Critical temperature of a superconductor

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Discussion Overview

The discussion revolves around the critical temperature (TC) of superconductors and its dependence on the isotopic mass of the element. Participants explore a specific problem involving the calculation of TC for different isotopic molar masses, examining the relationship defined by the equation TC * square root(M) = constant.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents a problem involving the calculation of TC for an isotopic molar mass of 136.3 g, given that TC for lead is 7.184 K at 207.7 g.
  • Another participant confirms that the approach taken is generally correct and asks for the calculated answer.
  • A participant shares their initial calculation of TC as 5.8196 K but expresses uncertainty about its correctness.
  • Another participant notes that a decrease in mass should result in an increase in TC, suggesting a potential error in the setup of the problem.
  • A participant revises their calculation and arrives at a new value of 8.868 K, indicating a possible correction in their approach.
  • Several participants acknowledge agreement on the revised value of TC.

Areas of Agreement / Disagreement

While there is some agreement on the revised calculation of TC as 8.868 K, the discussion reflects uncertainty regarding the initial setup and calculations, indicating that some aspects remain unresolved.

Contextual Notes

Participants have not fully detailed their mathematical steps, and there may be assumptions about the relationship between isotopic mass and critical temperature that are not explicitly stated.

viviane363
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I have this problem here that I don't understand:
The critical temperature of a superconductor, TC varies with the isotopic mass of the element making up the superconductor, M, according to the relation TC *square root(M) = a constant. In lead, TC = 7.184 K for the isotopic molar mass 207.7 g. What is the critical temperature for the isotopic molar mass 136.3 g?

What I did since TC *square root(M) = a constant, I wrote the same formula for the temp we are looking for and said that both equality are equal since a is constant, and then solve for TC(the one we are looking for), but the answer doesn't seem right.
Can you tell me what I am supposed to do? thanks
 
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Sounds like you're on the right track. What answer did you get?
 


I got 5.8196 K but it doesn't seem to be the right answer
 


You are right, since if the mass goes down then the TC should go up in order to compensate.

How did you set up the problem? (In mathematical terms so I can see where you went wrong)

I would guess it's a simple algebraic error.
 


i pose TC1*square root(M1)= a = TC2*square root(M2) oh! i might have made a mistake of rearranging and solving.now i got 8.868 K
 


Yea, that's what I got too.
 


Thank you very much
 

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