Electrical resistivity and conductivity ions. In biological membranes, currents are carried by ionic salts. Small holes in cell membranes, called ion channels, are selective to specific ions and determine the membrane resistance. The electrical resistivity of a metallic conductor decreases gradually as temperature is lowered. In ordinary conductors, such as copper or silver, this decrease is limited by impurities and other defects. Even near absolute zero, a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature. An electric current flowing in a loop of superconducting wire
Thermal conductivity is the electronic thermal conductivity when the electrochemical potential gradient inside the sample is zero, as a starting point. As next step the transport coefficients are written as following where formula_56 and "a" the Bohr radius. The dimensionless integrals "I" are defined as where "s"("x") is the dimensionless transport distribution function. The integrals "I" are the moments of the function where "x" is the energy of carriers. By substituting the previous formulas for the transport coefficient to the equation for "λ" we get the following equation From the previous equation we see that "λ" to be zero the bracketed term