A steel bar has an initial length of 40 meters when the temperature is 20 oC. At what final
temperature will the steel bar have a final length of 40.01 meters? The coefficient of linear expansion of steel is 12E-6 (1/C).
L = 40 + 12*10^-6/Co(T-20) = 40.01.
40 + 12*10^-6T - 240*10^-6 = 40.01.
40 - 0.00024 + 12*10^-6T = 40.01.
39.99976 + 12*10^-6 = 40.01.
12*10^-6T = 40.01 - 39.99976 = 0.01024.
T = 853.333 Degrees C.
To find the final temperature at which the steel bar will have a final length of 40.01 meters, we can use the formula for linear expansion:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the initial length
ΔT is the change in temperature
In this case, we want to find the final temperature (ΔT). We know that the initial length (L) is 40 meters, the change in length (ΔL) is 40.01 - 40 = 0.01 meters, and the coefficient of linear expansion (α) is 12E-6 1/°C.
Rearranging the formula, we get:
ΔT = ΔL / (α * L)
Now, let's substitute the values:
ΔT = 0.01 / (12E-6 * 40)
Calculating this, we find:
ΔT ≈ 0.01 / (0.00048)
ΔT ≈ 20.83 °C
Therefore, the steel bar will have a final length of 40.01 meters at a final temperature of approximately 20.83 °C.