Final answer:
The fractional change in length (Δl/l0) of a rod as its temperature increases by 84.0 °C is calculated using the formula Δl = αl0ΔT, where α is the coefficient of linear expansion and ΔT is the temperature change. The original length is not required as it cancels out in the equation Δl/l0 = αΔT.
Step-by-step explanation:
The question pertains to the fractional change in length (Δl/l0) of a rod made from a certain material as its temperature increases by 84.0 °C, without knowing the original length or the starting temperature. The equation for linear thermal expansion, which is Δl = αl0ΔT, can be used to find the fractional change in length. Here, α is the coefficient of linear expansion, l0 is the original length, and ΔT is the change in temperature.
To find the fractional change in length, we rearrange the equation as follows: Δl/l0 = αΔT. Since l0 is the same in both the numerator and denominator, it cancels out, and we don't need the original length to calculate the fractional change. Therefore, knowing the coefficient of linear expansion α, we can calculate the fractional change in length caused by the temperature increase of 84.0 °C.
If the specific coefficient of linear expansion for the material is known, one can plug in the values and solve for Δl/l0. However, without the value of α, we cannot provide a numerical answer.