Time-resolved spectroscopy is performed on eight bright , long gamma-ray bursts ( GRBs ) dominated by single emission pulses that were observed with the Fermi Gamma-ray Space Telescope . Fitting the prompt radiation of GRBs by empirical spectral forms such as the Band function leads to ambiguous conclusions about the physical model for the prompt radiation . Moreover , the Band function is often inadequate to fit the data . The GRB spectrum is therefore modeled with two emission components consisting of optically thin non-thermal synchrotron radiation from relativistic electrons and , when significant , thermal emission from a jet photosphere , which is represented by a blackbody spectrum . To produce an acceptable fit , the addition of a blackbody component is required in 5 out of the 8 cases . We also find that the low-energy spectral index \alpha is consistent with a synchrotron component with \alpha = -0.81 \pm 0.1 . This value lies between the limiting values of \alpha = -2 / 3 and \alpha = -3 / 2 for electrons in the slow and fast-cooling regimes , respectively , suggesting ongoing acceleration at the emission site . The blackbody component can be more significant when using a physical synchrotron model instead of the Band function , illustrating that the Band function does not serve as a good proxy for a non-thermal synchrotron emission component . The temperature and characteristic emission-region size of the blackbody component are found to , respectively , decrease and increase as power laws with time during the prompt phase . In addition , we find that the blackbody and non-thermal components have separate temporal behaviors as far as their respective flux and spectral evolutions .