Calculation of surface area of thin aluminium

A thin aluminium has a surface area of 1.5m² at 0°C. We are required to determine its surface area when it is cooled to -20°C, considering the linear expansivity of aluminium to be 2.5×10^-5k^-1.

Let the final surface area of aluminium be 'A'. The initial surface area of aluminium, 'A_0', is given as 1.5m². The change in temperature, ΔT, is (-20°C - 0°C) = -20°C. The linear expansivity of aluminium, α, is given as 2.5×10^-5k^-1.

Using the formula for linear expansion of solids, we can write:

ΔL = α * L * ΔT

where ΔL is the change in length, L is the original length, α is the linear expansivity, and ΔT is the change in temperature.

Since we are interested in the change in surface area, we can write:

ΔA = 2 * L * ΔL

where ΔA is the change in surface area, L is the length of the aluminium, and ΔL is the change in length.

We can rearrange the formula for ΔL to get:

ΔL = (α * L * ΔT)

Substituting this into the formula for ΔA, we get:

ΔA = 2 * L * (α * L * ΔT)

Simplifying, we get:

ΔA = 2αL²ΔT

Substituting the given values, we get:

ΔA = 22.5×10^-5 (1.5²) * (-20)

ΔA = -0.0018m²

Therefore, the final surface area of the thin aluminium will be:

A = A_0 + ΔA

A = 1.5 - 0.0018

A = 1.4982m²

Hence, the surface area of the thin aluminium when it is cooled to -20°C will be 1.4982m².