Thermal Physics -> Chapter 2 ( Thermal Expansion of Solids and Liquids )

Briefly define linear expansion

It’s the increase in length of an object per unit length and per unit temperature change

State the equations for linear expansion.

Δ L = α ⋅ L₀ ⋅ Δ T or L = L_o ( αΔ T + 1) ; Δ L → change in length, α → linear expansivity, L₀ → initial length, L → final length, Δ T → change in temperature.

Briefly define area expansion.

The increase in area of an object per unit area and per unit temperature change.

State the equations for area expansion.

ΔA = βAₒ . ΔT or A= Aₒ ( βΔT + 1 ) ; ΔA → difference in area, β → area expansivity, Aₒ → initial area, ΔT → difference in temperature, A → final area

Relationship between linear expansivity (α) and area expansivity (β)

β = 2α

Briefly define volume expansion.

The expansion of volume with temperature.

State the equations for volume expansion.

ΔV = λVₒ . ΔT or V = Vₒ (λΔT + 1) ; ΔV → difference in volume, λ → volume expansivity, Vₒ → initial volume, ΔT → change in temperature, V → final volume

Relationship between volume expansivity (λ) and linear expansivity (α)

λ = 3α

Formula to get the actual measurement when the current temperature is larger than the temperature at which the measuring instrument was calibrated.

Actual value = reading ( 1 + α ΔT ) ; α → linear expansivity of the material of the measuring instrument

Formula to get the actual measurement when the current temperature is larger than the temperature at which the measuring instrument was calibrated.

Actual value = reading ( 1 - α ΔT ) ; α → linear expansivity of the material of the measuring instrument

What is the difference between real expansion and apparent expansion in a liquid.

Real expansion is how much the liquid actually expands while apparent expansion is how much we think that the liquid expands, ignoring the expansion of the container in which the liquid is contained.

Relationship between real expansion, apparent expansion and the expansion of the container.

λ_real = 3α + λ_apparent ; λ_real → real expansion of the liquid, 3α → expansion of the container in which the liquid is present, λ_apparent → apparent expansion of the liquid

State the relationship between density of the liquid and the real expansion of the liquid.

d = d_o / ( 1 + λΔT) ; d → final density, d_o → initial density, λ → real expansivity of liquid, ΔT → difference in temperature.

Briefly describe the anomalous expansion of water.

When a given mass of water is heated up, like other liquids, its volume increases along with its temperature, but something strange happens between 0°C and 4°C. As you heat water from 0°C to 4°C, its volume actually decreases due to the formation of H bonds between water molecules. This unknown behaviour is known as the anomalous expansion of water. Water only starts to act normally again after the temperature of water is higher than 4°C, making water have its maximum density at 4°C.