With ohmic heating the reaction medium itself serves as an electrical resistor, and is heated by passing electricity through it. Internal energy transformation occurs, from electrical to thermal energy, thanks to ion movement and friction within the reaction medium. Since the heating process depends on the resistivity of the medium, the exact conditions vary from reaction to reaction.
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Read the original journal article in Green Chemistry:
Ohmic heating as a new efficient process for organic synthesis in water
Joana Pinto, Vera L. M. Silva, Ana M. G. Silva, Artur M. S. Silva, José C. S. Costa, Luís M. N. B. F. Santos, Roger Enes, José A. S. Cavaleiro, António A. M. O. S. Vicente and José A. C. Teixeira
Green Chem., 2013, Advance Article