Difference between Real Expansion and Apparent Expansion

• Real Expansion: Real expansion refers to the actual increase in volume of a substance due to a change in temperature. It considers the change in the substance’s physical dimensions without external constraints.
• Apparent Expansion: Apparent expansion takes into account the change in volume of a substance under certain constraints, such as a fixed shape or size. It is a measure of how the substance’s apparent dimensions change when external factors limit its expansion.

Numerical Forms

• Real Expansion (ΔVr): ΔVr = α * V₀ * ΔT, where α is the coefficient of linear expansion, V₀ is the initial volume, and ΔT is the change in temperature.
• Apparent Expansion (ΔVa): ΔVa = β * V₀ * ΔT, where β is the coefficient of cubical expansion.

Important Points

• Real expansion is concerned with the actual change in volume, while apparent expansion accounts for changes within specific constraints.
• The coefficient of linear expansion (α) is used for real expansion, and the coefficient of cubical expansion (β) is used for apparent expansion.
• The coefficients of expansion vary for different materials, indicating their sensitivity to temperature changes.

Simple Case Study

Consider a metal container used for storing liquids, such as a water bottle or a thermos. The material of the container has specific coefficients of linear (α) and cubical (β) expansion. Your task is to analyze the thermal expansion of the container when subjected to temperature variations.

• Coefficient of linear expansion (α) for the container material: α = 0.00002 per degree Celsius.
• Coefficient of cubical expansion (β) for the container material: β = 0.00003 per degree Celsius.
• Initial volume of the container (V₀): V₀ = 500 cm³.
• The container experiences a temperature change (ΔT) of 50 degrees Celsius.
• Calculating Real Expansion (ΔVr):
  • Coefficient of linear expansion (α): 0.00002 per degree CelsiusInitial volume of the container (V₀): 500 cm³Change in temperature (ΔT): 50 degrees Celsius
  Using the formula: ΔVr = α * V₀ * ΔT
  ΔVr = 0.00002 * 500 * 50 = 0.1 cm³
  Therefore, the real expansion (ΔVr) is 0.1 cm³.
• Calculating Apparent Expansion (ΔVa):
  • Coefficient of cubical expansion (β): 0.00003 per degree CelsiusInitial volume of the container (V₀): 500 cm³Change in temperature (ΔT): 50 degrees Celsius
  Using the formula: ΔVa = β * V₀ * ΔT
  ΔVa = 0.00003 * 500 * 50 = 0.75 cm³.
  Therefore, the apparent expansion (ΔVa) is 0.75 cm³.

More Interesting Links