An athelet takes 20 breaths per minute at room temperature. The air inhaled in each breath is `200mL` which contains `20%` oxygen by volume, while exhaled air contains `10%` oxygen by volume. Assuming that all the oxygen consumed if used for converting glucose into `CO_(2)` and `H_(2)O_((l))` , how much glucose will be burnt in the body in one hour and what is the heat produced ? `(` Room temperature `-27^(@)C` and enthalpy of combustion of glucose is `-2822.5kJ mol^(-1) at 0^(@)C)`

Explanation

Inhaled `O_(2)` in one breath `= (200 xx 20)/(100) mL = 40 mL`
Exhaled `O_(2)` in one breath `= (200 xx 10)/(100) mL = 20 mL`
Used `O_(2)` in one breath `= 40 - 20 = 20 mL`
Now `20` breaths are taken in `1min`
Breath taken in `1hour = 20 xx 60 = 120 0 breath`
Volume of `O_(2)` used in `1h`
`= 20 xx 1200 = 24000 mL at 27^(@)C`
`= (24000)/(300) xx 273 mL at 0^(@)C`
`= 21840 mL = 21.84 L at 0^(@)C`
For glucose:
`C_(2)H_(12)O_(6) +6O_(2) rarr 6CO_(2) +6H_(2)O DeltaH =- 2822.5 kJ`
`6 xx 22.4 L of O_(2)` is used for `180` g glucose
`21.84 L of O_(2)` is used for `= (180 xx 21.4)/(6 xx 22.4) = 29.25 g`
Also `6 xx 22.4 L of O_(2)` with glucose gives `= 2822.5 kJ 21.84 L O_(2)` with glucose give
`=(2822 xx 21.84)/(6 xx 22.4) = 458.66 kJ`