A snorkeler takes a syringe filled with 16 mL of air from the surface, where the pressure is 1.0 ATM, to an unknown depth. The volume of the air in the syringe at this depth is 7.5 mL. What Is the pressure at this depth? If the pressure increases by an additional 1 atm for every 10 m of depth, how deep is the snorkeler?
Ok so this is my answer
P1= 1.0 atm
V1= 16 mL
P2= ?
V2= 7.5 mL
P2 = P1xV1/V2
(1.0 atm)(16 mL)/7.5 mL = 2.1 atm
1 atm increase for every 10 m, I thin should be 11 m
I agree with both answers.
Well, it seems like you've got the first part right! The pressure at the unknown depth is indeed 2.1 ATM. As for determining the depth, since the pressure increases by 1 atm for every 10 m of depth, we can calculate it using the difference in pressure.
To find out the depth, we can use the equation:
ΔP = P2 - P1 = ρgh,
where ΔP is the change in pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the depth.
Since the change in pressure is 2.1 atm - 1 atm = 1.1 atm, and ρg is approximately 1, we can rewrite the equation as:
1.1 atm = 1 atm/10 m * h,
Simplifying, we find that:
h = 1.1 atm * 10 m/atm = 11 m.
So, according to my calculations, the snorkeler is approximately 11 meters deep.
Your calculations for finding the pressure at the unknown depth are correct. The pressure at this depth is indeed 2.1 atm.
To determine the depth at which the snorkeler is, you can use the information that the pressure increases by an additional 1 atm for every 10 m of depth.
To calculate the depth, you can use the following equation:
Depth = (P2 - P1) / (1 atm / 10 m)
Substituting the values:
Depth = (2.1 atm - 1.0 atm) / (1 atm / 10 m)
Depth = 1.1 atm / (1 atm / 10 m)
Depth = 11 m
Therefore, the snorkeler is at a depth of 11 meters.
Your calculations for finding the pressure at the unknown depth are correct. To calculate the pressure at this depth using Boyle's Law, you can use the formula:
P2 = P1 * (V1 / V2)
Where:
P1 = Initial pressure (1.0 atm)
V1 = Initial volume (16 mL)
P2 = Pressure at the unknown depth
V2 = Volume at the unknown depth (7.5 mL)
By substituting the given values into the formula:
P2 = (1.0 atm) * (16 mL / 7.5 mL) = 2.133 atm (rounded to three decimal places)
Therefore, the pressure at this depth is approximately 2.133 atm.
To determine how deep the snorkeler is, you can use the given information that the pressure increases by an additional 1 atm for every 10 m of depth. This indicates a linear relationship between pressure and depth.
To find the depth, you can use the formula:
Depth (in meters) = (P2 - P1) / ΔP * 10
Where:
P1 = Pressure at the surface (1 atm)
P2 = Pressure at the unknown depth (2.133 atm)
ΔP = Change in pressure for every 10 m (1 atm)
By substituting the values into the formula:
Depth = (2.133 atm - 1 atm) / (1 atm) * 10 = 11.33 m (rounded to two decimal places)
Therefore, the snorkeler is approximately 11.33 meters deep.