DSC Without Temperature Gradient

The steady-state calculations have set the stage for computation of the DSC performance without, or better with negligible, temperature gradient within the sample. A temperature gradient within the sample pan should not exceed 2-3 kelvins for typical standard DSC experiments. The first two equations of Fig. 4.67 express the heat-flow rates into the sample and reference making use of Newton s law of cooling (see Fig. 4.9). The heat-flow rate, dQ/dt, is strictly proportional to the difference between block temperature, T, and sample temperature, T. The proportionality 

The plot at the bottom of Fig. 4.68 shows the increase in block temperature, qt, and the change in sample temperature, Tj, in analogy to Fig. 4.55. Initially, at time zero, block and sample temperatures are identical. Then, as the experiment begins, the sample temperature lags increasingly behind T until steady state is reached. The difference between the block and sample temperatures at steady state is qCp/K, a quantity which is strictly proportional to the heating rate and the heat capacity of the 

For the measurement of a constant heat capacity, the sketches of Fig. 4.55 and 4.68 show that only measurement of and is necessary. The value of K can be obtained by calibration. With this discussion, the principle of heat capacity measurement is already clarified. The further mathematical treatment of the DSC will show how to handle the calibration by using a differential set-up that is designed, as mentioned above, to minimize the effort to evaluate heat losses and gains. 

Cp = Cr = heat capacity of the empty pan Cg = heat capacity of the sample and pan m = sample mass Cp = sample specific heat capacity 

In Fig. 4.70 the expression for the heat capacity is completed by inserting the top equations into the equation for AT of Fig. 4.69. The basic DSC equations contain the 

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