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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.
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Solution
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) = 4oC
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
\[\gamma = - 5 \times {10}^{- 4}\]
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