The outgassing equation based on the Temkin isotherm is applied to consider the outgassing behavior in the pump down of an unbaked vacuum system. A method to solve the equation approximately is discussed first, and then solutions of outgassing rates are derived. Solutions to the equation which can be used to predict the dependence of the outgassing rate on pumping time and pumping speed are discussed. The solutions finally obtained are able to explain the outgassing behavior observed experimentally for a 304 stainless steel chamber after exposure to moist air, in particular the dependence of the outgassing rate on time and pumping speed.