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 Figure 3 - The expression for average kinetic energy for an ideal gas. mi and vi represent the mass and velocity of each particle, respectively. N represents the number of particles. |
Temperature is defined as 'the average kinetic energy of all particles in the system.' According to the theory, there should be a standard deviation to go along with this average, but I have yet to see a thermometer that gives standard deviation. When one considers temperature in mixtures of different kinds of molecules or systems that are not at equilibrium, at the nanoscale there should be localized regions of various temperatures contributing to this average.
Temperature distribution is frequently calculated in non-equilibrium molecular dynamics simulations. In these theoretical models, the kinetic energy of each particle at various points in time is taken into account in order to provide a better understanding of molecular scale events. One might then define local temperature as - the average kinetic energy of a specified set of atoms within the system (figure 3). While this is still a statistical method, it allows discrete statements to be made about localized parts of a system. Take, for intance, the myosin molecule in the previous article. If one were to specify as the set of atoms those included in the beta sheet adjacent to the ATP binding site, then, considering the 6 trillion myosin molecules [myology] in a muscle cell may even provide a sufficient sample size for spectroscopic measurements.
While local temperature is relatively easy to describe theoretically, measurements are more difficult to make. However, novel methods are being developed that have the potential to verify theoretical models experimentally. For example, local temperatures and temperature gradients can now be directly measured by Scanning Thermal Microscopy (SThM). While the lateral resolution is currently limited to 150-200nm (sufficient for numerous microscale applications), it is reasonable to expect this resolution to improve in the future, perhaps eventually reaching the level of single molecules.
Acknowledgements - Thank you Andreas Janshoff for providing the vesicle images and explaining vesicle fabrication. I'm also grateful to T. Daniel P. Stack for comments about molecular assembly lines and to Daniel Kreuger for the keywords, 'Temperature Distribution in Non-Equilibrium Molecular Dynamics Simulations.'