Abstract: The analysis contrasting the feature of BBAL's equation of state (eos) with the feature of equation of state EOS(1) is presental. At range of low density of matter(ρ<10¹¹g cm^-3), the chemical potential of neutron and proton of BBAL's(eos) differs notablly from EOS(1).This results in that two equations of state mentioned above differ greatly in abundance of free neutron and free proton at low density.The difference between the balance expression for finite temperature correct (thermal effect) and for "zero temperature appoximation" has been investegated.The effect for finite temperature correct on the chemical potential of neutron and proton is small, but the effect on the mass number and charge number of the average heavy nucleus is marked.Having taken 15M_① model of weaver et al.as initial model,the collapse process of stellar core between the onset of collapse and core bounce has been calculated by using both the (eos) of BBAL and EOS(1).The results show that the difference betwean the calculational results of stellar collapse (at ρ_c~10¹⁴g cm^-3) with EOS (1) and with BBAL's (eos)is not so large, in spite of that BBAL's (eos) differ greatly from EOS(l) in abundance of free nucleon at low density. The difference between calculational result (at ρ_c~10¹⁴g cm^-3) of stellar collapse resulting from finite temperature correct and "zero temperature approximation" for both BBAL's (eos) and EOS(l) is more notable.