softmatter:Heat capacity

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The classic definition of heat capacity is the amount of energy needed to raise the temperature of a substance by one degree, thus having units of energy/temperature. Heat capacity is an extensive quantity (i.e. it is system size dependent), so typically we deal with specific heat capacity where the heat capacity is scaled by the mass of the system.

Calculation of CV from simulation

For an NVT system, there are two main methods for calculating heat CV.

  • By using the formula below, one can calculate CV by calculating the variance in the total system energy, and dividing by the Boltzmann factor and temperature squared.

C_V = \left ( \frac{\delta E}{\delta T}\right )_V = \frac{1}{k_B T^2} \left \langle(E-\left \langle E \right \rangle)^2 \right \rangle

  • Heat capacity can be calculated by first simulating several runs at different temperatures and calculating the total system energy at those points.
    • The slope of the plot of energy vs. temperature will yield CV.
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