An iorn rod (a=11.8 x 10^-6C^-1) has a length of 1000 meters(or 1 km) at 0 degrees Celsius. If the rod must expand 10 cm to bridge a gap, to what temperature must the rod be heated?
To find the temperature to which the iron rod must be heated in order to expand 10 cm, we can use the formula for linear thermal expansion:
ΔL = α * L * ΔT
where:
ΔL is the change in length of the rod
α is the coefficient of linear expansion
L is the original length of the rod
ΔT is the change in temperature
In this case, the change in length (ΔL) is 10 cm, or 0.1 meters. The original length (L) is given as 1000 meters. The coefficient of linear expansion (α) is 11.8 x 10^-6 C^-1.
Now, we can rearrange the formula to solve for ΔT:
ΔT = ΔL / (α * L)
Substituting the given values:
ΔT = 0.1 / (11.8 x 10^-6 * 1000)
Calculating this expression:
ΔT = 0.1 / 0.0118
ΔT ≈ 8.47
Therefore, the rod must be heated by approximately 8.47 degrees Celsius in order to expand 10 cm and bridge the gap.