## For a type-I superconductor, find the jump in entropy and specific heat across the transition from a superconductor to a normal state.

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1. (a) For a type-I superconductor, find the jump in entropy and specific heat across the transition from a superconductor to a normal state. Given the free energy variation between the normal (FN ) and superconducting (FS) phases at zero magnetic field is given by,

where µ0 is the permeability of the free space and Hc is the critical magnetic field whose temperature variation is emperically given by,

Tc being the transition temperature. Express your answer in terms of Hc(0), T, Tc and µ0.

2. (a) A superconducting Sn has a critical temperature of 3.7 K at zero magnetic field and a critical magnetic field of 0.036 T at 0 K. Find the critical field at 2K.

(b) Calculate the critical current and current density for a Pb wire have a diameter 1 mm at 4.2K. Tc for Pb is 7.18 K and Hc = 6.5 × 104 Am−1

3. Find the susceptibility and relative permeability of an ideal superconductor.

4. Derive expressions for the coherence length of superconductors using Heisenberg uncertainty principle. What is the typical value of the coherence length for a conventional superconductor?

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