To find the resistance of an aluminum wire at 424°C, given its initial resistance and temperature, and the temperature coefficient of resistivity, we apply the formula for temperature dependence of resistance. The resistance of the wire will increase due to the rise in temperature, calculated using the specific coefficient for aluminum.
The question relates to the effect of temperature on the resistance of an aluminum wire. To determine the wire's resistance at 424°C, when it is initially 4.50Ω at 24.0°C, we use the formula R = R_0(1 + α(T - T_0)), where R is the final resistance, R_0 is the initial resistance, α is the temperature coefficient of resistivity, and T and T_0 are the final and initial temperatures in Celsius respectively.
Plugging in the values: R = 4.50Ω(1 + 3.90 × 10^{-3}/°C × (424°C - 24.0°C)), we calculate the new resistance value. Therefore, the resistance of the aluminum wire at 424°C is obtained through this formula.
The resistance of an aluminum wire increases with temperature, and the temperature coefficient of resistivity is crucial for calculating the change. The resulting value gives us an understanding of how materials like aluminum behave under varying temperatures, which can be important in applications such as electrical wiring and power transmission.