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.

\[We know: f_4 = f_0 \left( 1 + \gamma ∆ t \right)\]

\[ \Rightarrow f_0 = \frac{f_4}{1 + \gamma ∆ t}\]

\[ \Rightarrow 0 . 998 = \frac{1}{1 + \gamma . 4}\]

\[ \Rightarrow 1 + 4\gamma = \frac{1}{0 . 998}\]

\[ \Rightarrow 4\gamma = \left( \frac{1}{0 . 998} \right) - 1\]

\[ \Rightarrow \gamma = 0 . 0005 = 5 \times {10}^{- 4} {}^o C^{- 1}\]

As the density decreases,

\[\gamma = - 5 \times {10}^{- 4} {}^o C^{-1}\]

Therefore,the average coefficient of volume expansion of water in the temperature range of 0 to 4°C will be 

\[\gamma = - 5 \times {10}^{- 4}\]