Area and volume expansivity are measures of how much a material expands when its temperature increases.

Area Expansivity
*Definition*
Area expansivity (β) is the fractional change in area of a material per unit change in temperature.

*Formula*
β = (ΔA / A₀) / ΔT

where:

- β = area expansivity (1/K or 1/°C)
- ΔA = change in area (m²)
- A₀ = initial area (m²)
- ΔT = change in temperature (K or °C)

*Unit*
The unit of area expansivity is typically:

1/K (per kelvin) or 1/°C (per degree Celsius)

Volume Expansivity
*Definition*
Volume expansivity (γ) is the fractional change in volume of a material per unit change in temperature.

*Formula*
γ = (ΔV / V₀) / ΔT

where:

- γ = volume expansivity (1/K or 1/°C)
- ΔV = change in volume (m³)
- V₀ = initial volume (m³)
- ΔT = change in temperature (K or °C)

*Unit*
The unit of volume expansivity is typically:

1/K (per kelvin) or 1/°C (per degree Celsius)

Relationship Between Area and Volume Expansivity
For isotropic materials, the relationship between area and volume expansivity is:

γ = 3β

This means that the volume expansivity is three times the area expansivity.

Applications
Area and volume expansivity are important in:

1. *Thermal engineering*: Designing heat exchangers, boilers, and other thermal systems.
2. *Materials science*: Understanding material properties and behavior under temperature changes.
3. *Aerospace engineering*: Designing aircraft and spacecraft components that withstand extreme temperatures.

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