Lecture Notes: Coefficient of Volume Expansion

Introduction

• Discusses the concept of volume expansion in materials.
• Applies to solids (e.g., rods, spheres, discs) and liquids.

Key Concepts

• Volume Expansion Coefficient (Beta, β)
  • Defined as the change in volume per unit original volume per unit change in temperature.
  • Formula: ( \beta = \frac{\Delta V}{V \cdot \Delta T} )
  • ( \Delta V ) is the change in volume, ( V ) is the original volume, ( \Delta T ) is the change in temperature.
  • Units: 1/°C or 1/K.

Formula for Change in Volume

• Change in volume formula: ( \Delta V = \beta \cdot V \cdot \Delta T )
  • ( V_f ), final volume = initial volume + ( \Delta V )
  • ( \Delta T = T_f - T_i ), where ( T_f ) is final temperature, ( T_i ) is initial temperature.

Relationship to Linear Expansion

• Volume expansion coefficient is approximately three times the linear expansion coefficient (( \alpha )).
  • ( \beta \approx 3 \cdot \alpha )
  • Useful for materials where both length, width, and height expand.

Practical Application

• Lists for linear and volume expansion coefficients are available for different materials, such as aluminum.
• For solids, typically use linear coefficients.
• For liquids and gases, use volume expansion coefficients.

Conclusion

• Provides a practical method to calculate volume expansion in different states of matter.
• Encourages viewers to ask questions and engage with content for further clarification.