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 temperature of the metal plate if it is heated until the sides are 1,005 m long.
To calculate the temperature of the metal plate when the sides are 1.005m long, we first need to find the change in length of the sides due to the expansion of the metal.
Given:
Initial side length (L1) = 1m
Final side length (L2) = 1.005m
Linear coefficient of expansion (α) = 12.5 x 10^-6 / K
The change in length (ΔL) can be calculated using the formula:
ΔL = L2 - L1
Plugging in the values:
ΔL = 1.005m - 1m
ΔL = 0.005m
Now, we can use the linear expansion formula to find the temperature change (ΔT):
ΔL = α * L1 * ΔT
Plugging in the values:
0.005m = (12.5 x 10^-6 / K) * 1m * ΔT
Solving for ΔT:
ΔT = 0.005m / (12.5 x 10^-6)
ΔT = 400 K
Finally, we can find the temperature of the metal plate when the sides are 1.005m long:
Temperature = Initial temperature + ΔT
Temperature = 283K + 400K
Temperature = 683K
Therefore, the temperature of the metal plate when the sides are 1.005m long is 683K.