Chapter 13, Problem 100RPP

Lakes freeze from top down we all know that ice cubes float in a glass of water. Why? Virtually every substance contracts when it solidifies—the solid is denser than the liquid. If this happened to water. Ice cubes would sink to the bottom of a glass, and ice sheets would sink to the bottom of a lake. Fortunately, this doesn't happen. Liquid water expands by $9\%$ when it freezes into solid ice at $\text{0 °C}$. from a liquid density of a little less than ${\text{1000 kg/m}}^{\text{3}}$ to a solid density of ${\text{917 kg/m}}^{\text{3}}$.

But this is not the only special thing about water. While the density of most substances increases when they are cooled, water density shows a very peculiar temperature dependence (see Figure 13.17). As the temperature decreases, water density increases, but only until $\text{4 °C}$, when water density reaches is maximum value. $$. As the temperature decreases further, water density decreases until at $\text{ 0 °C}$ water freezes and density abruptly decreases to ${\text{917 kg/m}}^{\text{3}}$. It is this peculiar water-density-temperature dependence that plays a vital role in the survival of animals and plants that live in water. In the winter when the water in a take freezes, the solid ice stays at the top, forming an ice sheet. Water just below the ice sheet cools, but when it reaches $\text{4 °C}$ it becomes the most dense and sinks to the bottom of the lake Since water colder than $\text{4 °C}$ is less dense, it stays above, keeping the bottom of the lake at a constant $\text{4 °C}$

Note that if water were most dense at the freezing point, then in the winter the very cold water at the surface of lakes would sink in this case the lake would freeze from the bottom up, and an life in it would be destroyed.

The expansion of water when it freezes has another important environmental benefit the so-called freeze-thaw effect on sedimentary rocks. Water is absorbed into cracks in these rocks and men freezes in cold weather. The solid ice expands and cracks me rock like a wood-cutter splitting logs. This continual process of liquid water absorption, freezing, and cracking releases mineral and nitrogen deposits into me soil and can eventual break the rock down into soil.

Using Newton’s second law, expressions for buoyant force and other forces, and the densities of liquid and solid water at $\text{0 °C}$, find the fraction of an iceberg or an ice cube that is under liquid water.

a. 0.84

b. 0.88

c. 0.92

d. 0.96

e. 1.00