I want to calculate the specific heat capacity at constant pressure for a single walled carbon nanotube by using fluctuation in enthalpy. The fluctuations were obtained from molecular dynamics simulation. I read some literature for the method of calculation. I am faced with two formulae for the calculation of specific heat capacity, but I'm not sure which one is true: $$ c_p=\frac{\langle\delta H^2\rangle}{k_B T^2} $$ was written in J. Phys. Chem. C 2010, 114, 19, 8717–8720 (Eq. (1)) . On the other hand, in the article Phys. Rev. B 74, 155441 (2006) (Eq.(4.1)) they mention a different equation from the one above: $$ c_p=\frac{\langle\delta H^2\rangle}{N k_B T^2} $$

where $N$ is the number of atoms in the simulation. Please help me to clarify the right equation.


1 Answer 1


The specific heat is defined as the heat capacity per particle which is correctly expressed in your second equation. Digging into details of the first paper shows that the provided equation is the heat-capacity and not the specific heat, have a look at Ref.24 of the paper. Thereby both equations are indeed correct but the former is the heat-capacity and the later is the specific heat of the system.

  • $\begingroup$ Thanks a lot. Why these formulas have same dimensions? I thinks specific heat capacity has J/(kg-K) unit while the heat capacity hase J/kg unit. Thanks again. $\endgroup$ Commented Jun 9, 2018 at 21:47
  • $\begingroup$ Well, you are indeed right. The particle number in the second equation works implicitly as the mass, assuming that mass=N*mass_of_particle. Thereby if you set the units such that mass_of_particle becomes one, everything will be in order. $\endgroup$
    – Shasa
    Commented Jun 10, 2018 at 23:48
  • $\begingroup$ But then are both formulas indeed for specific heat capacity? $\endgroup$
    – myradio
    Commented Jun 23, 2018 at 12:54

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