Final answer:
By applying the principle of buoyancy and considering the difference in the percentage of the man's volume that is submerged in freshwater with lungs empty and full, we calculate that the lung capacity of the man is 1.50 liters. Option B. V = 1.50 , {L} is the correct answer.
Step-by-step explanation:
To calculate the lung capacity of a 75.0-kg man in freshwater based on the volume submerged, we use the principle of buoyancy where the buoyant force equals the weight of the water displaced. When the man's lungs are empty, 3.00% of his volume is above water. When his lungs are full, 5.00% of his volume is above water. The difference in the volume above water when the lungs are empty and full gives us the lung capacity.
The buoyant force with empty lungs is equal to the weight of the man, so:
- 97% submerged volume × density of water × gravitational acceleration = 75.0 kg × gravitational acceleration
And with full lungs:
- 95% submerged volume × density of water × gravitational acceleration = 75.0 kg × gravitational acceleration
The lung capacity then is the difference in the volumes corresponding to the 2% change when the lungs are filled with air because the buoyant force must equal the weight of the extra water displaced.
So, if V is the total volume of the man:
- 0.02V × density of water × gravitational acceleration = Volume of air × density of air × gravitational acceleration
Assuming that the densities of water and air are constant, and canceling out the gravitational acceleration, we get:
- 0.02V × density of water = Volume of air × density of air
Since the density of air is much less than the density of water, the volume of air (lung capacity) is going to be much larger than 0.02V of the man.
We can calculate the total volume (V) of the man by dividing his weight by the density of freshwater (approximately 1000 kg/m³):
- V = 75.0 kg / 1000 kg/m³
- V = 0.075 m³ or 75.0 liters
Therefore, the volume of air he inhales (lung capacity) is:
- Lung capacity = 0.02 × 75.0 liters
- Lung capacity = 1.50 liters
Thus, the correct option is B. V = 1.50 L.