5. Ice and water Why does ice float on water? Because the density of ice is lowerl In fact, water is the only common liquid whose maximal density occurs above its freezing temperature, and this has important biological implications, e.g. stratification of water in lakes by temperature, and preventing ice from forming at the bottoms of lakes and them freezing solid. Between \( 0^{\circ} \mathrm{C} \) and \( 30^{\circ} \mathrm{C} \) the volume \( V \) (in cubic centimetres) of 1 kg of water at a temperature \( T \) is given by the formula, \[ V=999.87-0.06426 T+0.0085043 T^{2}-0.0000679 T^{3} \] Find the temperature at which water has its maximum density. \( { }^{1} \)

To find the temperature at which water has its maximum density, we need to analyze the derived volume equation. Since density is mass divided by volume, the maximum density occurs when volume is minimized. To do this, we can take the derivative of the volume function \( V \) with respect to \( T \), set it equal to zero, and solve for \( T \). This involves using calculus techniques to find the critical points. Upon calculating, you'll find that water has its maximum density at approximately \( 4^{\circ} \mathrm{C} \). Isn't it fascinating how something as simple as temperature can have such an impact on a property as crucial as density? The wonder of water doesn't stop there! It plays a pivotal role in our ecosystem. For instance, when lakes freeze, ice forms at the surface while the water below remains in liquid form, allowing aquatic life to thrive even in the coldest months. This unique behavior is essential for fish and other organisms that rely on water to stay alive, as they can continue their life cycle below the frozen layer, making it a vital aspect of freshwater ecology. So, next time you see a frozen lake, remember how it's protecting the life underneath!