Resistivity and Temperature

[langenase]

Homework Statement

I'm supposed to estimate at what temp. copper will have the same resistivity as tungsten at 20 deg. C.

Homework Equations

The only equation I think is relevant is
p=p0[1+alpha(T-T0)]

The Attempt at a Solution

I know the resistivity of both copper and tungsten at 20 degrees C. I just don't know what I should do about the resistivity, p0, at temperature, T0 since I don't know either of those quantities.
I can't cancel those variables out when I set p(tungsten)=p(copper) so I'm not sure what to do.

 

[dynamicsolo]

Homework Equations

The only equation I think is relevant is
p=p0[1+alpha(T-T0)]

The Attempt at a Solution

I know the resistivity of both copper and tungsten at 20 degrees C. I just don't know what I should do about the resistivity, p0, at temperature, T0 since I don't know either of those quantities.
I can't cancel those variables out when I set p(tungsten)=p(copper) so I'm not sure what to do.

T0 is whatever temperature you want to use as a reference. Since you have resistivities for these metals at 20º C., that will be your T0. You want to find the temperature at which copper has the same resistivity as tungsten at 20ºC., so which resistivity goes where in the equation you gave?

The only real issue now is: what value are you supposed to use for alpha, which is the coefficient for the rate at which resistivity changes with temperature (it would have units of ohm-m/C (or K)? Are you working from tables in a text?

 

[m2003]

As a scientist, the first step in solving this problem would be to gather more information. The equation provided, p=p0[1+alpha(T-T0)], is known as the temperature coefficient of resistivity and can be used to calculate the change in resistivity with temperature. In this equation, p0 is the resistivity at a reference temperature, T0, and alpha is the temperature coefficient of resistivity. Without knowing the values for p0 and T0 for both copper and tungsten, it is impossible to solve for the temperature at which they will have the same resistivity.

To solve this problem, you will need to find the resistivity values for both copper and tungsten at a different temperature, preferably one that is close to the reference temperature T0. Once you have these values, you can plug them into the equation and solve for T, the temperature at which they will have the same resistivity.

Additionally, it is important to note that the temperature coefficient of resistivity, alpha, is not constant and can vary for different materials. Therefore, it is important to use accurate and up-to-date values for alpha when solving this problem.

In summary, to estimate at what temperature copper will have the same resistivity as tungsten at 20 degrees C, you will need to gather more information, specifically the resistivity values for both materials at a different temperature, and use the temperature coefficient of resistivity equation to solve for the temperature at which they will have the same resistivity.