Textbook Question
(b) Which units are appropriate for expressing atmospheric pressures, N, Pa, atm, kg/m2?
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Ch.10 - Gases
Chapter 10, Problem 15b
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 (b) atmospheres
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First, understand that pressure is defined as force per unit area. The formula for pressure is \( P = \frac{F}{A} \), where \( P \) is pressure, \( F \) is force, and \( A \) is area.
Next, calculate the force exerted by the person. Since weight is a force due to gravity, use the formula \( F = m \cdot g \), where \( m \) is mass (75 kg) and \( g \) is the acceleration due to gravity (approximately 9.81 m/s²).
Convert the contact area from cm² to m² for consistency in units. Since 1 cm² = 0.0001 m², the area \( A \) is \( 5.0 \text{ cm}^2 \times 0.0001 \text{ m}^2/\text{cm}^2 = 0.0005 \text{ m}^2 \).
Substitute the values of force and area into the pressure formula to find the pressure in pascals (Pa). \( P = \frac{F}{A} \).
Finally, convert the pressure from pascals to atmospheres. Use the conversion factor \( 1 \text{ atm} = 101325 \text{ Pa} \). Divide the pressure in pascals by 101325 to get the pressure in atmospheres.
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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.
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Units of Pressure
Pressure can be expressed in various units, including pascals (Pa), atmospheres (atm), and millimeters of mercury (mmHg). To convert pressure from pascals to atmospheres, one can use the conversion factor: 1 atm = 101,325 Pa. Understanding these units is essential for accurately reporting the pressure exerted.
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Weight and Force
Weight is the force exerted by gravity on an object and is calculated as the product of mass and gravitational acceleration (W = mg). In this scenario, the person's weight (75 kg) contributes to the total force acting on the stool, which is crucial for determining the pressure on the surface below.
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Related Practice
Textbook Question
(c) Which is most likely to be a gas at room temperature and ordinary atmospheric pressure, F2, Br2, K2O?
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Textbook Question
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
1
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Textbook Question
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) 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.
Textbook Question
(b) What pressure, in atmospheres, is exerted on the body of a diver if she is 10 m below the surface of the water when the atmospheric pressure is 100 kPa? 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