A rectangular aluminum plate has an area of 0.41 m2 at 23°C. If it is heated until its area has increased by 4.4 10-6 m2, what is the final temperature of the plate?
°C
To determine the final temperature of the plate, we can use the formula for thermal expansion:
ΔA = α * A * ΔT,
where ΔA represents the change in area, α represents the coefficient of linear expansion for aluminum, A represents the initial area, and ΔT represents the change in temperature.
Given:
ΔA = 4.4 * 10^(-6) m^2 (change in area)
A = 0.41 m^2 (initial area)
α = coefficient of linear expansion for aluminum
ΔT = final temperature - 23°C (change in temperature)
To find α, we need the coefficient of linear expansion for aluminum. Assuming that this is not given, we will use the approximate value of α = 2.3 * 10^(-5) °C^(-1), which is a commonly used value for aluminum.
Substituting the given values into the formula, we have:
4.4 * 10^(-6) = (2.3 * 10^(-5) °C^(-1)) * (0.41 m^2) * ΔT.
Simplifying the equation, we get:
ΔT = (4.4 * 10^(-6)) / ((2.3 * 10^(-5) °C^(-1)) * (0.41 m^2)).
Calculating this expression gives us ΔT = 0.0533 °C.
Therefore, the final temperature of the plate is 23°C + 0.0533°C = 23.0533°C.