Question

At what temperature will silver have a resistivity that is two times the resistivity of iron at room temperature? (Assume room temperature is 20° C.)

Answer 1

The temperature of silver at this given resistivity is 2971.1 ⁰C

Step-by-step explanation:

The resistivity of silver is calculated as follows;

`R_t = R_o[1 + \alpha(T-T_o)]\\\\`

where;

Rt is the resistivity of silver at the given temperature

Ro is the resistivity of silver at room temperature

α is the temperature coefficient of resistance

To is the room temperature

T is the temperature at which the resistivity of silver will be two times the resistivity of iron at room temperature

`R_t = R_o[1 + \alpha(T-T_o)]\\\\\R_t = 1.59*10^(-8)[1 + 0.0038(T-20)]`

Resistivity of iron at room temperature = 9.71 x 10⁻⁸ ohm.m

When silver's resistivity becomes 2 times the resistivity of iron, we will have the following equations;

`R_t,_(silver) = 2R_o,_(iron)\\\\1.59*10^(-8)[1 + 0.0038(T-20)] =(2 *9.71*10^(-8))\\\\\ \ (divide \ through \ by \ 1.59*10^(-8))\\\\1 + 0.0038(T-20) = 12.214\\\\1 + 0.0038T - 0.076 = 12.214\\\\0.0038T +0.924 = 12.214\\\\0.0038T = 12.214 - 0.924\\\\0.0038T = 11.29\\\\T = (11.29)/(0.0038) \\\\T = 2971.1 \ ^0C`

Therefore, the temperature of silver at this given resistivity is 2971.1 ⁰C