Respuesta :
Answer and Explanation: One ATP release approximately 30.5kJ/mol of energy. Using Avogadro's constant, it is known one mol corresponds to [tex]6.02.10^{23}[/tex] molecules, so 106 ATP molecules releases:
E = [tex]30.5.10^{3}*\frac{106}{6.02.10^{23}}[/tex]
E = [tex]537.04.10^{-20}[/tex]J
A cell is approximately a sphere. Volume of a sphere is given by
V = [tex]\frac{4}{3}.\pi.r^{3}[/tex]
Changing radius from mm to m:
r = [tex]10^{-2}[/tex]m
Then, volume is
V = [tex]\frac{4}{3}.\pi.(10^{-2})^{3}[/tex]
V = [tex]4.2.10^{-6}[/tex] m³
Power density is given by
[tex]power=\frac{energy}{volume}[/tex]
[tex]power=\frac{537.04.10^{-20}}{4.2.10^{-6}}[/tex]
[tex]power=128.10^{-14}[/tex]
power = 12.8.[tex]10^{-15}[/tex] W/m³
Power density for a the cell is 12.8.[tex]10^{-15}[/tex] W/m³.
Power density for battery is
100 cm³ = [tex]10^{-4}[/tex]m³
power = [tex]\frac{15}{10^{-4}}[/tex]
power = [tex]15.10^{4}[/tex]W/m³
Comparing cell and battery, battery has a greater power density.
