91Ó°ÊÓ

Global warming produces a rise in the water level in the sea. So, a linear expansion occurred in the water level. The linear expansion caused by the variation in temperature is expressed as follows;

$\mathit{Δ}\mathit{L}\mathbf{=}\mathit{Î\pm }\mathit{L}\mathit{Δ}\mathit{T}$…â¶Ä¦â¶Ä¦â¶Ä¦(1)

Here, is the change in length, is the coefficient of linear expansion, is the initial length, and is the temperature change.

The initial length and change in temperature are given.

$$\begin{gathered} \mathrm{Δ}T=1.00°C \\ L=1.00\text{km} \end{gathered}$$

The coefficient of linear expansion of water is unknown, but you can calculate it from the coefficient of volume expansion of water. It is denoted as .

$$\begin{gathered} \mathrm{β}=210×{10}^{-6}1{/}^{o}C \\ \mathrm{Î\pm }=\frac{\mathrm{β}}{3} \\ \mathrm{Î\pm }=\frac{210×{10}^{-6}1{/}^{o}C}{3} \\ \mathrm{Î\pm }=70×{10}^{-6}1{/}^{o}C \end{gathered}$$

Substitute the values in the equation (1), and we get,

$$\begin{gathered} \mathrm{Δ}L=\left(70×{10}^{-6}\text{1/}°\text{C}\right)×\left(1.00\text{km}×1.00°C\right) \\ =70.0×{10}^{-6}\text{km} \end{gathered}$$

Therefore, the change in length of water level is .