For lead the superconductivity occurs at 7.19 k when there is zero app...
Given information:
- Critical temperature of lead for zero applied magnetic field: 7.19 K
- Magnetic field at which superconductivity stops at 2.0 K: 0.074 T
Objective:
To determine the magnetic field at which superconductivity will not occur at any temperature.
Solution:
To understand the relationship between temperature, magnetic field, and superconductivity, we need to consider the concept of critical magnetic field.
Critical Magnetic Field (Hc):
The critical magnetic field is the maximum magnetic field that a superconductor can withstand while maintaining superconductivity at a given temperature. Beyond this critical field, the superconductivity is suppressed.
Temperature-Field Phase Diagram:
The temperature-field phase diagram represents the regions where superconductivity exists and where it is suppressed for a specific material. It shows the critical temperature (Tc) and critical magnetic field (Hc) values.
Given information on the temperature-field phase diagram:
- Tc = 7.19 K (critical temperature for zero applied magnetic field)
- Hc = 0.074 T at 2.0 K (critical magnetic field at 2.0 K)
Explanation:
To find the magnetic field at which superconductivity will not occur at any temperature, we need to determine the critical magnetic field at every temperature and identify the point where it becomes zero.
Step 1: Calculate Hc at 7.19 K:
Since the critical temperature for zero applied magnetic field is 7.19 K, the critical magnetic field at this temperature is 0 T.
Step 2: Interpolate Hc at 2.0 K:
The given information states that at 2.0 K, the critical magnetic field is 0.074 T. We can assume that the relationship between temperature and critical magnetic field is linear. Using this assumption, we can interpolate the critical magnetic field at 7.19 K.
Using the formula:
(Hc2 - Hc1) / (T2 - T1) = (H - Hc1) / (T - T1)
where:
Hc1 = 0 T (at 7.19 K)
Hc2 = 0.074 T (at 2.0 K)
T1 = 7.19 K
T2 = 2.0 K
H = unknown (the magnetic field at which superconductivity will not occur at any temperature)
Substituting the values into the formula:
(0.074 - 0) / (2.0 - 7.19) = (H - 0) / (T - 7.19)
Simplifying the equation:
0.074 / (-5.19) = H / (T - 7.19)
Cross-multiplying and solving for H:
H = (0.074 / -5.19) * (T - 7.19)
Step 3: Calculate H at T = 0 K:
To find the magnetic field at which superconductivity will not occur at any temperature, we can substitute T = 0 K into the equation we derived in Step 2.
H = (0.074 / -5.19) * (0 - 7