2.30 Suppose that the radius of a typical cell is 10 mm and that inside it 106 ATP molecules are hydrolyzed each second. What is the power density of the cell in watts per cubic meter (1 W = 1 J s−1)? A computer battery delivers about 15 W and has a volume of 100 cm3. Which has the greater power density, the cell or the battery?

Answer and Explanation: One ATP release approximately 30.5kJ/mol of energy. Using Avogadro's constant, it is known one mol corresponds to molecules, so 106 ATP molecules releases:

E =

E = J

A cell is approximately a sphere. Volume of a sphere is given by

V =

Changing radius from mm to m:

r = m

Then, volume is

V =

V = m³

Power density is given by

power = 12.8. W/m³

Power density for a the cell is 12.8. W/m³.

Power density for battery is

100 cm³ = m³

power =

power = W/m³

Comparing cell and battery, battery has a greater power density.

as technology advances, new experiments often expose problems in accepted theories. c

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