Question

How many meters of stairway (in height) could a 70 kg man climb if all the energy available in metabolizing an 11 g spoonful of sugar to carbon dioxide and water could be converted to work? For 1 mol of glucose oxidized to CO2 and H2O, 673 kcal of heat is released.

Answer 1

Given that the weight of the man = 70 Kg

Now we calculate the potential energy required to climb.1 meter

h= 1 m ; m = 70 Kg ; g = 9.81 m/sec²

PE = mgh = 70*9.81*1 = 686.7 J

Now calculating energy from 11 g of sugar.We will consider that sugar described here is glucose.

molar mass of glucose = 180 g/mol

11 g of glucose contains = 1 *11/180 = 0.061 mol

It is given that 1 mol of glucose releases 673 Kcal of heat

then, 0.061 mol glucose will yield = 0.061 * 673 = 41.053 Kcal

Converting this to joules,

1 Kcal = 4184 J  

41.053 Kcal = 41.053*4184 J = 171765.752 J

The amount of energy available to climb stairs = 171765.752 J

The amount of energy required to climb 1 m = 686.7 J

Height that can be climbed with the available energy = amount of energy available to climb stairs / amount of energy required to climb 1 m

= 171765.572 / 686.7 = 250.13 m

The 70 Kg man can reach a height of 250.13 metres.