Concept explainers
CP Oscillations of a Piston. A vertical cylinder of radius r contains an ideal gas and is fitted with a piston of mass m that is free to move (Fig. P18.79). The piston and the walls of the cylinder are frictionless, and the entire cylinder is placed in a constant-temperature bath. The outside air pressure is p0. In equilibrium, the piston sits at a height h above the bottom of the cylinder. (a) Find the absolute pressure of the gas trapped below the piston when in equilibrium. (b) The piston is pulled up by a small distance and released. Find the net force acting on the piston when its base is a distance h + y above the bottom of the cylinder, where y ≪ h. (c) After the piston is displaced from equilibrium and released, it oscillates up and down. Find the frequency of these small oscillations. If the displacement is not small, are the oscillations simple harmonic? How can you tell?
Figure P18.79
Want to see the full answer?
Check out a sample textbook solutionChapter 18 Solutions
University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)
- 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_forwardCylinder A contains oxygen (O2) gas, and cylinder B contains nitrogen (N2) gas. If the molecules in the two cylinders have the same rms speeds, which of the following statements is false? (a) The two gases haw different temperatures. (b) The temperature of cylinder B is less than the temperature of cylinder A. (c) The temperature of cylinder B is greater than the temperature of cylinder A. (d) The average kinetic energy of the nitrogen molecules is less than the average kinetic energy of the oxygen molecules.arrow_forwardAn ideal gas is trapped inside a tube of uniform cross-sectional area sealed at one end as shown in Figure P19.49. A column of mercury separates the gas from the outside. The tube can be turned in a vertical plane. In Figure P19.49A, the column of air in the tube has length L1, whereas in Figure P19.49B, the column of air has length L2. Find an expression (in terms of the parameters given) for the length L3 of the column of air in Figure P19.49C, when the tube is inclined at an angle with respect to the vertical. FIGURE P19.49arrow_forward
- A sealed cubical container 20.0 cm on a side contains a gas with three times Avogadros number of neon atoms at a temperature of 20.0C. (a) Find the internal energy of the gas. (b) Find the total translational kinetic energy of the gas. (c) Calculate the average kinetic energy per atom, (d) Use Equation 10.13 to calculate the gas pressure. (e) Calculate the gas pressure using the ideal gas law (Eq. 10.8).arrow_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) An ideal gas occupies a volume of 1.0 cm3 at 20.C and atmospheric pressure. Determine the number of molecules of gas in the container, (b) If the pressure of the 1.0-cm3 volume is reduced to 1.0 1011 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container?arrow_forward
- The density of helium gas at 0°C is ρ0 = 0.179 kg/m3. The temperature is then raised to T = 170°C, but the pressure is kept constant. Assuming that helium is an ideal gas, calculate the new density ρf of the gas. kg/m3arrow_forward*26. Go The drawing shows an ideal gas confined to a cylinder by a massless piston that is attached to an ideal spring. Outside the cylinder is a vacuum. The cross- sectional area of the piston is A = 2.50 × 10-³ m². The initial pressure, volume, and temperature of the gas are, respectively, Po, Vo = 6.00 × 10-ª m², and T. = 273 K, and the spring is initially stretched by an amount xo = 0.0800 m with respect to its unstrained length. The gas is heated, so that its final pressure, volume, and temperature are P, V;, and T., and the spring is stretched by an amount x; = 0.1000 m with respect to its unstrained length. What is the final temperature of the gas? Pistonarrow_forward14. GO Four closed tanks, A, B, C, and D, each contain an ideal gas. The table gives the absolute pressure and volume of the gas in each tank. In each case, there is 0.10 mol of gas. Using this number and the data in the table, compute the temperature of the gas in each tank. A B C D Absolute pressure (Pa) Volume (m³) 25.0 30.0 20.0 2.0 4.0 5.0 5.0 75arrow_forward
- A cylinder with a diameter of 5.64 cm has a movable piston attached to a spring as shown in Figure P.40. The cylinder contains 1.32 liters of an ideal gas at 17.8°C and 0.93 atm pressure. After the gas is heated briefly and allowed to expand, it is found that the spring compresses 3.42 cm and the temperature of the gas increases to 103°C. What is the change in volume for this expansion?_______ mLWhat is the change in pressure?_______ atmWhat is the spring constant k?_______ N/marrow_forwardA container having a volume of 2.30 L holds 1.80 g of helium gas at a temperature of 29.0 °C. (a) Find the pressure in the container. P = atm (b) Helium behaves as an ideal monoatomic gas. Find the internal energy of the system. Eint =arrow_forwarda 6.0 cm diameter cyliinder of nitrogen gas has a 4.0 cm thick movable copper piston. the cylinder is oriented vertically as shown in the figure, and the air above the piston is evacuated. when the gas temperature is 25 degree C the piston floats 20 cm above the bottom of the cylinder what is the gas pressure? how many gas molecules are in the cylinder?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics 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
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning