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Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. We will estimate this effect in this problem, assuming the thermal coefficient of volume expansion is 210×106/∘C for sea water. Calculate the change in length, in meters, of a column of water 1.00 km high for a temperature increase of 1.00∘C. Note that this calculation is only approximate because ocean warming is not uniform with depth.

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Answer:

0.07 m

Explanation:

[tex]L_0[/tex] = Initial length = 1 km = 1000 m

[tex]\Delta T[/tex] = Change in temperature =  1.00°C

[tex]\alpha[/tex] = Coefficient of linear thermal expansion

Volumetric coefficient of expansion of water

[tex]\beta=210\times 10^{-6}^{\circ}C\\\Rightarrow \beta=3\alpha\\\Rightarrow \alpha=\dfrac{\beta}{3}\\\Rightarrow \alpha=\dfrac{210\times 10^{-6}}{3}\\\Rightarrow \alpha=70\times 10^{-6}\ ^{\circ}C[/tex]

Change in length is given by

[tex]\Delta L=L_0\alpha \Delta T\\\Rightarrow \Delta L=1000\times 1\times 70\times 10^{-6}\\\Rightarrow \Delta L=0.07\ m[/tex]

The change in length is 0.07 m

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