Heat Energy and Expansion
Heat Energy and Expansion
Applications of thermal expansion
  1. Expansion in Buildings:
    • Explanation: Buildings experience thermal expansion and contraction due to temperature variations. Materials like concrete and steel expand when heated and contract when cooled.
    • Application: Architects and engineers consider thermal expansion in building design to prevent structural damage. Expansion joints allow controlled movement, avoiding cracks and deformations.
  2. Steel Bridges and Railway Lines:
    • Explanation: Steel bridges and railway lines are exposed to temperature changes, causing them to expand and contract. Without proper measures, this could lead to structural issues.
    • Application: Expansion joints and careful material selection help accommodate thermal expansion in steel structures, ensuring safety and durability.
  3. Sagging of Telegraph Wires:
    • Explanation: Telegraph wires sag due to thermal expansion. As temperatures rise, the wires expand, leading to sagging between poles.
    • Application: Engineers account for thermal expansion when installing telegraph wires, maintaining proper tension to prevent excessive sag during temperature changes.
  4. Bimetallic Strip and Its Application:
    • Explanation: A bimetallic strip consists of two different metals bonded together. It bends when exposed to temperature changes due to different rates of thermal expansion.
    • Application: Bimetallic strips are used in thermostats, circuit breakers, and temperature-controlled switches. The bending action triggers mechanical movements or electrical contacts based on temperature fluctuations.
  5. Expansion in the Balance Wheel of Clocks and Watches:
    • Explanation: The balance wheel in clocks and watches experiences thermal expansion and contraction. It's crucial for maintaining accurate timekeeping.
    • Application: Watchmakers account for thermal effects in the balance wheel's design to ensure consistent and precise timekeeping, especially in mechanical timepieces.
  6. Expansion in Glass:
    • Explanation: Glass undergoes thermal expansion and contraction with temperature changes. It expands when heated and contracts when cooled.
    • Application: Architects and manufacturers consider the thermal properties of glass in construction to prevent stress and breakage. Proper framing and design account for glass expansion.
  7. Thermostats:
    • Explanation: Thermostats use the expansion and contraction of materials, often bimetallic strips, to sense temperature changes. This triggers the control of heating or cooling systems.
    • Application: In heating, ventilation, and air conditioning (HVAC) systems, thermostats play a crucial role in maintaining desired temperatures by responding to thermal expansion and contraction.

Note: Thermal expansion is a disadvantage in wristwatches and clocks as the expansion causes it to loose time.


Expansion in liquids

When liquids are heated, they generally expand, meaning they take up more space. This happens because the molecules in the liquid gain energy and move faster, causing the substance to occupy a larger volume. Conversely, when liquids cool down, they contract, becoming more compact. Understanding this expansion and contraction of liquids is important in various everyday situations, from cooking to the functioning of thermometers. The expansion of a liquid is usually dependent on the expansion of the containing vessel.


Real cubic expansivity

This is the actual increase in volume of a liquid per unit volume per degree rise in temperature when the expansion of the vessel is considered. $$ {\gamma_r} = {\gamma_a} + {\gamma_c} $$ $$ where {\gamma_r} = \text{real expansivity} $$ $$ {\gamma_a} = \text{apparent expansivity} $$ $$ {\gamma_c} = \text{cubic expansivity of container} $$


Apparent cubic expansivity

This is the cubic expansivity of a liquid when the expansion of the containing vessel is not considered.

$$ {\gamma_a} = \frac{\text{apparent increase in volume}}{\text{original volume × temp. rise}} $$ $$ {\gamma_a} = \frac{V_e}{V_r × ∆\theta} $$ $$ \text{where }{V_e} = \text{Vol. of liquid expelled} $$ $$ {V_r} = \text{Vol. of liquid remaining} $$ $$ ∆\theta = \text{temperature rise} $$

Calculations

Example 1: The temperature of glass containing 100cm³ of mercury is raised from 10°C to 100°C. Calculate the apparent cubic expansivity of Mercury. [Real cubic expansivity of mercury = 1.8 × 10-4K-1] [cubic expansivity of glass = 2.4 × 10-5K-1](WAEC)

Solution

$$ {\gamma_r} = 1.8 × {10^{-4}{K^{-1}}} $$ $$ {\gamma_c} = 2.4 × {10^{-5}{K^{-1}}} $$ $$ {\gamma_a} = ? $$ $$ \text{apparent cubic expansion, } {∆V_a} = ? $$ $$ {\gamma_a} = {\gamma_r} - {\gamma_c} $$ $$ {\gamma_a} = 1.8 ×{10^{-4}} - 2.4 × {10^{-5}} $$ $$ {\gamma_a} = 1.56 × {10^{-4}{K^{-1}}} $$ $$ {\gamma_a} = \frac{{∆V_a}}{{V_1}{∆\theta}} $$ $$ {∆V_a} = 1.56 × {10^{-4}} × 100 × 90 $$ $$ {∆V_a} = 1.404cm³ $$

Example 2: The cubic expansivity of mercury is 1.8 × 10-4K -1 and the linear expansivity of glass is 8.0 × 10-6K-1, calculate the apparent expansivity of mercury in a glass container. (WAEC)

Solution

$$ {\gamma_a} = ? $$ $$ {\gamma_r} = 1.8 × {10^{-4}{K^{-1}}} $$ $$ {\gamma_c} = 3\alpha = 3 × 8.0 × {10^{-6}} $$ $$ {\gamma_c} = 2.4 × {10^{-5}{K^{-1}}} $$ $$ {\gamma_a} = {\gamma_r} - {\gamma_c} $$ $$ {\gamma_a} = 1.8 × {10^{-4}} - 2.4 × {10^{-5}} $$ $$ {\gamma_a} = 1.56 × {10^{-4}{K^{-1}}} $$
Anomalous expansion of water

Water behaves uniquely during temperature changes. Unlike most liquids that contracts when cooled, water demonstrates anomalous expansion at 4°C to 0°C.

As it cools, water initially contracts. This contraction continues until it reaches about 4°C, where something remarkable happens. Beyond this point, water diverges from typical behavior and begins to expand as it gets colder. Hence water expands rather than contracts when cooled from 4°C to O°C.

The expansion reaches its maximum density at approximately 4°C. This means that water has its highest density at 4°C.

When water freezes, it defies the norm once again by expanding instead of contracting. This unique behavior results in ice being less dense than liquid water. This distinctive property of water is vital for aquatic ecosystems and has widespread implications in nature.


Apparent Cubic Expansivity Calculator







Formulas :
  1. For 1: \(\ {\gamma_a} = {\gamma_r} - {\gamma_c}\)

  2. For 2: \(\ {\gamma_a} = \frac{{∆V_a}}{{V_1}{∆\theta}}\)

  3. For 3: \(\ {\gamma_a} = \frac{{m_e}}{{m_r} × {∆\theta}}\)

  4. For 4: \(\ {∆V_a} = {\gamma_a} × {V_1} × {∆\theta} \)

  5. For 5: \(\ {\gamma_r} = {\gamma_a} + {\gamma_c} \)
Select the scenario to use the calculator. Input the values for the parameters to solve using the calculator. Use the information below as a guide.

Summary