An iron plate is a 10 cm square at 12 °C. The linear expansion coefficient of iron is 11 x 10-6/°C. Calculate: b) The new area at 51 °C.
To calculate the new area of the iron plate at 51 °C, we need to first calculate the change in dimensions of the plate from 12 °C to 51 °C using the linear expansion coefficient of iron.
The change in temperature is 51 °C - 12 °C = 39 °C
The change in length (ΔL) can be calculated using the formula:
ΔL = α * L * ΔT
where α is the linear expansion coefficient, L is the original length, and ΔT is the change in temperature.
ΔL = (11 x 10^(-6)/°C) * 10 cm * 39 °C
ΔL = 0.00429 cm
Since the change is uniform in both dimensions (length and width), we can assume that the plate expands equally in both directions. Therefore, the new dimensions of the plate will be:
Length = 10 cm + ΔL = 10 cm + 0.00429 cm = 10.00429 cm
Width = 10 cm + ΔL = 10 cm + 0.00429 cm = 10.00429 cm
The new area of the plate can be calculated as:
New area = Length * Width
New area = 10.00429 cm * 10.00429 cm
New area = 100.086 cm^2
Therefore, the new area of the iron plate at 51 °C is approximately 100.086 cm^2.