The formula for finding the change in size (expansion or contraction) of an object when its temperature changes is given by the thermal expansion formula. The formula varies depending on the type of material being considered: linear expansion for solids, area expansion for liquids, and volume expansion for gases. Here are the formulas for each case:
- Linear expansion (solids): ΔL = αL₀ΔT
Where: ΔL is the change in length α is the coefficient of linear expansion of the material L₀ is the initial length of the object ΔT is the change in temperature
The coefficient of linear expansion, α, is a characteristic property of the material and represents the fractional change in length per degree Celsius or Kelvin.
- Area expansion (liquids): ΔA = βA₀ΔT
Where: ΔA is the change in area β is the coefficient of area expansion of the liquid A₀ is the initial area of the liquid ΔT is the change in temperature
The coefficient of area expansion, β, is a characteristic property of the liquid and represents the fractional change in area per degree Celsius or Kelvin.
- Volume expansion (gases): ΔV = γV₀ΔT
Where: ΔV is the change in volume γ is the coefficient of volume expansion of the gas V₀ is the initial volume of the gas ΔT is the change in temperature
The coefficient of volume expansion, γ, is a characteristic property of the gas and represents the fractional change in volume per degree Celsius or Kelvin.
Note that these formulas are approximate and assume that the temperature change is relatively small compared to the initial temperature. Additionally, the coefficients of expansion (α, β, γ) are specific to each material and can be found in tables or provided for specific substances.