Question

Global warming will produce rising sea levels partly due to melting ice caps and partly due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of 1.00°C . Assume the column is not free to expand sideways. As a model of the ocean, that is a reasonable approximation, as only parts of the ocean very close to the surface can expand sideways onto land, and only to a limited degree. As another approximation, neglect the fact that ocean warming is not uniform with depth.

Answer 1

0.07 m

Step-by-step explanation:

`L_0` = Initial length = 1000 m

`\Delta T` = Change in temperature = 1.00°C

Volumetric coefficient of expansion of water

`\beta=210* 10^(-6)\\\Rightarrow \beta=3\alpha\\\Rightarrow \alpha=(\beta)/(3)\\\Rightarrow \alpha=(210* 10^(-6))/(3)\\\Rightarrow \alpha=70* 10^(-6)\ ^(\circ)C`

Change in length is given by

`\Delta L=L_0\alpha \Delta T\\\Rightarrow \Delta L=1000* 1* 70* 10^(-6)\\\Rightarrow \Delta L=0.07\ m`

The change in length is 0.07 m