Question

A metal plate is a 1 m square at 283 K. There is a hole of 600 mm in diameter in the The linear coefficient of expansion of the metal is 12,5 x 10-6/K. Calculate: a) The diameter of the hole at this temperature.

Answer 1

The increase in area of the hole at this temperature

Answer 2

To calculate the diameter of the hole at 283 K, we first need to calculate the change in temperature from the original temperature to 283 K:

ΔT = 283 K - 293 K = -10 K

Now, we can calculate the change in the side length of the metal plate using the linear coefficient of expansion:

ΔL = α * L * ΔT
ΔL = 12.5 x 10^-6/K * 1 m * -10 K
ΔL = -0.000125 m

The change in diameter of the hole will be twice the change in side length of the metal plate:

Δd = 2 * ΔL
Δd = 2 * -0.000125 m
Δd = -0.00025 m

Finally, we can calculate the diameter of the hole at 283 K:

d1 = 0.6 m (original diameter)
d2 = d1 + Δd
d2 = 0.6 m - 0.00025 m
d2 ≈ 0.59975 m

Therefore, the diameter of the hole at 283 K is approximately 0.59975 m.