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Thermal Expansion and Water Overflow Analysis

Apr 5, 2025

Measuring Overflow of Water Due to Thermal Expansion

Introduction

  • Discussion on measuring overflow from a filled glass due to thermal expansion.
  • Scenario: A Pyrex glass filled with water at room temperature (20°C) heated to 50°C resulting in overflow.

Properties of Materials

  • Pyrex Glass

    • Initial Volume: 500 cm³
    • Coefficient of Volume Expansion: (\beta = 0.1 \times 10^{-4})
  • Water

    • Initial Volume: 500 cm³
    • Coefficient of Volume Expansion: (\beta = 2.2 \times 10^{-4})

Concept of Thermal Expansion

  • Both Pyrex glass and water expand when heated.
  • Water has a significantly higher volume expansion than Pyrex glass.
  • Differences in expansion coefficients cause overflow.

Calculation Steps

  1. Calculate Change in Volume of Pyrex Glass

    • Formula: (\Delta V = \beta \times V_0 \times \Delta T)
    • Values: (\Delta T = 30°C)
    • Result: (\Delta V_{\text{glass}} = 0.15\text{ cm}^3)
  2. Calculate Change in Volume of Water

    • Formula: (\Delta V = \beta \times V_0 \times \Delta T)
    • Result: (\Delta V_{\text{water}} = 3.3\text{ cm}^3)
  3. Determine Overflow Volume

    • Overflow: (3.3 - 0.15 = 3.15\text{ cm}^3) overflowed.

Key Understanding

  • Overflow is due to different expansion rates.
  • If Pyrex and water had the same coefficients, no overflow would occur.

Conclusion

  • Summary: Calculated overflow due to thermal expansion differences.
  • Note: Understanding the coefficients of volume expansion is crucial.

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References

  • Coefficient of volume expansion principles.
  • Calculation methods for thermal expansion.