A student had a breakfast of 200 food calories. He thinks of burning this energy by drawing water from the well and watering the trees in his school. Depth of the well is about 25 m. The pot can hold 25 L of water and each tree requires one pot of water. How many trees can he water? (Neglect the mass of the pot and the energy spent by walking. `("Take g" = 10 ms^(-2))`

Explanation

To draw 25 L of water from the well, the student has to do work against gravity by burning his energy.
Mass of the water `=25L=25kg(1L=1kg)`
The work required to draw 25 kg of water = gravitational potential energy gained by water.
`W=mgh=25xx10xx25=6250J`
The total energy gained from the food = 200 food cal = 200 kcal
`=200xx10^(3)xx4.186J=8.37xx10^(5)J`
If we assume that by using this energy the student can drawn .n. pots of water from the well the total energy spent by him `=8.37xx10^(5)J=nmgh`
`n=(8.37xx10^(5)J)/(6250J)~~134`
This n is also equal to the number of trees that he can water. Is it possible to draw 134 pots of water from the well just by having breakfast? No. Actually the human body does not convert entire food energy into work. It is only approximately `20%` efficient. It implies that only `20%` of 200 food calories is used to draw water from the well. So `20 %` of the 134 is only 26 pots of water. It is quite meaningful. So he can water only 26 trees.