wherein the chemical potential of an ideal gas can be evaluated analytically. Now let's focus on ⁠ μ μ e x , ⁠ since the potential energy of an ⁠ ( N + 1 ) ⁠ -particle system can be separated into the potential energy of an ⁠ N ⁠ -particle system and the potential of the excess particle interacting with the ⁠ N ⁠ -particle system, that is,