quantities approach the values for a classical ideal gas in the limit of large temperature. The above values can be used to calculate other thermodynamic quantities. For example, the relationship between internal energy and the product of pressure and volume is the same as that for a classical ideal gas over all temperatures: A similar situation holds for the specific heat at constant volume The entropy is given by: Note that in the limit of high temperature, we have which, for α=3/2 is simply a restatement of the Sackur–Tetrode equation. In one dimension bosons with delta interaction behave as fermions, they obey Pauli exclusion principle. In one dimension Bose gas with delta interaction can be solved exactly by Bethe ansatz. The bulk free energy and thermodynamic potentials were calculated by Chen-Ning Yang. In one dimensional case correlation functions also were evaluated. In one dimension Bose gas is equivalent to quantum non-linear Schrödinger equation. See also Tonks–Girardeau gas References General references Bose–Einstein statistics Ideal gas Quantum mechanics Thermodynamics Satyendra Nath Bose