Final answer:
The diameter of a circular hole in an aluminum plate will increase when the temperature is raised, due to the thermal expansion of the material. The expansion can be calculated using the coefficient of area expansion for aluminum, considering the change in area is related to the change in diameter for a circular hole.
Step-by-step explanation:
The question involves the concept of thermal expansion in materials, which in physics refers to the tendency of matter to change its shape, area, and volume in response to a change in temperature. When an aluminum plate heats up, the diameter of a hole in the plate will also increase. Since the thermal expansion is uniform, the change in the area of the hole can be determined by using the coefficient of area expansion of aluminum.
Let's denote the initial diameter of the hole as D0 and the final diameter as D, the initial temperature T0 as 23°C and the final temperature T as 90°C. The coefficient of area expansion α for aluminum is given as 4.6 × 10⁻⁵°C⁻ⁱ. To find the new diameter, we can use the formula for linear expansion and adapt it for area expansion:
A = A0 + αA0ΔT
Where A is the final area, A0 is the initial area, and ΔT is the change in temperature. Since the hole is circular, the area is related to the diameter by the equation A = π(d/2)^2. Solving for the final diameter using these equations gives us:
D = 2((A0 + αA0ΔT)/π)
Note that the expansion is very small, and this is reflected in the relatively small coefficient of area expansion for aluminum. The final answer will provide the increased diameter of the circular hole at the elevated temperature of 90°C.