Thermal Expansion

Thermal Expansion

The increase in length, area, or volume of a material when its temperature rises. It occurs because atoms move farther apart as their kinetic energy increases

vibrate

As temperature goes up, atoms _______ more.

Asymmetry of the Lennard-Jones potential

• Strong repulsion when close

• Weaker attraction when farther

• Atoms spend slightly more time farther apart

• Increasing the average spacing → expansion

Isotropic Expansion

• Expansion that occurs equally in all directions.

• Most solids behave like this way under ordinary conditions

• So they keep their shape but scale up in size.

Gases, liquids

_____ and _______ expand significantly with heat, driving natural convection currents such as rising hot air, ocean mixing, and weather patterns.

Expansion Joints

Gaps placed in structures (bridges, railroad tracks) to allow thermal expansion and prevent buckling or cracking.

Coefficient of Linear Expansion (α)

A material constant that tells how much a material’s length changes per degree of temperature change.

Units: 1/°C or 1/K

Linear Expansion

Predicts how much a material’s length changes with temperature.

ΔL = αLΔT

Mathematical representation of the Linear Expansion

dL/dT = αL

Differential form of the Linear Expansion that describes the instantaneous change in length per degree.

Area Expansion

Increase in the surface area of an object when heated. Applied to 2-D shapes like plates or thin sheets.

ΔA = 2αAΔT

Mathematical representation of the Area Expansion

Volume Expansion

Increase in volume of an object when temperature rises; affects solids, liquids, and gases.

Coefficient of Volume Expansion (β)

A constant describing how much a material’s volume changes per degree.

β = 3a

Coefficient of Volume Expansion for Solids.

ΔV = βVΔT

Mathematical Representation of the Volume Expansion.

Hole Expansion Paradox

When a metal plate with a hole is heated, the hole gets bigger, because the entire metal expands uniformly as if the removed piece were still present.

Bimetallic Strip

A strip made up of two metals with different expansion coefficients. Heating makes it bend, allowing it to act as a simple thermometer or thermostat switch.

T_0

(i)

T > T_0

(ii)

expands, smaller α

In a Bimetallic Strip, the side with the larger α _______ more, causing the strip to curve toward the metal with the _________.

4 °C

Temperature at which the water is most dense

contracts, cooled, density decreases

Between 4°C and 0°C, water ______ when ______ (________________).

insulates

Cold surface water below 4°C stays on top and can freeze, forming ice that _________ the warmer 4°C water below. This allows aquatic life to survive winter.

Thermal Stress

Stress produced when an object’s temperature changes but expansion or contraction is physically blocked. Can cause cracking or breaking

Compressive Thermal Stress

Thermal stress that occurs when object wants to expand but is constrained.

Tensile Thermal Stress

Thermal stress that occurs when object wants to contract but is constrained.

Young’s Modulus (Y)

A measure of a material’s stiffness. How much stress is needed to produce a certain strain.

F/A = Y(ΔL/L_0)

Stress-Strain Relation

ΔLthermal = ΔLelastic; αL_0ΔT = (F/A)(L_0/Y)

Set the thermal expansion equal to the elastic compression