Question

A beaker is filled up to brim with water at 4°C. At one time the temperature is increased by a few degrees about 4°C and at another time it is decreased by a few degrees below 4°C. One shall observe that
A). Water overflows in both the cases
B). The level remains constant in each case
C). In the previous case, water overflows while in the latter case its level comes down
D). Water overflows in the latter case, while comes down in the previous case.

Answer 1

Hint: The density of water keeps changing with the temperature of the ambient it is present. There is a relation between the density of a substance and the volume of that substance. We will exploit these concepts in order to reach the solution.

Formula Used:
$\rho =\dfrac{M}{V}$

Complete step-by-step solution:
Water shows different densities at different temperatures. Its density increases, and decreases with the temperature. The density of water starts decreasing after the temperature of $4{}^\circ C$.
Interestingly, the density of water again starts decreasing when the temperature is lowered below $4{}^\circ C$.
Hence, it can be concluded that the density of water is maximum at the ambient temperature of $4{}^\circ C$.
Hence, both an increase and decrease in temperature from $4{}^\circ C$ will cause the density of water to decrease.
Now, it is also given in the question that water is filled up to the brim of the beaker. And nowhere it is mentioned that any extra amount of water is added or taken out of the beaker. Hence, we can assume that the mass of water will remain fixed.
We know that density is given by the relation:
$\rho =\dfrac{M}{V}$ -----(i)
Where, $M$ is the mass of the substance and $V$ is the volume of the substance. $\rho $ is the density of the substance.
For a fixed mass, we can say that:
$\rho $$\dfrac{1}{V}$ -----(ii)
Thus, for a fixed mass, as the density decreases, the volume of the substance increases.
Hence, we can say that with the increase or decrease in temperature of water from $4{}^\circ C$, the density of water starts to decrease. This decrease in the density of the water results in an increase in the volume of the water.
With the increase in the volume of water, and owing to the fact that the water is filled up to the brim of the beaker, the results in the overflow of the water.
Hence, water will overflow in both cases. Thus, the answer is an option (a).

Note: Keep in mind that the variation in the density, and hence the volume, does not follow a linear trend. The volume of water decreases with the increase in temperature up to $4{}^\circ C$. Beyond $4{}^\circ C$, the volume of water increases with the increase in temperature. The density of water is maximum at $4{}^\circ C$.