Question

Consider a metal rod that is 2.51 m in length at a temperature of 11.5°c. The coefficient of linear expansion is 4.82×10-5°c-1. Suppose you have another rod made of the same material. You don't know the original length or the starting temperature, but you do know that the temperature increases by 84.0 c°. What is the fractional change in length (Δl/l0)?

Answer 1

The fractional change in length due to thermal expansion is found by multiplying the coefficient of linear expansion by the change in temperature. When simplified, the original length cancels out and isn't needed in the calculation.

Step-by-step explanation:

To calculate the fractional change in length (Δl/l0) of a rod due to thermal expansion, you can use the formula Δl = αΔTl0, where Δl is the change in length, α is the coefficient of linear expansion, ΔT is the change in temperature, and l0 is the original length of the rod. Given that the coefficient of linear expansion (α) is 4.82×10-5°C-1 and the change in temperature (ΔT) is 84.0 °C, the fractional change in length is simply the product of α and ΔT since the original length (l0) will cancel out when calculating Δl/l0. Therefore, Δl/l0 = αΔT = (4.82×10-5°C-1)(84.0 °C).