An iron plate is 10cm square at 12°c The linear expansion cofficient is 11×10 CALCULATE the area expansion cofficient of iron

Answer 1

To calculate the area expansion coefficient of iron, we first need to calculate the linear expansion of the iron plate when its temperature is increased to a higher temperature, let's say T °C.

Given:
Initial temperature, T1 = 12°C
Initial side length of iron plate, L1 = 10 cm
Linear expansion coefficient of iron, α = 11×10^(-6) per °C

Linear expansion ΔL can be calculated using the formula:
ΔL = α * L1 * ΔT
where ΔT is the change in temperature, T - T1.

Let's consider an increase in temperature of ΔT °C, thus T = 12 + ΔT.

So, the new side length (L2) of the iron plate after the temperature increase can be calculated as:
L2 = L1 + ΔL
L2 = L1 + α * L1 * ΔT
L2 = L1(1 + α*ΔT)

Now, the area expansion coefficient β can be calculated as:
β = 2α

Let's calculate the value of β using the given linear expansion coefficient α:
β = 2 * 11×10^(-6)
β = 22×10^(-6) per °C

Therefore, the area expansion coefficient of iron is 22×10^(-6) per °C.