Question

The density of water at 0 degree Celsius is $0.998g/c{m^3}$ and at 4 degree Celsius is $1.000g/c{m^3}$. Calculate the average coefficient of volume expansion of water in the temperature range of 0 to 4 degree Celsius.

Answer 1

Hint: Here we first use the relation between the densities of water at different temperatures and further we substitute the given values in this equation. Also, we will study the basics of density and how the density is affected by mass.

Formula used:
${f_0} = \dfrac{{{f_1}}}{{1 + \gamma \Delta T}}$

Complete step by step solution:
Here, we get the relation between the density of water at 0 degree Celsius and density at 4 degree Celsius as:
$\eqalign{
  & {f_0} = \dfrac{{{f_1}}}{{1 + \gamma \Delta T}} \cr
  & \Rightarrow 0.998 = \dfrac{1}{{1 + \gamma \times 4}} \cr} $
$\eqalign{
  & \Rightarrow 1 + 4\gamma = \dfrac{1}{{0.998}} \cr
  & \Rightarrow 4 + \gamma = \dfrac{1}{{0.998}} - 1 \cr} $
$\therefore \gamma = 0.0005 \approx 5 \times {10^{ - 4}}$
Therefore, the average coefficient of volume expansion of water in the temperature range of 0 to 4 degree Celsius is $\gamma = - 5 \times {10^{ - 4}}$. Also, as density decreases $\gamma = 5 \times {10^{ - 4}}$ .

Additional information:
Here, we know that density of an object or body is defined as a measure of mass per unit volume. Also, the average density of an object or body is equal to its total mass divided by its total volume.
Therefore, we can say that an object made from a dense material such as iron will have less volume than an object of equal mass made from some less dense substance such as water.
Further, we should also know about the buoyant force. This is an upward force exerted by a fluid which opposes the weight of a partially or fully immersed object in the fluid. Here, in the fluid, pressure increases with depth as a result of the weight of the overlying fluid. So, the pressure at the bottom of a column of fluid is greater than at the top of the column.
Pressure is defined as the force exerted on an object per unit area. Unit of pressure is Pascal which is represented as P. The unit of pressure can also be written as Newton per meter square.

Note:
Here, we should remember that as the mass of an object or body increases, its volume gets decreased and therefore vice versa. Also, density of water is taken at $997kg/{m^3}$.