To estimate the coefficient of volume expansion for water at room temperature (20°C) from a graph, we first need to understand what the coefficient of volume expansion represents. It quantifies how much the volume of a substance changes with a change in temperature. For water, this value is particularly interesting because it varies with temperature.

Estimating Coefficient of Volume Expansion at 20°C

From the graph you mentioned (Fig. 21-11), you would typically look for the slope of the curve that represents the volume change of water as it is heated from a lower temperature to around 20°C. The coefficient of volume expansion (β) can be estimated using the formula:

• β = (ΔV / V₀) / ΔT

Where:

• ΔV is the change in volume.
• V₀ is the original volume.
• ΔT is the change in temperature.

By selecting two points on the graph at 20°C and a lower temperature (for example, 0°C), you can find the corresponding volumes. The change in volume (ΔV) is the difference between these two volume readings, and ΔT is the difference in temperature (20°C - 0°C = 20°C). Plugging these values into the formula will give you an estimate of β at room temperature.

Coefficient of Volume Expansion Near 4°C

Water exhibits a unique behavior near 4°C, where it reaches its maximum density. The coefficient of volume expansion at this temperature is significantly lower than at higher temperatures. Near 4°C, the coefficient of volume expansion is approximately:

• β ≈ 0

This means that as water is heated from 0°C to 4°C, it actually contracts slightly before expanding again as it is heated further. This property is crucial for aquatic life, as it allows ice to float on top of water, insulating the water below and maintaining a stable environment for organisms during cold weather.

Summary of Key Points

In summary, to find the coefficient of volume expansion for water at 20°C, you would analyze the graph for the change in volume over the change in temperature. Near 4°C, the coefficient is very low, reflecting the unique properties of water as it approaches its maximum density. Understanding these concepts is essential in fields ranging from meteorology to engineering, where the behavior of water under temperature changes is critical.