A 65kg person's density is 990kg/m^3 with 2.4 L of air in lungs. What vol of air would the person have to expel to bring the density to that of water 1000 kg/m^3 (neglect the mass of air)?

To solve this problem, we need to find the volume of air that needs to be expelled in order to bring the person's density to that of water (1000 kg/m^3).

Step 1: Calculate the initial mass of the person
The density of a person is given as 990 kg/m^3. Since the person weighs 65 kg, we can use the formula:
Mass = Density × Volume
65 kg = 990 kg/m^3 × Volume
Volume = 65 kg / 990 kg/m^3
Volume ≈ 0.0657 m^3

Step 2: Determine the volume of air in the lungs
The volume of air in the lungs is given as 2.4 L. We need to convert this to cubic meters by dividing by 1000 (since 1 L = 0.001 m^3).
Volume of air in lungs = 2.4 L / 1000
Volume of air in lungs = 0.0024 m^3

Step 3: Calculate the final volume of the person after expelling air
To find the final volume of the person after expelling air, we subtract the volume of air in the lungs from the initial volume of the person:
Final volume = Initial volume - Volume of air in lungs
Final volume = 0.0657 m^3 - 0.0024 m^3
Final volume ≈ 0.0633 m^3

Step 4: Calculate the volume of air that needs to be expelled
To calculate the volume of air that needs to be expelled, we subtract the final volume from the volume of the person if their density were to match that of water (1000 kg/m^3):
Volume of air to be expelled = Initial volume - Final volume
Volume of air to be expelled = 0.0657 m^3 - 0.0633 m^3
Volume of air to be expelled ≈ 0.0024 m^3

Therefore, the person would have to expel approximately 0.0024 cubic meters (or 2.4 liters) of air to bring their density to that of water (1000 kg/m^3), neglecting the mass of air.

To determine the volume of air that the person would have to expel in order to bring their density to that of water, we can use the formula for density:

Density = Mass / Volume

Given:
Mass of the person = 65 kg
Density of the person = 990 kg/m^3
Density of water = 1000 kg/m^3
Volume of air in the person's lungs = 2.4 L

First, we need to find the volume of the person by dividing the mass by the density:

Volume of person = Mass / Density
Volume of person = 65 kg / 990 kg/m^3

Now we can calculate the volume of the person:

Volume of person = 0.0657 m^3 (rounded to four decimal places)

To find the volume of air that the person would have to expel, we subtract the volume of the person from the desired volume of water:

Volume of air to be expelled = Volume of water - Volume of person
Volume of air to be expelled = 1.0 m^3 - 0.0657 m^3

Therefore, the person would have to exhale approximately 0.9343 m^3 of air in order to bring their density to that of water.