Question

A length of aluminum wire is connected to a precision 10.00-V power supply, and a current of 0.4192 A is precisely measured at 23.5 ∘C. The wire is placed in a new environment of unknown temperature where the measured current is 0.3718 A . The temperature coefficient of resistivity of aluminum is 0.00429 (∘C)−1.

What is the unknown temperature?

Answer 1

The unknown temperature can be found using the temperature coefficient of resistivity formula, which measures how much the resistance of a material changes with temperature. By rearranging the formula and plugging in the given values, we can calculate the change in temperature to be approximately -7.025 °C. To find the unknown temperature, we add this change to the initial temperature of 23.5 °C.

Step-by-step explanation:

The unknown temperature can be found using the temperature coefficient of resistivity formula:

α = (ρ_2 - ρ_1) / (ρ_1 * ΔT)

Where α is the temperature coefficient of resistivity, ρ_1 and ρ_2 are the resistivity values at temperatures T_1 and T_2 respectively, and ΔT is the change in temperature. Rearranging the formula, we have:

ΔT = (ρ_2 - ρ_1) / (α * ρ_1)

Plugging in the values, we have

ΔT = (ρ_2 - ρ_1) / (α * ρ_1) = (0.3718 - 0.4192) / (0.00429 * 0.4192)

Solving for ΔT, we find that the change in temperature is approximately -7.025 °C (negative because the resistance decreases as temperature increases). To find the unknown temperature, we add this change to the initial temperature of 23.5 °C:

Unknown temperature = 23.5 + (-7.025) = 16.475 °C