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.

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Tide

Homework Helper
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

Homework Helper
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

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

Carl

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