What is the temperature of the bath?

[lw11011]

At 50 degrees Celsius, the resistance of a segment of gold wire is 54. When the wire is placed in a liquid bath, the resistance increases to 189. The temperature coefficient is 0.0034 (degrees Celsius)^-1 at 20 degrees Celsius.
What is the temperature of the bath? Answer in units of degrees Celsius.

 

[Tide]

What have you done so far?

 

[lw11011]

I tried to use the equation:
p-po = (po)a(T-To)
To= reference temperature
po= resistivity at that temperature
a= temperature coefficient of resistivity

So I did:
189-54 = (54)(0.0034)(T-50)

But I know the answer I got that way is wrong.

 

[CarlB]

It sure looks to me like you've got the right equation. Are you sure you solved it correctly?

The form of the equation that I am familiar with is

R = \alpha T

where T is given in degrees Kelvin. But this reduces to your form in either degrees K or degrees C (or F).

Carl

 

[lw11011]

When I use the formula I mentioned above, I get T=785.29 degrees Celsius. I don't know if I solved it incorrectly but I did:
189-54=(54)(0.0034)(T-50)
135=(0.1836)(T-50)
735.29=T-50
T= 785.29

 

[CarlB]

Sure looks right to me. But that's a mighty hot bath. Maybe a molten salt bath.

Carl