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I want to calculate specific heat capacity at constant pressure for a single walled carbon nanotube by using of fluctuation in enthalpy. The fluctuations were obtained from molecular dynamics simulation. I read some literature for method of calculation. I faced with two formula to calculation of specific heat capacity, but I'm not sure which is true: $$ c_p=\frac{<\delta H^2>}{k_B T^2} $$ where was written in https://pubs.acs.org/doi/abs/10.1021/jp910246t (Eq. (1)) . On the other hand in the article https://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.155441 (Eq.(4.1)) was mentioned different equation than above: $$ c_p=\frac{<\delta H^2>}{N k_B T^2} $$

where N is number of atoms in the simulation. please help me to clarify right equation. Thanks in advances.

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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.

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  • $\begingroup$ 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. $\endgroup$ – Farrokh Yousefi Jun 9 '18 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 Jun 10 '18 at 23:48
  • $\begingroup$ But then are both formulas indeed for specific heat capacity? $\endgroup$ – myradio Jun 23 '18 at 12:54

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