A metal plate is a 1 m square at 283 K. There is a hole of 600 mm in diameter in the centre. The linear coefficient of expansion of the metal is 12,5 × 10-6/K. Calculate c) The increase in area of the hole at this temperature.
To calculate the increase in area of the hole at 283 K, we first need to determine the original area of the hole and then calculate the change in area with an increase in temperature.
Given:
Original diameter of the hole, D = 600 mm = 0.6 m
Original radius of the hole, r = D/2 = 0.6/2 = 0.3 m
Original area of the hole = πr^2 = π(0.3)^2 = 0.09π m^2
The increase in temperature, ΔT = 283 K
Linear coefficient of expansion, α = 12.5 × 10^-6/K
Change in temperature, ΔT = 283 K
Change in area of the hole = Original area of the hole * 2αΔT
Change in area of the hole = 0.09π * 2*12.5×10^-6 * 283
Change in area of the hole ≈ 0.09π * 7.125×10^-3
Change in area of the hole ≈ 0.000639π m^2
Therefore, the increase in area of the hole at 283 K is approximately 0.000639π m^2.