The value of Tg derived from these two calculation methods are different. what is the fundamental difference and which one is more accurate?
From the thermodynamical point of view, the glassy state is not at equilibrium, henceforth the transition to this state doesn't correspond to a critical temperature which could be precisely measured as for structural or magnetic phase transitions. Consequently, the accuracy of Tg has no physical meaning. Unfortunately, we only can observe anomalies in physical properties (viscosity, specific heat, specific volume, sound velocities......) which occur in the same temperature range but may somewhat differ depending on experimental conditions. Historically, the glassy state was obtained when a liquid drop didn't fall within a 20mn time.
Before years ago when I start my research it take me a time to grasp what you are asking for. In my opinion it is matter of school of science which method was used to determine the glass transition temperature. Probably every school of science has their own arguments ( I dont remember áll) and they are related to how the glass transition is defined e.g.:
The Tg is the temperature where the relaxation time become 10 sec or 100 sec or 1013 poise.
You should remember that the glass transition is an interval not single temperature as in phase transitions that depend on heating/cooling annealing (thermal history of the sample)
Onset Tg is related with the . point where process of relaxation is fastest since the driving force of the process of relaxation is deviation from equilibrium
inflection point and half delta Cp has also their mathematical meaning and are more close to so called fictive temperature see :
http://www.sciglassweb.com/glossary/html/glos80o5.htm
http://onlinelibrary.wiley.com/doi/10.1111/j.1151-2916.1976.tb09376.x/abstract
or any other source https://www.google.bg/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=fictive+temperature+glass
I am using onset as well defined point.
You can find a typical heat capacity vs. temperature plot for glass-forming substances with the corresponding location of the glass transition temperature (Tg) at Fig. 1 from the following paper:
Article Aspects of the non-crystalline state
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