Introduction:
In a crystal containing a paramagnetic impurity, the energy levels of the impurity are affected by the presence of a magnetic field. This, in turn, influences the specific heat of the crystal at high temperatures. The specific heat is a measure of the amount of heat energy required to raise the temperature of a substance.

Explanation:
At high temperatures, the specific heat of a crystal containing a paramagnetic impurity varies with T-2. This can be understood by considering the following factors:

1. Paramagnetic behavior:
Paramagnetic materials are characterized by the presence of unpaired electrons in their atomic or molecular orbitals. In the presence of a magnetic field, these unpaired electrons align themselves with the field, leading to a net magnetization of the material.

2. Energy levels and magnetic field:
The energy levels of the impurity in the crystal are influenced by the magnetic field. In a paramagnetic material, the energy levels split into sublevels due to the interaction between the magnetic field and the magnetic moment of the unpaired electrons.

3. Boltzmann distribution:
At high temperatures, the thermal energy (kT) is comparable to the energy splitting between the sublevels. According to the Boltzmann distribution, the population of electrons in different energy levels is determined by the energy difference and the temperature.

4. Specific heat and energy levels:
The specific heat of a crystal is directly related to the distribution of energy levels and the population of electrons in these levels. At high temperatures, the energy levels are densely populated due to the Boltzmann distribution.

5. T-2 dependence:
The specific heat of a crystal containing a paramagnetic impurity is proportional to the number of energy levels available to the electrons. As the energy levels are proportional to the magnetic field, the specific heat varies with T-2.

Conclusion:
In conclusion, the specific heat of a crystal containing a paramagnetic impurity at high temperatures varies with T-2. This can be understood by considering the paramagnetic behavior, the influence of the magnetic field on the energy levels, the Boltzmann distribution, and the relationship between specific heat and energy levels.