Urea-induced denaturations of RNase T1 and reduced and carboxyamidated RNase T1 (RTCAM) as a function of temperature were analyzed using the linear extrapolation method, and denaturation m values, ΔCp, ΔH, ΔS, and ΔG quantities were determined. Because both ΔCp and m values are believed to reflect the protein surface area newly exposed on denaturation, the prediction is that the ratio of m values for RNase T1 and RTCAM should equal the ΔCp ratio for the two proteins. This is not the case, for it is found that the m value of RTCAM is 1.5 times that of RNase T1, while the denaturation ΔCp's for the two proteins are identical. The paradox of why the two parameters, m and ΔCp, are not equivalent in their behavior is of importance in the interpretations of their respective molecular-level meanings. It is found that the measured denaturation ΔCp's are consistent with ΔCp's calculated on the basis of empirical relationships between the change in surface area on denaturation (ΔASA), and that the measured m value of RNase T1 agrees with m calculated from empirical data relating m to ΔASA. However, the measured m of RTCAM is so much out of line with its calculated m as to call into question the validity of always equating m with surface area newly exposed on denaturation.