Calculate the linear expansivity of a material of length 120m that assumes a new length of 12.05m when heated through a temperature of 90°C
Surely you mean the length was 12.0m. If so, then
12.05 = 12.0(1 + 90α)
1 + 90α = 1.004167
α = 0.004167/90 = 0.0000463
To calculate the linear expansivity of a material, we can use the formula:
Linear expansivity (α) = (final length - initial length) / (initial length * change in temperature)
Given:
Initial length (L1) = 120m
Final length (L2) = 12.05m
Change in temperature (ΔT) = 90°C
Using the formula, we can substitute these values to calculate the linear expansivity:
α = (L2 - L1) / (L1 * ΔT)
α = (12.05m - 120m) / (120m * 90°C)
First, let's convert the length from meters to centimeters so the units match:
L1 = 120m = 12000cm
L2 = 12.05m = 1205cm
Now we can substitute the values into the formula:
α = (1205cm - 12000cm) / (12000cm * 90°C)
α = -9780cm / 1080000cm * °C
Simplifying:
α ≈ -0.009°C^(-1)
Therefore, the linear expansivity of the material is approximately -0.009°C^(-1).