Final answer:
To find when an aluminum rod will fit a hole in a hot engine block, calculate the temperature change using the coefficient of linear expansion for aluminum. However, the notion of a rod fitting loosely due to temperature differences is flawed, as engine components are designed with expansion tolerances.
Step-by-step explanation:
When examining the fit of connecting rods in a radial engine, the subject of thermal expansion is crucial. As a given material, like aluminum, heats up, it expands. If a cold aluminum rod fits loosely into its hole on an aluminum engine block, and the hole is 10.0% bigger than the rod at 22.0°C, we can calculate the temperature at which the rod will expand to fit the hole perfectly by using the coefficient of linear expansion for aluminum.
To find the necessary temperature change, ΔT, we'll use the formula ΔL/L = αΔT. In this case, ΔL/L is 10.0% or 0.1, and the coefficient of linear expansion for aluminum (α) is approximately 22×10⁻⁶/C. Reorganizing the formula to solve for ΔT gives us ΔT = ΔL/(Lα). Considering the 10.0% increase in diameter corresponds to 0.1 times the original length (L), we can plug in the values to solve for ΔT.
The temperature at which the rod will match the hole can then be calculated by adding the temperature change ΔT to the original temperature of the rod, 22.0°C. However, the resulting temperature might exceed reasonable operational limits for the engine or aluminum, making the scenario unrealistic. Furthermore, the initial premise that an aluminum rod fits loosely in an aluminum block due to temperature differences is flawed because typically, components in engines are designed to operate at various temperatures, and allowances for expansion are made within their design specifications.