Ch.10 - Gases

Problem 15a

Chapter 10, Problem 15a

A person weighing 75 kg is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is 5.0 cm2, calculate the pressure exerted on the underlying surface in (a) bars

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Convert the weight of the person from kilograms to newtons by multiplying by the acceleration due to gravity (9.8 m/s^2).

Calculate the pressure using the formula: Pressure = Force / Area.

Convert the contact area from cm^2 to m^2 by multiplying by 1e-4.

Substitute the force (in newtons) and the area (in m^2) into the pressure formula to find the pressure in pascals (Pa).

Convert the pressure from pascals to bars, knowing that 1 bar = 100,000 Pa.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Pressure

Pressure is defined as the force exerted per unit area. In this context, it is calculated by dividing the weight of the person by the contact area of the stool's foot that is in contact with the ground. The formula for pressure (P) is P = F/A, where F is the force (weight) and A is the area.

Units of Pressure

Pressure can be expressed in various units, including pascals (Pa), bars, and atmospheres. One bar is equivalent to 100,000 pascals. Understanding how to convert between these units is essential for solving problems related to pressure, especially when the required answer is in a specific unit like bars.

Weight and Force

Weight is the force exerted by gravity on an object and is calculated as the mass of the object multiplied by the acceleration due to gravity (approximately 9.81 m/s² on Earth). In this scenario, the weight of the person (75 kg) is the force that will be used to calculate the pressure exerted on the surface when the stool tilts.

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Textbook Question

Which of the following statements is false? (a) Gases are far less dense than liquids. (b) Gases are far more compressible than liquids. (c) Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors. (d) The volume occupied by a gas is determined by the volume of its container.

(b) Which units are appropriate for expressing atmospheric pressures, N, Pa, atm, kg>m2?

A person weighing 75 kg is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is 5.0 cm2, calculate the pressure exerted on the underlying surface in (c) pounds per square inch

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Textbook Question

A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 3.0 x 4.1 in contact with the floor. The total mass of the shelves plus the books stacked on them is 266 kg.

Calculate the pressure in pascals exerted by the shelf footings on the surface.

(a) How high in meters must a column of ethanol be to exert a pressure equal to that of a 100-mm column of mercury? The density of ethanol is 0.79 g/mL, whereas that of mercury is 13.6 g/mL. Assume that the density of the water is 1.00 5 1.00 3 103 kg/m3. The gravitational constant is 9.81 m/s2, and 1 Pa 5 1 kg/ms2.

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