An iron plate is a 10 cm square at 12 °C. The linear expansion coefficient of iron is 11 x 10-6/°C. Calculate: b) The lengths of the sides at 51 °C.
To calculate the lengths of the sides at 51°C, we first need to calculate the increase in temperature from 12°C to 51°C:
ΔT = 51°C - 12°C = 39°C
Next, we can use the linear expansion formula to calculate the change in length of the sides:
ΔL = α * L * ΔT
Where:
ΔL = Change in length
α = Linear expansion coefficient (11 x 10^-6/°C)
L = Initial length (10 cm)
ΔT = Change in temperature (39°C)
Now, we can calculate the change in length:
ΔL = 11 x 10^-6 * 10 cm * 39°C
ΔL = 0.00429 cm
Since the change in length will be the same for all sides of the square plate, the final length of the sides at 51°C can be calculated as:
Length at 51°C = Initial length + Change in length
Length at 51°C = 10 cm + 0.00429 cm
Length at 51°C = 10.00429 cm
Therefore, the length of the sides of the iron plate at 51°C is approximately 10.00429 cm.