What temperature change is required to change the length of a 5.5-m steel beam by 0.0012 m?
what's the coefficient of expansion? Look at the units.
ΔT = __________ K
doesn't it have units something like m/°K ?
No thats it :(
To find the temperature change required to change the length of the steel beam, you can use the coefficient of linear expansion for steel. The formula to calculate the change in length is:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L0 is the original length of the beam
ΔT is the temperature change
In this case, we are given ΔL = 0.0012 m and L0 = 5.5 m.
To find the coefficient of linear expansion for steel, you can refer to a reference book or search online. The coefficient of linear expansion for steel is approximately 11 x 10^-6 /°C or 11 x 10^-6 /K.
Substituting the known values into the formula:
0.0012 m = (11 x 10^-6 /°C) * (5.5 m) * ΔT
Simplifying the equation:
ΔT = 0.0012 m / [(11 x 10^-6 /°C) * (5.5 m)]
ΔT = 0.0012 m / (60.5 x 10^-6 /°C)
ΔT ≈ 19.83°C
Therefore, a temperature change of approximately 19.83°C is required to change the length of the 5.5 m steel beam by 0.0012 m.