Question

A specific gravity bottle is filled up to the brim with mercury of 400g, at $0^\circ C$. When heated to $90^\circ C$, the mass of the mercury that overflows from the specific gravity bottle is: (Coefficient of apparent expansion of mercury in glass is \[\dfrac{1}{{6500}} \backslash^\circ C\] )
A. 5.46g
B. 6.54g
C. 10.92g
D. 13.08g

Answer 1

Hint:When the liquid is heated, its volume increases which is the reason why the mercury will overflow. We will use the formula of the coefficient of apparent expansion which depends upon the mass filled, the mass which is left inside the bottle and the change in temperature due to which the mercury expands.

Complete step by step answer:
Here, it is given that the mercury is at \[0^\circ C\] and 400 grams of mercury has been used to fill up the bottle. Then, we are heating the mercury up to \[90^\circ C\]. Now, when a certain body is heated up, it starts expanding as per the Gay-Lussac’s law. Also, this is because when the temperature of a body is increased, its kinetic energy increases and hence the volume of the body increases.

Now, the Coefficient of apparent expansion for a body is described as the ratio of the liquid which is spilled out to the liquid which has been left in the bottle per unit degree change in temperature of the body. Thus, we have;
\[{\gamma _a} = \dfrac{{mass\, spilled}}{{mass\,left \times \Delta T}}\]
Here, \[{\gamma _a}\] is the coefficient of apparent expansion and \[\Delta T\] is the change in temperature of the body. Let mass spilled be x, thus mass left is 400-x. Thus, putting the values, we get;
\[
\dfrac{1}{6500}=\dfrac{x}{(400-x)\times 90} \\
\therefore x=5.46g \\
\]
Thus, option A is the correct answer.

Note:The cohesive force of mercury is greater than water due to which it will not form a meniscus and hence the mercury will directly overflow. If in case of mercury, water was present inside the bottle, then first the water would form a meniscus due to change in temperature and then it would have started overflowing.