Suppose, because of the doubling of atmospheric CO\(_2\) concentration, an ocean water column receives an additional net energy input of 4 W/m\(^2\). If the entire water column of depth 1 km heats up uniformly, the water temperature will increase by 1 K in \(\underline{\hspace{1cm}}\) years (round off to the nearest integer).
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Correct Answer: 32
Solution and Explanation
- \( m \) is the mass of water,
- \( c \) is the specific heat capacity of seawater,
- \( \Delta T \) is the change in temperature.
The rate of heat input is given by the net energy input of 4 W/m\(^2\). By substituting the values and solving for the time, we find that the water temperature will increase by 1 K in: \[ \text{Time} \approx 5 \, \text{years}. \] Thus, the temperature increase will occur in \( 5 \) years.
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