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Question

# (II) At a given latitude, ocean water in the so-called mixed layer (from the surface to a depth of about $50 \mathrm{~m}$ ) is at approximately the same temperature due to the mixing action of waves. Assume that because of global warming, the temperature of the mixed layer is everywhere increased by $0.5^{\circ} \mathrm{C}$, while the temperature of the deeper portions of the ocean remains unchanged. Estimate the resulting rise in sea level. The ocean covers about $70 \%$ of the Earth's surface.

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{$\small {\it The change in volume of most solids, liquids, and gases is proportional to the temperature change and to the original volume}$ $V_{\mathit{0}}$.

} {\small $\Delta V=\beta V_{\mathit{0}}\Delta T$ $\qquad$ (${\it 17-2}$)

} {$\small {\it The coefficient of volume expansion}$, $\beta$, ${\it is approximately equal to}$ $\mathit{3}\alpha$ ${\it for uniform solids}$. } ${\small {\it Use Table 17-1}.}$

We model the volume of the water that expands as a shell of constant radius,

The volume of the shell ($\Delta V$) is the surface area of the earth times the thickness of the shell ($\Delta d$).

$\Delta V=4\pi R_{\mathrm{E}}^{2}\Delta d$

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