Critical temperature of a superconductor

In summary, the critical temperature of a superconductor, TC, is related to the isotopic mass, M, by the equation TC * square root(M) = a constant. For lead, with an isotopic molar mass of 207.7 g, TC = 7.184 K. To find the critical temperature for an isotopic molar mass of 136.3 g, the same equation can be used and solved for TC. After correcting a possible algebraic error, the correct answer is 8.868 K. This aligns with the understanding that as the mass decreases, the critical temperature should increase.
  • #1
viviane363
17
0
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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  • #2


Sounds like you're on the right track. What answer did you get?
 
  • #3


I got 5.8196 K but it doesn't seem to be the right answer
 
  • #4


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.
 
  • #5


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
 
  • #6


Yea, that's what I got too.
 
  • #7


Thank you very much
 

1. What is the critical temperature of a superconductor?

The critical temperature of a superconductor is the temperature at which it transitions from its superconducting state to its normal conducting state. This is often referred to as the "critical temperature" or "transition temperature".

2. How is the critical temperature of a superconductor determined?

The critical temperature of a superconductor is determined by measuring its resistance as the temperature is gradually decreased. When the superconductor reaches its critical temperature, its resistance suddenly drops to zero.

3. What factors can affect the critical temperature of a superconductor?

The critical temperature of a superconductor can be affected by several factors, including the material it is made of, impurities in the material, and external magnetic fields. In general, higher quality materials and lower levels of impurities can result in a higher critical temperature.

4. Why is the critical temperature of a superconductor important?

The critical temperature of a superconductor is important because it is the temperature at which the superconductor can exhibit its unique properties, such as zero electrical resistance and perfect diamagnetism. It also allows scientists to study the effects of temperature on superconductivity and potentially discover new materials with higher critical temperatures.

5. Can the critical temperature of a superconductor be increased?

Yes, the critical temperature of a superconductor can be increased through various methods, such as improving the quality of the material, reducing impurities, and applying external pressure or magnetic fields. However, there is currently a theoretical limit to the critical temperature that a superconductor can achieve, known as the BCS theory limit.

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