# Comment on “Concepts against mathematics: self-inconsistency in thermodynamic evaluations, V. A. Drebushchak, Journal of Thermal Analysis and Calorimetry (2011) 103:753–759”

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## Keywords

Polymer Physical Chemistry Differential Equation Analytical Chemistry Inorganic ChemistryIn 2011, Drebushchak published his paper [1]. Swendsen already published a Comment on it [2]. However, his Comment has a disadvantage: he commented on the main body of Drebushchak’s paper but did not comment on the paradox that Drebushchak had proposed in the Appendix of his paper.

I would like to Comment on this paradox (I insert the letter “D” into Drebushchak’s equation numbers).

*R*is the gas constant. Both sides of this equation were multiplied by d

*T*:

*R*d

*T*= d

*RT*= d(

*PV*), Eq. D39 was transformed into

*T*, one obtained the paradox:

*T*:

*T*, one obtains:

*n*times, one obtains

*R,*and multiplying it by d

*T*, one obtains

*T*, one again obtains:

*n*times, one obtains

It is obvious that Drebushchak’s paradox does not have connection to the heat capacities but results from inappropriate use of the differential equation. Its explanation is, of course, the following one. In the left part of Eq. D42, there is the value *C* _{P}d*T*. This means that we have a system with a constant pressure and want to calculate *C* _{P}d*T* for it, which is unknown to us. In the right part of this equation, there is a value *C* _{V}d*T* which is known to us. To obtain *C* _{P}d*T*, we have to add to *C* _{V}d*T* a term d(*PV*) which characterizes our system with a constant pressure. Therefore, in this term, *P* is constant.

## References

- 1.Drebushchak VA. Concepts against mathematics: self-inconsistency in thermodynamic evaluations. J Therm Anal Calorim. 2011;103:753–9.CrossRefGoogle Scholar
- 2.Swendsen RH. In defense of thermodynamics, comment on concepts against mathematics: self-inconsistency in thermodynamic evaluations. J Therm Anal Calorim. 2012;110(3):1547–51.CrossRefGoogle Scholar