Question

The density of water at 0°C is 0.998 g cm^–3 and at 4°C is 1.000 g cm^–1. Calculate the average coefficient of volume expansion of water in the temperature range of 0 to 4°C.

Answer 1

Given:
Density of water at 0°C, ( f₀)= 0.998 g cm^-3
Density of water at 4°C, ​(f₄) = 1.000 g cm-3
Change in temperature, (Δt) = 4^oC
Let the average coefficient of volume expansion of water in the temperature range of 0 to 4°C be γ.
$$\begin{gathered} \mathrm{We}\mathrm{know}:f_4=f_0\left(1+\gamma ∆t\right) \\ \Rightarrow f_0=\frac{f_4}{1+\gamma ∆t} \\ \Rightarrow 0.998=\frac{1}{1+\gamma .4} \\ \Rightarrow 1+4\gamma =\frac{1}{0.998} \\ \Rightarrow 4\gamma =\left(\frac{1}{0.998}\right)-1 \\ \Rightarrow \gamma =0.0005=5\times {10}^{-4}{}^{\mathrm{o}}{\mathrm{C}}^{-1} \end{gathered}$$
As the density decreases,
$\gamma =-5\times {10}^{-4}{}^{\mathrm{o}}{\mathrm{C}}^{-1}$
Therefore,the average coefficient of volume expansion of water in the temperature range of 0 to 4°C will be $\gamma =-5\times {10}^{-4}$^oC^-1.