Thermodynamics: calculate thermodynamic derivative from data?

  • #1

Summary:

How can I calculate a thermodynamic derivative like dE/dV (where E is internal energy) from a data that seem to be total kinetic and potential energy values?
I don't understand how to use output from an NPT molecular dynamics simulation to compute a thermodynamic derivative.

I need to compute this (where "d" is a partial derivative, "T" is a subscript that means, "at constant temperature," and "E" is internal energy):
-(dE/dV)T

I have a simulation output file that has these columns:
Time, temperature, kinetic energy, potential energy, total energy

I think I need to add the kinetic and potential energy columns to get the internal energy. But how do I compute the partial of E with respect to V at constant T? E.g., what is the reference point for calculating the delta? Is it E at one time step minus E at the previous time step?

I have another file that provides the volume at each time step. It fluctuates because this is an NPT simulation.

Any hints would be very helpful. Thank you.
 

Answers and Replies

  • #2
jambaugh
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It sounds like you are not clear on the meaning of ##-(\frac{dE}{dV})_T##. This is the rate of energy change per change of volume for the system kept at a constant temperature.

You need to experimentally, or via simulation, change the volume while maintaining or reversibly bringing the system back to the given temperature and see how the energy changed.

Experimentally (in principle) I would use a calorimeter to measure how much heat the system loses when the volume increased a small amount and then how much heat I needed to add (via electric heating element) to bring it back up to the original temperature. The difference is the ##\partial E## for the ##\partial V## at that temperature. In practice this is probably a horribly inaccurate way to do things but that's the kind of think you should be simulating where you can directly compute energy.
 

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