Question

Which of the following option(s) is/are correct for a Type I superconductor?

• A. The phase transition to the normal state in the absence of a magnetic field is of second order
• B. With increase in temperature, the critical magnetic field decreases linearly to zero
• C. Below the critical temperature, the entropy in the superconducting state is less than that in the normal state
• D. The phase transition to the normal state in the presence of a magnetic field is of first order

Hint:

In Type I superconductors, the phase transition to the normal state in the absence of a magnetic field is second-order, and in the presence of a magnetic field, it is first-order. Additionally, the superconducting state has lower entropy than the normal state.

Answer 1

The Correct Option is A, C, D

1. Option (A): The phase transition to the normal state in the absence of a magnetic field is of second order:
This statement is true for Type I superconductors. The phase transition from the superconducting state to the normal state, when there is no external magnetic field, is second-order. This means that at the critical temperature, the superconducting properties gradually vanish without a latent heat being involved.
Therefore, (A) is correct.

2. Option (B): With increase in temperature, the critical magnetic field decreases linearly to zero:
This statement is incorrect for Type I superconductors. In Type I superconductors, the critical magnetic field \( H_c \) decreases as the temperature approaches the critical temperature \( T_c \), but it does not follow a linear relationship. Instead, it decreases in a more complex way, typically in the form of a power law or other nonlinear dependence.
Therefore, (B) is incorrect.

3. Option (C): Below the critical temperature, the entropy in the superconducting state is less than that in the normal state:
This statement is true for Type I superconductors. In the superconducting state, the entropy is lower compared to the normal state, which reflects the fact that superconductivity is a more ordered phase with less randomness in the system.
Therefore, (C) is correct.

4. Option (D): The phase transition to the normal state in the presence of a magnetic field is of first order:
This statement is true for Type I superconductors. When a magnetic field is applied, the phase transition from the superconducting state to the normal state is of first order. This means there is a discontinuous change in the properties, such as a jump in the magnetization, at the critical temperature.
Therefore, (D) is correct.

Thus, the correct options are (A), (C), and (D).