Question

Many cells in the human body maintain an electric potential difference across their cellular membranes, typically through the use ion-specific pumps and channels that generate an excess of negative charges on the inside of the cellular membrane and an excess of positive charges on the outside. Let us estimate the total energy stored in the human body by this type of charge separation. Part a Different cells can have vastly different cell sizes; but as an approximation, let us assume that all cells in the body are spheres that are 16 micrometers (1.6 x 10~5m) in diameter. The current best estimate in the scientific literature is that there are approximately 40 trillion human cells (4 x 1013 cells) in an adult human body. First, calculate the volume of the human body based on these estimates. Does the answer seem reasonable? Enter answer here m3 Tt 0 of 10 attempts used CHECK ANSWER Part b Different cells types maintain different membrane potentials, but as an approximation, let us assume that all cells in the body maintain a -40 mV potential across its 7 nm thick cellular membrane, and that this bi-lipid cellular membrane acts as a dielectric with a dielectric constant of 9. The thickness of the membrane is 1000-times smaller than the 16-micrometer diameter of our model cell, so we can reasonably approximate it as being (locally) flat and treat the membrane as as a parallel-plate capacitor with an plate area equal to the surface area of the cell. Based on these estimates and approximations, calculate the total energy stored in the human body by charge separation across the cellular membranes. What does your answer imply about the how energy is stored in the human body?

Answer 1

Vol of one cell=4/3pir^3

total cells =4*10^13

Total volume=vol. of 1 cell*total no of cells

=8.57*10^-2 m^3

This is a fairly reasonable value since it is approximately 85.7 Litres

b)capacitance=k*epsilon₀(area)/d(thickness)

=9*8.85*10^-12*4pi*(0.8*10^-5)^2/7*10^-9

=91.47*10^-13F

Energy stored=0.5CV^2

=.5*91.47*10^-13*(40*10^-3)^2

=7.3*10^-15J

Total energy=7.3*10^-15J*no of cells

=0.292J