A vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P18.40). The piston is not restricted in its motion in any way and is supported by the gas at pressure P below it. Atmospheric pressure is P0. We wish to find the height h in Figure P18.40. (a) What analysis model is appropriate to describe the piston? (b) Write an appropriate force equation for the piston from this analysis model in terms of P, P0, m, A, and g. (c) Suppose n moles of an ideal gas are in the cylinder at a temperature of T. Substitute for P in your answer to part (b) to find the height h of the piston above the bottom of the cylinder.
Figure P18.40
Trending nowThis is a popular solution!
Chapter 19 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- A vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P16.56). The piston is not restricted in its motion in any way and is supported by the gas at pressure P below it. Atmospheric pressure is P0. We wish to find die height h in Figure P16.56. (a) What analysis model is appropriate to describe the piston? (b) Write an appropriate force equation for the piston from this analysis model in terms of P, P0, m, A, and g. (c) Suppose n moles of an ideal gas are in the cylinder at a temperature of T. Substitute for P in your answer to part (b) to find the height h of the piston above the bottom of the cylinder.arrow_forwardA manometer containing water with one end connected to a container of gas has a column height difference of 0.60 m (Fig. P15.72). If the atmospheric pressure on the right column is 1.01 105 Pa, find the absolute pressure of the gas in the container. The density of water is 1.0 103 kg/m3. FIGURE P15.72arrow_forwardA gas is in a container of volume V0 at pressure P0. It is being pumped out of the container by a piston pump. Each stroke of the piston removes a volume Vs through valve A and then pushes the air out through valve B as shown in Figure P19.74. Derive an expression that relates the pressure Pn of the remaining gas to the number of strokes n that have been applied to the container. FIGURE P19.74arrow_forward
- A manometer is shown in Figure P15.36. Rank the pressures at the five locations indicated from highest to lowest. Indicate equal pressures, if any. FIGURE P15.36arrow_forward(a) Given that air is 21% oxygen, find the minimum atmospheric pressure that gives a relatively safe partial pressure of oxygen of 0.16 atm. (b) What is the minimum pressure that gives a partial pressure of oxygen above the quickly fatal level of 0.06 atm? (c) The air pressure at the summit of Mount Everest (8848 m) is 0.334 atm. Why have a few people climbed it without oxygen, while some who have tried, even though they had trained at high elevation, had to tum back?arrow_forwardConsider the piston cylinder apparatus shown in Figure P20.81. The bottom of the cylinder contains 2.00 kg of water at just under 100.0c. The cylinder has a radius of r = 7.50 cm. The piston of mass m = 3.00 kg sits on the surface of the water. An electric heater in the cylinder base transfers energy into the water at a rate of 100 W. Assume the cylinder is much taller than shown in the figure, so we dont need to be concerned about the piston reaching the top of the cylinder. (a) Once the water begins boiling, how fast is the piston rising? Model the steam as an ideal gas. (b) After the water has completely turned to steam and the heater continues to transfer energy to the steam at the same rate, how fast is the piston rising?arrow_forward
- When a person sits erect, increasing the vertical position of their brain by 36.0 cm, the heart must continue to pump blood to the brain at the same rate. (a) What is the gain in gravitational potential energy for 100 mL of blood raised 36.0 cm? (b) What is the drop in pressure, neglecting any losses due to friction? (c) Discuss how the gain in gravitational potential energy and the decrease in pressure are related.arrow_forwardA vertical cylindrical tank contains 1.80 mol of an ideal gas under a pressure of 0.300 atm at 20.0C. The round part of the tank has a radius of 10.0 cm, and the gas is supporting a piston that can move up and down in the cylinder without friction. There is a vacuum above the piston. (a) What is the mass of this piston? (b) How tall is the column of gas that is supporting the piston?arrow_forwardA cylinder containing ideal gas is sealed by a piston that is above the gas. The piston is a cylindrical object, with a weight of 22.0 N, which can slide up or down in the cylinder without friction. The inner radius of the cylinder, and the radius of the piston, is 8.00 cm. The top of the piston is exposed to the atmosphere, and the atmospheric pressure is 101.3 kPa. The cylinder has a height of 30.0 cm, and, when the temperature of the gas is 20°C, the bottom of the piston is 11.0 cm above the bottom of the cylinder. (A) Find the number of moles of ideal gas in the cylinder. (B) Heat is added, gradually raising the temperature of the gas to 160°C. Calculate the distance between the bottom of the cylinder and the bottom of the piston when the piston comes to its new equilibrium position.arrow_forward
- A cylinder containing ideal gas is sealed by a piston that is above the gas. The piston is a cylindrical object, with a weight of 34.0 N, which can slide up or down in the cylinder without friction. The inner radius of the cylinder, and the radius of the piston, is 6.00 cm. The top of the piston is exposed to the atmosphere, and the atmospheric pressure is 101.3 kPa. The cylinder has a height of 30.0 cm, and, when the temperature of the gas is 20°C, the bottom of the piston is 15.0 cm above the bottom of the cylinder. (a) Determine the pressure of the gas in the cylinder. kPa (b) Find the number of moles of ideal gas in the cylinder. moles (c) Heat is added, gradually raising the temperature of the gas to 185°C. Calculate the distance between the bottom of the cylinder and the bottom of the piston when the piston comes to its new equilibrium position. cmarrow_forwardA 0.435 kg0.435 kg metal cylinder is placed inside the top of a plastic tube, the lower end of which is sealed off by an adjustable plunger. The cylinder comes to rest some distance above the plunger. The plastic tube has an inner radius of 6.56 mm6.56 mm and is frictionless. Neither the plunger nor the metal cylinder allow any air to flow around them. If the plunger is suddenly pushed upwards, increasing the pressure between the plunger and the metal cylinder by a factor of 2.792.79, what is the initial acceleration ?a of the metal cylinder? Assume the pressure outside of the tube is 1.00 atm1.00 atm and that the top of the tube is open to the air.arrow_forwardA rigid tank having a volume of 0.100 m3 contains helium gas at 175 atm. How many balloons can be inflated by opening the valve at the top of the tank? Each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of 1.45 atm. (Remember that the tank cannot be completely emptied of gas.)arrow_forward
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning