$3.00 \, M^3$ Of Water Is At $20.0^{\circ} C$. If You Raise Its Temperature To $60.0^{\circ} C$, By How Much Will Its Volume Expand?Water:$\beta = 207 \times 10^{-6} \, C^{-1}$ (Unit: $m^3$)

Introduction

Thermal expansion is a fundamental concept in physics that describes how the volume of a substance changes in response to a change in temperature. In this article, we will explore the thermal expansion of water and calculate the volume expansion of a given amount of water when its temperature is raised from $20.0^{\circ} C$ to $60.0^{\circ} C$. We will use the given coefficient of thermal expansion for water, $\beta = 207 \times 10^{-6} \, C^{-1}$, to perform the calculation.

Thermal Expansion Formula

The thermal expansion of a substance can be calculated using the following formula:

$\Delta V = \beta V_i \Delta T$

where:

• $\Delta V$ is the change in volume
• $\beta$ is the coefficient of thermal expansion
• $V_i$ is the initial volume
• $\Delta T$ is the change in temperature

Given Values

• Initial volume: $V_i = 3.00 \, m^3$
• Initial temperature: $T_i = 20.0^{\circ} C$
• Final temperature: $T_f = 60.0^{\circ} C$
• Coefficient of thermal expansion: $\beta = 207 \times 10^{-6} \, C^{-1}$

Calculating Volume Expansion

To calculate the volume expansion, we need to find the change in temperature, $\Delta T$, which is given by:

$\Delta T = T_f - T_i = 60.0^{\circ} C - 20.0^{\circ} C = 40.0^{\circ} C$

Now, we can plug in the values into the thermal expansion formula:

$\Delta V = \beta V_i \Delta T$ $= (207 \times 10^{-6} \, C^{-1}) (3.00 \, m^3) (40.0^{\circ} C)$ $= 2.484 \times 10^{-3} \, m^3$

Discussion

The calculated volume expansion of $2.484 \times 10^{-3} \, m^3$ represents the change in volume of the water when its temperature is raised from $20.0^{\circ} C$ to $60.0^{\circ} C$. This value is extremely small, indicating that the volume of water changes very little with temperature.

Conclusion

In conclusion, we have calculated the volume expansion of a given amount of water when its temperature is raised from $20.0^{\circ} C$ to $60.0^{\circ} C$. The calculated value of $2.484 \times 10^{-3} \, m^3$ represents the change in volume of the water, which is extremely small. This calculation demonstrates the concept of thermal expansion and its application to real-world scenarios.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Additional Information

• The coefficient of thermal expansion for water is a measure of how much the volume of water changes in response to a change in temperature.
• The thermal expansion formula can be used to calculate the volume expansion of any substance, given its coefficient of thermal expansion and the initial and final temperatures.
• The calculated volume expansion can be used to determine the change in volume of a substance in various engineering and scientific applications.
  Thermal Expansion of Water: Q&A =====================================

Introduction

In our previous article, we explored the thermal expansion of water and calculated the volume expansion of a given amount of water when its temperature is raised from $20.0^{\circ} C$ to $60.0^{\circ} C$. In this article, we will answer some frequently asked questions (FAQs) related to thermal expansion of water.

Q: What is thermal expansion?

A: Thermal expansion is the change in volume of a substance in response to a change in temperature. It is a fundamental concept in physics that describes how the volume of a substance changes when its temperature is raised or lowered.

Q: Why does water expand when heated?

A: Water expands when heated because the molecules of water gain kinetic energy and start moving faster. As the molecules move faster, they spread out and occupy more space, causing the volume of water to increase.

Q: Is thermal expansion unique to water?

A: No, thermal expansion is not unique to water. All substances expand when heated, but the rate of expansion varies from one substance to another. The coefficient of thermal expansion is a measure of how much a substance expands when its temperature is raised by one degree Celsius.

Q: What is the coefficient of thermal expansion?

A: The coefficient of thermal expansion is a measure of how much a substance expands when its temperature is raised by one degree Celsius. It is typically denoted by the symbol $\beta$ and is expressed in units of $C^{-1}$ (per degree Celsius).

Q: How is the coefficient of thermal expansion calculated?

A: The coefficient of thermal expansion can be calculated using the following formula:

$\beta = \frac{\Delta V}{V_i \Delta T}$

where:

• $\Delta V$ is the change in volume
• $V_i$ is the initial volume
• $\Delta T$ is the change in temperature

Q: What are some real-world applications of thermal expansion?

A: Thermal expansion has many real-world applications, including:

• Thermometers: Thermometers use the principle of thermal expansion to measure temperature.
• Expansion joints: Expansion joints are used in buildings and bridges to accommodate thermal expansion and prevent damage.
• Heat exchangers: Heat exchangers use thermal expansion to transfer heat from one fluid to another.
• Thermal energy storage: Thermal energy storage systems use thermal expansion to store thermal energy.

Q: Can thermal expansion be used to generate electricity?

A: Yes, thermal expansion can be used to generate electricity. One example is the thermoelectric generator, which uses the Seebeck effect to convert thermal energy into electrical energy.

Conclusion

In conclusion, thermal expansion is a fundamental concept in physics that describes how the volume of a substance changes in response to a change in temperature. We have answered some frequently asked questions related to thermal expansion of water and explored its real-world applications.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Additional Information

• The coefficient of thermal expansion for water is a measure of how much the volume of water changes in response to a change in temperature.
• Thermal expansion has many real-world applications, including thermometers, expansion joints, heat exchangers, and thermal energy storage systems.
• Thermal expansion can be used to generate electricity using thermoelectric generators.