What is the temperature of the bath?

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Homework Help Overview

The discussion revolves around determining the temperature of a liquid bath based on the resistance changes of a gold wire. The problem involves concepts from thermodynamics and electrical properties of materials, specifically relating to resistivity and temperature coefficients.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the resistivity equation and its components, questioning the accuracy of the calculations and the assumptions made regarding temperature and resistance.

Discussion Status

There is an ongoing examination of the calculations provided by the original poster, with some participants affirming the use of the correct equation while others express skepticism about the resulting temperature. The conversation reflects a mix of validation and inquiry into the methodology used.

Contextual Notes

Participants note the unusual result of a very high temperature, suggesting potential implications about the nature of the bath, such as it being a molten salt bath. There is also an emphasis on ensuring the correct interpretation of the temperature coefficient and reference points.

lw11011
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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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What have you done so far?
 
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.
 
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

[tex]R = \alpha T[/tex]

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

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

Carl
 

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