Hence, $V_o(1+{\gamma }^{\Delta T})=V_o(1+2\alpha \Delta T)$

$\Rightarrow \gamma =2\alpha$