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The DSC trace below was recorded for a thermotropic calamitic liquid crystal. The heating rate was 5 $^\text{o}$C min$^{-1}$; a heating scan is followed by a cooling scan.

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Based on the previously reported result, there are two phase transitions to be expected in the temperature range of interest: from crystal to a nematic phase, then to an isotropic phase.

From the DSC trace, how can we say something about the order of the phase transition?

1. The most popular answer from this site says:

If you want to see whether your transitions are first or second order, you must run modulated DSC, where the non-reversing and reversing part of the heat flow is related to the first and second-order transitions, respectively.

What is the reason for first-order phase transition being non-reversing while second-order being reversing?

2. Second-order phase transition $\implies \Delta S = 0 \implies \Delta H = 0$ at transition temperature. Based on this, shouldn't any second-order phase transition not shown in the DSC trace (because no heat exchanged at constant pressure during that transition)?

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