Abstract By considering a gedankenexperiment of adiabatically lowering a box containing matter with rest energy E and entropy S to a black hole, Bekenstein claimed that the necessary condition for the validity of the generalized second law of thermodynamics is S/E ≤ 2πR, where R is the effective radius of the box, Unruh and Wald claimed that this condition is not necessary but the acceleration radiation can guarantee the generalized second law. In this paper, we point out that Unruh and Wald's conclusion does not hold because the Hawking radiation near the horizon is not thermal. Bekenstein's conclusion also does not hold because the thin box approximation is not correct near the horizon. Neither Hawking radiation nor S/E ≤ 2πR. can guarantee the second law. We have sufficient reasons to conjecture that the gravitation can influence the state equation of matter. For radiation, the usual state equation ρ = αT4 and s =4/3αT3 do not hold in the strong gravitation field, e.g., near theblackhole's horizon. We have derived the state equation for radiation near ths horizon and find that it is very different from that in flat spacetime. The second law may be valid if some restrictions on one parameter of the state equation are imbo-sed. As a corollary, an upper bound on S/E which resembles the Bekenatein's result is found.