Thermal Expansion: Understanding the Effects of Heat in A-Level Science
What Is Thermal Expansion?
Thermal expansion refers to the increase in size of a material when its temperature rises due to the increase in the kinetic energy of its particles.
Types of Thermal Expansion
Linear Expansion
Change in length of solids:
ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta TΔL=αL0ΔT
Where:
- ΔL\Delta LΔL: Change in length (mmm).
- α\alphaα: Coefficient of linear expansion (1/∘C1/^\circ C1/∘C).
- L0L_0L0: Original length (mmm).
- ΔT\Delta TΔT: Temperature change (∘C^\circ C∘C).
Areal Expansion
Change in surface area:
ΔA=2αA0ΔT\Delta A = 2\alpha A_0 \Delta TΔA=2αA0ΔT
Where A0A_0A0 is the original area (m2m^2m2).
Volume Expansion
Change in volume of solids and liquids:
ΔV=βV0ΔT\Delta V = \beta V_0 \Delta TΔV=βV0ΔT
Where:
- ΔV\Delta VΔV: Change in volume (m3m^3m3).
- β=3α\beta = 3\alphaβ=3α: Coefficient of volume expansion (1/∘C1/^\circ C1/∘C).
- V0V_0V0: Original volume (m3m^3m3).
Real-Life Applications of Thermal Expansion
Bridges and Railroads
Expansion joints are used to prevent buckling due to temperature changes.
Thermometers
Thermal expansion of liquids is used to measure temperature.
Bimetallic Strips
Used in thermostats to control heating and cooling systems.
Example Problem
A steel rod of length 2 m2 \, \text{m}2m expands when heated from 20∘C20^\circ \text{C}20∘C to 100∘C100^\circ \text{C}100∘C. The coefficient of linear expansion for steel is 12×10−6/∘C12 \times 10^{-6} /^\circ \text{C}12×10−6/∘C. Find the change in length.
- Formula:
ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta TΔL=αL0ΔT
- Substitute Values:
ΔL=12×10−6⋅2⋅(100−20)=0.00192 m or 1.92 mm\Delta L = 12 \times 10^{-6} \cdot 2 \cdot (100 – 20) = 0.00192 \, \text{m} \, \text{or} \, 1.92 \, \text{mm}ΔL=12×10−6⋅2⋅(100−20)=0.00192mor1.92mm
Common Mistakes in Thermal Expansion Problems
- Forgetting to convert units (e.g., mm to m).
- Mixing up coefficients of linear and volume expansion.
- Using the wrong formula for specific expansion types.
Practice Questions
- A copper rod expands 1.2 mm1.2 \, \text{mm}1.2mm when heated. If its original length is 1 m1 \, \text{m}1m and ΔT=50∘C\Delta T = 50^\circ \text{C}ΔT=50∘C, find α\alphaα.
- Explain the purpose of expansion joints in bridges.
- Describe one application of volume expansion in liquids.