Erratum to “Serious analytical inconsistencies challenge the validity of the energy balance theory” [Heliyon 6 7 (July 2020) e04204]

In the original published version of this article, errors were introduced to two equations shown on page 9. These have now been corrected. The publisher apologizes for these mistakes. There was also a typographical error in another equation on page 10. This has now been corrected. The author apologizes for this mistake. Correct versions of each equation can be found below. Both the HTML and PDF versions of the article have been updated to correct the errors.

$$\begin{gathered} \frac{\left\{\left(\frac{1}{{\rho }_C}-\frac{1}{{\rho }_F}\right)\left(\frac{r_P{k}_P}{{\rho }_P}-\frac{r_F{k}_F}{{\rho }_F}\right)-\left(\frac{r_C{k}_C}{{\rho }_C}-\frac{r_F{k}_F}{{\rho }_F}\right)\left(\frac{1}{{\rho }_P}-\frac{1}{{\rho }_F}\right)\right\}{x}_{P,E{I}_{avg}}}{\left(\frac{1}{{\rho }_C}-\frac{1}{{\rho }_F}\right)\left(\frac{r_P{k}_P}{{\rho }_P}-\frac{r_F{k}_F}{{\rho }_F}\right)-\left(\frac{r_C{k}_C}{{\rho }_C}-\frac{r_F{k}_F}{{\rho }_F}\right)\left(\frac{1}{{\rho }_P}-\frac{1}{{\rho }_F}\right)} \\ -\frac{\left\{\left(\frac{1}{{\rho }_C}-\frac{1}{{\rho }_F}\right)\left(\frac{k_P}{{\rho }_P}-\frac{k_F}{{\rho }_F}\right)-\left(\frac{k_C}{{\rho }_C}-\frac{k_F}{{\rho }_F}\right)\left(\frac{1}{{\rho }_P}-\frac{1}{{\rho }_F}\right)\right\}{x}_{P,E{I}_{avg}}}{\left(\frac{1}{{\rho }_C}-\frac{1}{{\rho }_F}\right)\left(\frac{k_P}{{\rho }_P}-\frac{k_F}{{\rho }_F}\right)-\left(\frac{k_C}{{\rho }_C}-\frac{k_F}{{\rho }_F}\right)\left(\frac{1}{{\rho }_P}-\frac{1}{{\rho }_F}\right)} \end{gathered}$$

Thus, system (16) is equivalent to

$$\begin{array}{l}{x}_{F,E{E}_{avg}}+x_{C,E{E}_{avg}}+x_{P,E{E}_{avg}}=1\\ \left(\frac{1}{{\rho }_C}-\frac{1}{{\rho }_F}\right)x_{C,E{E}_{avg}}+\left(\frac{1}{{\rho }_P}-\frac{1}{{\rho }_F}\right)x_{P,E{E}_{avg}}=\frac{1}{{\rho }_{E{I}_{avg}}}-\frac{1}{{\rho }_F}\\ x_{P,E{E}_{avg}}=x_{P,E{I}_{avg}}\end{array}$$

$$\Delta \mathrm{m}=\stackrel{>\mathrm{0}}{\overbrace{E_{eq}}}\stackrel{<0}{\overbrace{\left(\frac{1}{{\rho }_F}-\frac{1}{{\rho }_P}\right)}}\stackrel{<0}{\overbrace{\left(x_{F,E{I}_{avg}}-x_{F,E{E}_{avg}}\right)}}+\stackrel{>\mathrm{0}}{\overbrace{E_{eq}}}\stackrel{>0}{\overbrace{\left(\frac{1}{{\rho }_C}-\frac{1}{{\rho }_P}\right)}}\stackrel{\ge 0}{\overbrace{\left(x_{C,E{I}_{avg}}-x_{C,E{E}_{avg}}\right)}}>0$$