Askiitians Tutor Team
Last Activity: 14 Days ago
To understand why the length of the scale decreases even after returning to the original temperature, we need to delve into the concept of thermal expansion and how materials behave under temperature changes. The formula you provided, ΔL = L × α × ΔT, is indeed a fundamental equation for linear thermal expansion, where ΔL is the change in length, L is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature.
Thermal Expansion Basics
When a material is heated, its particles gain energy and move more vigorously, causing the material to expand. Conversely, when it cools, the particles lose energy and the material contracts. This behavior is consistent across most materials, but the degree of expansion or contraction depends on the material's properties, specifically the coefficient of linear expansion (α).
Step-by-Step Analysis
- Initial Length Calculation: You start with a scale of 100 cm at 20 degrees Celsius. The coefficient of linear expansion (α) is given as 10-2 per degree Celsius.
- Heating the Scale: When you increase the temperature from 20 to 30 degrees Celsius, the change in temperature (ΔT) is 10 degrees. Plugging this into the formula gives:
ΔL = 100 cm × 10-2 × (30 - 20) = 100 × 0.01 × 10 = 10 cm.
So, the new length becomes 100 cm + 10 cm = 110 cm.
- Cooling the Scale: Now, when you decrease the temperature back to 20 degrees Celsius, the change in temperature is from 30 to 20 degrees, which is -10 degrees. Using the new length of 110 cm:
ΔL = 110 cm × 10-2 × (20 - 30) = 110 × 0.01 × (-10) = -11 cm.
This means the scale contracts by 11 cm, resulting in a final length of 110 cm - 11 cm = 99 cm.
Understanding the Discrepancy
The key point here is that the amount of expansion and contraction is not the same due to the different lengths involved at each temperature. When the scale was heated to 110 cm, it expanded based on that new length. When it cooled back down, it contracted from that longer length, resulting in a final length of 99 cm instead of returning to the original 100 cm.
Real-World Analogy
Think of it like a balloon. When you blow air into a balloon, it expands. If you then let some air out, the balloon shrinks, but not necessarily back to its original size because the material has been stretched. Similarly, the scale's material has undergone a change in structure due to the heating and cooling process, leading to a permanent change in its length.
Conclusion
This phenomenon highlights an important aspect of material science: the behavior of materials under thermal stress can lead to irreversible changes. Understanding these principles is crucial in fields like engineering and construction, where precise measurements and material properties are vital for safety and functionality.