What pressure, in atmospheres, is exerted on the body of a diver if they are 15 ft below the surface of the water when the atmospheric pressure is 750 torr? Assume that the density of the water is 1.00 g/cm3=1.00×103 kg/m3. The gravitational constant is 9.81 m/s2, and 1 Pa=1 kg/m-s2.

Verified step by step guidance

1. Convert the depth from feet to meters using the conversion factor: 1 ft = 0.3048 m.
2. Calculate the pressure exerted by the water using the formula: \( P_{\text{water}} = \rho \cdot g \cdot h \), where \( \rho \) is the density of water, \( g \) is the gravitational constant, and \( h \) is the depth in meters.
3. Convert the atmospheric pressure from torr to pascals using the conversion factor: 1 torr = 133.322 Pa.
4. Add the pressure exerted by the water to the atmospheric pressure to find the total pressure in pascals.
5. Convert the total pressure from pascals to atmospheres using the conversion factor: 1 atm = 101325 Pa.

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases with depth in a fluid and can be calculated using the formula P = ρgh, where P is the pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the height of the fluid column above the point in question.

Conversion of Units

In chemistry and physics, it is often necessary to convert between different units of measurement. For this problem, understanding how to convert pressure from torr to atmospheres is essential, as 1 atm is equivalent to 760 torr. This conversion allows for consistent units when calculating the total pressure experienced by the diver.

Total Pressure Calculation

The total pressure experienced by an object submerged in a fluid is the sum of the atmospheric pressure and the hydrostatic pressure due to the fluid above it. In this case, the total pressure on the diver can be calculated by adding the atmospheric pressure (in atmospheres) to the hydrostatic pressure calculated from the depth of the water.