A nerve cell is shaped like a cylinder. The membrane wall of the cylinder has a +0.07 V potential difference from the inside to the outside of the wall. To help maintain this potential difference, sodium ions are pumped from inside the cell to the outside. For a typical cell, 10^9 ions are pumped each second.
a. Determine the change in chemical energy each second required to produce this increase in electric potential energy.
b. If there are roughly 7×10^11 of these cells in the body, how much chemical energy is used in pumping sodium ions each second?
c. Estimate the fraction of a person's metabolic rate used to pump these ions. Assume the metabolic rate to be 100 W.