3.00 m^3 of water is at 20.0°C.
If you raise its temperature to 60.0°C, by how much will its volume expand?
Water
B = 207•10-6 0-1
(Unit = m^3)
The Correct Answer and Explanation is:
To determine how much the volume of water expands when its temperature increases from 20.0°C to 60.0°C, we can use the formula for thermal expansion of a liquid:
[
\Delta V = \beta V_0 \Delta T
]
Where:
- (\Delta V) is the change in volume,
- (\beta) is the coefficient of volume expansion,
- (V_0) is the initial volume, and
- (\Delta T) is the change in temperature.
Step-by-step solution:
- Identify the given values:
- The initial volume of water, (V_0 = 3.00 \, m^3).
- The temperature change, (\Delta T = 60.0°C – 20.0°C = 40.0°C).
- The coefficient of volume expansion for water, (\beta = 207 \times 10^{-6} \, 1/°C).
- Apply the formula:
We plug the given values into the thermal expansion formula: [
\Delta V = (207 \times 10^{-6} \, 1/°C) \times (3.00 \, m^3) \times (40.0°C)
] - Calculate the change in volume: [
\Delta V = 207 \times 10^{-6} \times 3.00 \times 40.0
] [
\Delta V = 0.02484 \, m^3
] - Conclusion:
The volume of water will expand by 0.02484 m³ when its temperature increases from 20.0°C to 60.0°C.
Explanation:
Thermal expansion occurs because the molecules in a substance move more energetically as the temperature increases, causing them to occupy a larger volume. In the case of water, the coefficient of volume expansion ((\beta)) is a measure of how much the volume of a unit mass of water changes per degree Celsius of temperature change. For water, this coefficient is relatively small, meaning that the volume change for a given temperature rise is modest.
In this example, we used the given values and applied the equation for thermal expansion. The result tells us that for every 40°C increase in temperature, the volume of the water expands by approximately 0.02484 cubic meters. Understanding how materials expand or contract with temperature changes is important in various fields, including engineering and environmental science, as it can affect the behavior of liquids in confined spaces or open bodies of water.