Use the following data to determine the maximum rate at which a standard man can

Question

Use the following data to determine the maximum rate at which a standard man can climb a mountain: Blood contains 15.9 wt% hemoglobin (with molecular weight 65,000 g/mol). Each hemoglobin molecule can carry four oxygen molecules. The heart pumps 106 cm3/s blood of density 1.06 g/cm3. Each oxygen molecule can oxidize one sugar unit (the chemical formula per sugar unit is CH2O, which is an organic alcohol group) to CO2 and H2O; the oxidation of 1 g sugar yields about 17 kJ of energy, of which 25% can be used to do muscle work. (Assume the climber has a mass of 60 kg.)

Explanation / Answer

in on e second, blood pumps, 106 cm^3 blood
V = 106*10^-6 m^3
blood density = 1.06 g/cm^3
hence mass of blood pumped in 1 s = 1.06*106 g = 112.36 g
hemoglobin = 17.86524 g
number of molecules of haemoglobin = 17.86524/65000 = 2.748810^-4 mol
1 molecule of haemoglobin = 4 oxygen molecules = 4 sugar units
so toal sugar units in one second = 0.001099 moles
0.00109939938461538461538461538462 mole sugar = 0.03298198153846153846153846153846 grams sugar
1 g sugar = 17,000 J * 0.25
hence energy = 140.17342 J / sec
so maximum climb rate = r
60*9.81*r = 140.1734215
hence
r = 0.238147 m/s

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