He didn't give me the answer. However he said my approach is right and the reason why we can handle N as if it were a deterministic variable is that we are always interested in the thermodynamic limit, where all variables, including N, take a well-defined value. I think the question also assume u is a constant...stevendaryl said:
Fermi energy, also known as Fermi level, is the maximum energy that a particle in a system can have at absolute zero temperature. It represents the energy required for an electron to move from the highest occupied energy level to the lowest unoccupied energy level in a system.
Fermi energy is directly proportional to the heat capacity of a Fermi gas. This means that as the Fermi energy increases, so does the heat capacity. This is because the Fermi energy determines the number of energy levels that can be occupied by particles in a system, and a higher number of energy levels means a higher heat capacity.
Yes, Fermi energy can be changed by altering the temperature or pressure of a system. In a Fermi gas, increasing the temperature or decreasing the pressure will result in an increase in the Fermi energy. Similarly, decreasing the temperature or increasing the pressure will result in a decrease in the Fermi energy.
Fermi energy is an important concept in materials science as it helps to understand the behavior of electrons in a material. It determines the electrical and thermal conductivity of a material, as well as its magnetic and optical properties. The Fermi energy also plays a crucial role in the band structure of materials, which affects their electronic and mechanical properties.
Fermi energy can be calculated using the Fermi-Dirac distribution, which describes the probability of a particle occupying an energy level in a Fermi gas. It can also be calculated using the density of states, which is a measure of the number of energy levels available for particles in a system. Additionally, Fermi energy can be experimentally determined through techniques such as photoemission spectroscopy or electrical conductivity measurements.