Question

You are shoveling bituminous Pennsylvania coal (with an energy content of 13,870 Btu/lb) from a coal box into a furnace. On average, with each lift and throw, you raise a 1.8 kg shovel containing 4.7 kg of coal by a height of 0.85 m. Assume your body is working with an efficiency of 15.9%. How many thousands of times more chemical energy is in the coal you move than is in the sugars and fats your body is burning to move it?

Answer 1

The energy content of the coal is:13,870 Btu/lb

Now, let us convert this in J/kg first.

1 Btu = 1055.06 J .... So, 13,870 Btu = 13,870 Btu *(1055.06 J/1 Btu) = 1.46 x 10⁷ J

1 lb = 0.4536 kg

So, the energy content will be:

(1.46 x 10^7 J/0.4536 kg) = 3.22 x 10⁷ J/kg

Total lifted coal is 4.7 kg. So, total energy will be:

E1 = 4.7 kg x 3.22 x 10⁷ J/kg = 1.51 x 10⁸ J

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Now, the mass of shovel + coal : m = (1.8 + 4.7 ) kg = 6.5 kg

Height : h = 0.85 m

Gravitational acceleration of earth surface: g = 9.8 m/s²

So, the energy required to lift the coal is:

E2 = m*g*h = (6.5 kg) *(9.8 m/s²) * (0.85 m) = 54.1 J

Now, body efficiency is 15.9%

So, that means just 15.9% of energy of sugar and fat burning in the body will be utilized as work. So, the energy of the body due to fat and sugar burning is:

E3 = 54.1 J * (100/15.9) = 341 J

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So, the energy of the coal and energy of burning of body and sugar ratio is:

E1/E3 = 1.51 x 10⁸ J/  341 J = 443000 (approx)

So, almost 443 thousands times more chemical energy is in the coal we move than is in the sugars and fats of our body is burning to move it.