Answer:
The transition temperature is 0.920 K and the critical field at 0 K is 8.956 Wb/m².
Step-by-step explanation:
To determine the transition temperature and critical field at 0 K, we need to use the following formula:
Bc(T) = Bc(0)[1-(T/Tc)^2]
where:
Bc(T) = critical magnetic field at temperature T
Bc(0) = critical magnetic field at 0 K
T = temperature
Tc = transition temperature
We have the critical fields at 6 K and 8 K:
Bc(6 K) = 7.616 Wb/m²
Bc(8 K) = 4.284 Wb/m²
We can use these values to find the transition temperature:
7.616 = Bc(0)[1-(6/Tc)^2]
4.284 = Bc(0)[1-(8/Tc)^2]
Dividing the two equations, we get:
7.616/4.284 = [1-(6/Tc)^2]/[1-(8/Tc)^2]
Simplifying the right-hand side:
7.616/4.284 = [(8/Tc)^2 - 1]/[(6/Tc)^2 - 1]
Let x = (8/Tc)^2
Then (6/Tc)^2 = x/64
Substituting into the equation above:
7.616/4.284 = (x - 1)/(x/64 - 1)
Simplifying:
7.616/4.284 = 64(x - 1)/(x - 64)
Multiplying both sides by (x - 64):
7.616/4.284 * (x - 64) = 64(x - 1)
Simplifying:
(x - 64)/(x - 1) = 7.616/4.284 * 1/64
Multiplying both sides by (x - 1):
x - 64 = 7.616/4.284 * 1/64 * (x - 1)
Simplifying:
x = 74.14
Substituting back into (8/Tc)^2 = x:
(8/Tc)^2 = 74.14
8/Tc = ±8.607
Tc = 0.920 K or 0.103 K
Since the transition temperature should be higher than the critical field at 0 K, we choose Tc = 0.920 K.
Now we can use either of the equations for Bc(T) to find Bc(0):
7.616 = Bc(0)[1-(6/0.920)^2]
Bc(0) = 8.956 Wb/m²
Therefore, the transition temperature is 0.920 K and the critical field at 0 K is 8.956 Wb/m².