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NeTakaya
4 years ago
8

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?
Physics
1 answer:
Ipatiy [6.2K]4 years ago
5 0

Answer and Explanation: One ATP release approximately 30.5kJ/mol of energy. Using Avogadro's constant, it is known one mol corresponds to 6.02.10^{23} molecules, so 106 ATP molecules releases:

E = 30.5.10^{3}*\frac{106}{6.02.10^{23}}

E = 537.04.10^{-20}J

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

V = \frac{4}{3}.\pi.r^{3}

Changing radius from mm to m:

r = 10^{-2}m

Then, volume is

V = \frac{4}{3}.\pi.(10^{-2})^{3}

V = 4.2.10^{-6} m³

Power density is given by

power=\frac{energy}{volume}

power=\frac{537.04.10^{-20}}{4.2.10^{-6}}

power=128.10^{-14}

power = 12.8.10^{-15} W/m³

Power density for a the cell is 12.8.10^{-15} W/m³.

Power density for battery is

100 cm³ = 10^{-4}m³

power = \frac{15}{10^{-4}}

power = 15.10^{4}W/m³

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

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