The Concept of Thermal Expansion: Finding the Final Temperature
How can we determine the final temperature of an aluminum baseball bat when its length changes with temperature?
Given: An aluminum baseball bat has a length of 0.86 m at a temperature of 17 °C. When the temperature of the bat is raised, the bat lengthens by 0.00016 m. Determine the final temperature of the bat.
Answer:
The question involves the concept of thermal expansion to find the final temperature of an aluminum baseball bat. By using the formula for thermal expansion and given the initial length, the final length, and the initial temperature of the bat, one can compute for the final temperature.
This question is about thermal expansion, which describes how the size of an object changes with a change in temperature. Specifically, it asks for the final temperature of the aluminum baseball bat, given its initial length, final length, and initial temperature.
The formula for linear thermal expansion is ΔL = αLΔT, where ΔL is the change in length, L is the initial length, ΔT is the change in temperature, and α is the coefficient of linear expansion for the material (in this case, aluminum, which has a α value of approximately 22 x 10^-6 °C^-1).
Substituting the given values, (0.86 m + 0.00016 m = 0.86 m + α * 0.86 m * ΔT), we find that the ΔT = (0.00016 m) / (22 x 10^-6 °C^-1 * 0.86 m), then add this ΔT to the initial temperature of 17 °C to find the final temperature.
For a more in-depth understanding of thermal expansion and its applications, feel free to explore more resources on the topic.