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.
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.