The density of water at 0 dgree C is 0.988 g/cm3 and at 4 dgree C is 1.000 g/cm3. CAlculate the average coefficient of volume expansion of water in the temp. range 0 to 4 C.

To calculate the average coefficient of volume expansion of water between 0°C and 4°C, we can use the formula for volume expansion, which relates the change in volume to the change in temperature. The average coefficient of volume expansion (β) is defined as the change in volume per unit volume per degree change in temperature. Let's break this down step by step.

Understanding the Concept

The coefficient of volume expansion is a measure of how much the volume of a substance changes with temperature. For liquids like water, this value can vary with temperature. In this case, we have the densities of water at two specific temperatures:

• At 0°C: Density = 0.988 g/cm³
• At 4°C: Density = 1.000 g/cm³

Calculating the Change in Volume

First, we need to find the change in volume of a specific mass of water as it heats from 0°C to 4°C. Let's assume we have 1 cm³ of water at 0°C. The mass of this water can be calculated using its density:

Mass at 0°C:
Mass = Density × Volume = 0.988 g/cm³ × 1 cm³ = 0.988 g

Now, we need to find the volume of this mass of water at 4°C using the density at that temperature:

Volume at 4°C:
Volume = Mass / Density = 0.988 g / 1.000 g/cm³ = 0.988 cm³

Finding the Change in Volume

The change in volume (ΔV) as the temperature increases from 0°C to 4°C can be calculated as follows:

ΔV:
ΔV = Volume at 4°C - Volume at 0°C = 0.988 cm³ - 1.000 cm³ = -0.012 cm³

Calculating the Average Coefficient of Volume Expansion

Now that we have the change in volume, we can calculate the average coefficient of volume expansion (β) using the formula:

β = (ΔV / V₀) / ΔT

Where:

• ΔV = Change in volume = -0.012 cm³
• V₀ = Initial volume = 1 cm³
• ΔT = Change in temperature = 4°C - 0°C = 4°C

Substituting the values into the formula gives:

β = (-0.012 cm³ / 1 cm³) / 4°C

Calculating this yields:

β = -0.003 cm³/cm³/°C

Interpreting the Result

The negative sign indicates that the volume of water decreases as it cools from 0°C to 4°C, which is a unique property of water. This behavior is crucial for aquatic life, as it allows ice to float on water, insulating the liquid below and maintaining a stable environment.

In summary, the average coefficient of volume expansion of water between 0°C and 4°C is approximately -0.003 cm³/cm³/°C. This calculation highlights the fascinating properties of water and its behavior under temperature changes.