Linear Expansion of Solids, Volume Contraction of Liquids, Thermal Physics Problems
The Organic Chemistry Tutor・15 minutes read
Thermal expansion causes objects to expand when heated and contract when cooled, with changes in length, area, or volume calculable using specific formulas involving the coefficients of linear and volume expansion. For example, an aluminum bar increases from 1.25 m to 1.2502 m when heated from 20°C to 75°C, while a lead plate's dimensions and area also change with temperature, demonstrating the principles of thermal expansion.
Insights
- Thermal expansion is a process where materials change size in response to temperature changes, and it can be quantified using specific formulas. For example, the formula Delta L = Alpha × L₀ × Delta T helps calculate how much an object, like an aluminum bar or a lead plate, will expand or contract based on its original length, the temperature change, and its material's expansion coefficient.
- Different materials exhibit varying degrees of expansion; for instance, aluminum expands by approximately 0.000172 m when heated from 20°C to 75°C, while a lead plate expands in both length and width when heated from 15°C to 95°C, resulting in a new area of 96.4464 cm². This demonstrates that understanding thermal expansion is crucial for applications where precise measurements are necessary, as it can significantly affect the dimensions and properties of materials.
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Recent questions
What is thermal expansion?
Thermal expansion is the phenomenon where materials change their dimensions in response to temperature variations. When an object is heated, its particles gain energy and move apart, causing the object to expand. Conversely, when the temperature decreases, the particles lose energy and come closer together, leading to contraction. This behavior is observed in solids, liquids, and gases, although the degree of expansion varies among different materials. Understanding thermal expansion is crucial in various applications, such as engineering and construction, where temperature fluctuations can significantly affect the integrity and functionality of structures and components.
How is Delta L calculated?
Delta L, or the change in length due to thermal expansion, is calculated using the formula: Delta L = Alpha × L₀ × Delta T. In this equation, Alpha represents the coefficient of linear expansion specific to the material, L₀ is the original length of the object, and Delta T is the change in temperature. This formula allows for the precise determination of how much an object will expand or contract when subjected to temperature changes. By knowing these variables, one can predict the dimensional changes in materials, which is essential for ensuring proper fit and function in various applications, from manufacturing to construction.
What happens to aluminum when heated?
When aluminum is heated, it undergoes thermal expansion, resulting in an increase in its length. For instance, if an aluminum bar measuring 1.25 meters at 20°C is heated to 75°C, the change in length can be calculated using the coefficient of linear expansion for aluminum, which is approximately 25 × 10⁻⁶ °C⁻¹. The resulting length change is about 0.000172 meters, leading to a new length of approximately 1.250172 meters, which can be rounded to 1.2502 meters. This expansion is a critical consideration in applications where aluminum components are used, as it can affect the fit and performance of assembled parts.
How does temperature affect a lead plate?
The temperature significantly affects the dimensions of a lead plate due to thermal expansion. For example, a lead plate measuring 8 cm by 12 cm at 15°C will experience changes in both length and width when the temperature rises to 95°C. The coefficient of linear expansion for lead is approximately 29 × 10⁻⁶ °C⁻¹. By applying the thermal expansion formula, the change in length can be calculated, resulting in an increase of about 0.02784 cm for the length. Consequently, the new length becomes 12.02784 cm. Similarly, the width will also change, affecting the overall area of the plate, which is crucial for applications where precise dimensions are necessary.
What is volume expansion?
Volume expansion refers to the increase in volume of a material when it is subjected to a rise in temperature. This phenomenon is described by the formula Delta V = Beta × V₀ × Delta T, where Beta is the coefficient of volume expansion, V₀ is the original volume, and Delta T is the temperature change. For solids, the coefficient of volume expansion is typically about three times the coefficient of linear expansion. For instance, if a brass solid with an initial volume of 240 cubic feet experiences an 80°C temperature increase, the change in volume can be calculated, resulting in a new volume of approximately 241.75 cubic feet. Understanding volume expansion is essential in various fields, including engineering and materials science, to ensure that structures can accommodate changes in volume without failure.
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Summary
00:00
Thermal Expansion Effects on Materials Explained
- Thermal expansion occurs when objects are heated, causing them to expand, and when cooled, leading to contraction, represented by the change in length, Delta L.
- Delta L is calculated using the formula: Delta L = Alpha × L₀ × Delta T, where Alpha is the coefficient of linear expansion, L₀ is the original length, and Delta T is the temperature change.
- For an aluminum bar of 1.25 m at 20°C, with Alpha = 25 × 10⁻⁶ °C⁻¹, increasing the temperature to 75°C results in a length change of approximately 0.000172 m.
- The new length of the aluminum bar after heating is 1.250172 m, which can be rounded to 1.2502 m.
- A lead plate measuring 8 cm × 12 cm at 15°C has a coefficient of linear expansion of 29 × 10⁻⁶ °C⁻¹; increasing the temperature to 95°C affects both length and width.
- The change in length for the lead plate is calculated as Delta L = 29 × 10⁻⁶ × 12 cm × 80°C, resulting in a change of approximately 0.02784 cm.
- The new length of the lead plate becomes 12.02784 cm, while the change in width is calculated similarly, yielding a change of approximately 0.01856 cm.
- The new area of the lead plate is calculated as 96.4464 cm², with a change in area of about 0.446 cm², using the formula Delta A = L₀ × W₀ × 2AlphaDeltaT.
- Volume expansion is described by Delta V = Beta × V₀ × Delta T, where Beta is the coefficient of volume expansion, and for solids, Beta is approximately three times Alpha.
- For a brass solid with an initial volume of 240 cubic feet and a temperature increase of 80°C, the change in volume is 1.75 cubic feet, resulting in a new volume of 241.75 cubic feet.
25:55
Calculating Volume Change with Temperature Variation
- To calculate volume change (ΔV), use the formula ΔV = V * β * ΔT, where β ≈ 3 * α, with α being the linear expansion coefficient and ΔT the temperature change.
