Explanation:

Second order phase transitions are continuous transitions from one phase to another without a sudden change in any thermodynamic quantity. Examples include liquid-gas transition, ferromagnetic-paramagnetic transition, and superconductor-normal transition.

Out of the given options, only entropy remains continuous during a second order phase transition. This can be explained as follows:

- Specific heat (option A): Specific heat is defined as the amount of heat required to raise the temperature of a substance by one degree. During a second order phase transition, the specific heat usually diverges (i.e., becomes infinite) at the transition point, indicating the presence of critical fluctuations. Therefore, specific heat is not continuous during a second order phase transition.

- Magnetic susceptibility (option C): Magnetic susceptibility is a measure of the response of a material to an applied magnetic field. During a second order phase transition, the magnetic susceptibility may diverge or become very large, indicating the presence of critical phenomena. Therefore, magnetic susceptibility is not continuous during a second order phase transition.

- Isothermal compressibility (option D): Isothermal compressibility is a measure of the change in volume of a substance in response to a change in pressure at constant temperature. During a second order phase transition, the isothermal compressibility may diverge or become very large, indicating the presence of critical fluctuations. Therefore, isothermal compressibility is not continuous during a second order phase transition.

- Entropy (option B): Entropy is a thermodynamic quantity that measures the degree of disorder or randomness in a system. During a second order phase transition, the entropy remains continuous, indicating that there is no sudden change in the degree of disorder or randomness in the system. Therefore, entropy is continuous during a second order phase transition.

To summarize, during a second order phase transition, specific heat, magnetic susceptibility, and isothermal compressibility may diverge or become very large, indicating the presence of critical phenomena. However, entropy remains continuous, indicating that there is no sudden change in the degree of disorder or randomness in the system.