Question

The density of water at $0^{\circ }C$ is $0.998gc{m}^{-3}$ and at $4^{\circ }C$ is $1.000gc{m}^{-3}$. Calculate the average coefficient of volume expansion of water in the temperature range $0$ to $4^{\circ }C$.

Answer 1

The density at $0^{\circ }C$ is ${\rho }_{0^{o}C}=0.998g/m^3$

The density at $4^{\circ }c$ is ${\rho }_{4^{o}C}=1g/m^3$

The change in density is given by:

${\rho }_{0^{o}C}=\frac{{\rho }_{4^{o}C}}{1+\gamma \Delta T}$

$\Rightarrow 0.998=\frac{1}{1+\gamma \times 4}$

$\Rightarrow 1+4\gamma =\frac{1}{0.998}$

$\Rightarrow 4\gamma =\frac{1}{0.998}-1\Rightarrow \gamma =0.0005\approx 5\times {10}^{-4}$

As density decreases $\gamma =-5\times {10}^{-4}$