Question

The density of water at $4{}^{\circ }C$ in S.I. units is $X$ $kg{m}^{-3}$. Find ${\displaystyle \frac{X}{250}}$
A. 1
B. 2
C. 3
D. 4

Answer 1

Hint: Density is defined as the ratio of the mass of a substance to the volume occupied by the substance. The S.I. unit of density is $kg{m}^{-3}$. At a temperature of $4{}^{\circ }C$, water has a density of 1000$kg{m}^{-3}$.

Complete step-by-step answer:
Density of water at $4{}^{\circ }C$ is 1000$kg{m}^{-3}$. Therefore, $X=1000$. Then, ${\displaystyle \frac{X}{250}}$ will be equal to ${\displaystyle \frac{1000}{250}}=4$. Hence, the correct option is (D) 4.

Additional Information:
Density is defined as the mass present in one unit volume of a substance. It tells us how much mass is present in one unit of volume of a substance. It is given by $\rho \text{ = }{\displaystyle \frac{\text{mass}}{\text{volume occupied by that mass}}}$ , where $\rho$ is the density of the substance. Since density is mass upon volume, its S.I. unit is $kg{m}^{-3}$. 1 $kg{m}^{-3}$ means that 1 kilogram of mass is present in each 1$m^3$ volume of the substance. One of the factors that affect the density of a substance is temperature. A substance has three phases – liquid phase, solid phase and gas phase. As the temperature of the substance changes, the phase of the substance changes i.e. as we go increasing the temperature, a solid converts into a liquid and further increase of temperature converts the liquid into a gas. The change in phase affects the volume of the substance. Solids have the least volume and the gases have the maximum volume. Since, density of a substance is inversely proportional to its volume, the density of the substance also changes with temperature. A substance in the gas phase has the least density and its density increases as it is converted from gas to liquid and then to solid, by lowering the temperature. Water is solid (ice) at a temperature below zero degree Celsius. Between zero degree Celsius and 100 degree Celsius, it is a liquid and above 100 degree Celsius, it is a gas (steam).

Note: According to above theory, for water, ice should have the maximum density amongst the three phases. However, it is not true for water. Water shows an exception in the concept of density and has a maximum density at a temperature of $4{}^{\circ }C$ , which is in the liquid phase.