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.