Essential University Physics: Volume 1 (3rd Edition)
3rd Edition
ISBN: 9780321993724
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 18, Problem 70P
A horizontal piston-cylinder system containing n mol of ideal gas is surrounded by air at temperature T0 and pressure p0. If the piston is displaced slightly from equilibrium, show that it executes
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A frictionless piston of mass m = 3.0 kg is a precise fit in the narrow vertical cylindrical neck of a large container of volume V = 1000 litres and can move frictionless. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A = 1.00 x 10-4 m2.
a) Assuming that the pressure and volume of the gas change slowly and isothermally, determine the differential equation of motion for small displacements of the piston about its equilibrium position and hence calculate the angular frequency of oscillation.
[Hint: find an equilibrium pressure and consider how small displacement of the piston from the equilibrium position changes the volume and pressure in the vessel].
b) Without calculation, consider whether the frequency will increase or decrease if the pressure and volume of the gas were to change adiabatically. Explain your reasoning.
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Chapter 18 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Ch. 18.2 - Two identical gas-cylinder systems are taken from...Ch. 18.2 - Name the basic thermodynamic process involved when...Ch. 18.3 - The same amount of heat flows into equal volumes...Ch. 18 - Prob. 1FTDCh. 18 - Prob. 2FTDCh. 18 - Prob. 3FTDCh. 18 - Why cant an irreversible process be described by a...Ch. 18 - Are the initial and final equilibrium states of an...Ch. 18 - Does the first law of thermodynamics apply to...Ch. 18 - Prob. 7FTD
Ch. 18 - Figure 18.18 shows two processes, A and B. that...Ch. 18 - When you let air out of a tire, the air seems...Ch. 18 - Blow on the back of your hand with your mouth wide...Ch. 18 - You boil water in an open pan. Of which of the...Ch. 18 - Three identical gas-cylinder systems are...Ch. 18 - Prob. 13FTDCh. 18 - In what sense can a gas of diatomic molecules be...Ch. 18 - Prob. 15ECh. 18 - Prob. 16ECh. 18 - A 40-W heat source is applied to a gas sample for...Ch. 18 - Find the rate of heat flow into a system whose...Ch. 18 - In a certain automobile engine, 17% of the total...Ch. 18 - An ideal gas expands from the state (p1, V1) to...Ch. 18 - Repeat Exercise 20 for a process that follows the...Ch. 18 - A balloon contains 0.30 mol of helium. It rises,...Ch. 18 - The balloon of Exercise 22 starts at 100 kPa...Ch. 18 - How much work does it take to compress 2.5 mol of...Ch. 18 - By what factor must the volume of a gas with =...Ch. 18 - Prob. 26ECh. 18 - A carbon-sequestration scheme calls for...Ch. 18 - A gas mixture contains 2.5 mol of O2 and 3.0 mol...Ch. 18 - A mixture of monatomic and diatomic gases has...Ch. 18 - What should be the approximate specific-heat ratio...Ch. 18 - Prob. 31ECh. 18 - An ideal gas expands to 10 times its original...Ch. 18 - During cycling, the human body typically releases...Ch. 18 - A 0.25-mol sample of ideal gas initially occupies...Ch. 18 - As the heart beats, blood pressure in an artery...Ch. 18 - It takes 1.5 kJ to compress a gas isothermally to...Ch. 18 - A gas undergoes an adiabatic compression during...Ch. 18 - A gas with = 1.40 occupies 6.25 L when its at...Ch. 18 - A gas sample undergoes the cyclic process ABCA...Ch. 18 - Prob. 40PCh. 18 - A gasoline engine has compression ratio 8.5 (sec...Ch. 18 - By what factor must the volume of a gas with =...Ch. 18 - Volvos B5340 engine, used in the V70 series cars,...Ch. 18 - A research balloon is prepared for launch by...Ch. 18 - Prob. 45PCh. 18 - By what factor does the internal energy of an...Ch. 18 - An ideal monatomic gas is compressed to half its...Ch. 18 - A gas expands isothermally from state A to state...Ch. 18 - A 3.50-mol sample of ideal gas with molar specific...Ch. 18 - Prove that the slope of an adiabat at a given...Ch. 18 - An ideal gas with = 1.67 starts at point A in...Ch. 18 - The gas of Example 18.4 starts at state A in Fig....Ch. 18 - The gas of Example 18.4 starts at state A in Fig....Ch. 18 - A 25-L sample of ideal gas with = 1.67 is at 250...Ch. 18 - Prob. 55PCh. 18 - A 25-L sample of ideal gas with = 1.67 is at 250...Ch. 18 - Youre the product safety officer for a company...Ch. 18 - Figure 18.22 shows data and a fit curve from an...Ch. 18 - External forces compress 21 mol of ideal monatomic...Ch. 18 - A gas with = 7/5 is at 273 K when its compressed...Ch. 18 - An ideal gas with = 1.3 is initially at 273 K and...Ch. 18 - The curved path in Fig. 18.23 lies on the 350-K...Ch. 18 - Repeat part (a) of Problem 62 for the path ACDA in...Ch. 18 - A gas mixture contains monatomic argon and...Ch. 18 - How much of a triatomic gas with Cv = 3R would you...Ch. 18 - An 8.5-kg rock at 0C is dropped into a...Ch. 18 - A piston-cylinder arrangement containing 0.30 mol...Ch. 18 - Experimental studies show that the pV curve for a...Ch. 18 - Show that the application of Equation 18.3 to an...Ch. 18 - A horizontal piston-cylinder system containing n...Ch. 18 - Prob. 71PCh. 18 - The table below shows measured values of pressure...Ch. 18 - In a reversible process, a volume of air V0= 17 m3...Ch. 18 - A real gas is more accurately described using the...Ch. 18 - Repeat Exercise 20 for an expansion along the path...Ch. 18 - The adiabatic lapse rate is the rate at which air...Ch. 18 - The nuclear power plant at which youre the public...Ch. 18 - Prob. 78PCh. 18 - One scheme for reducing greenhouse-gas emissions...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...Ch. 18 - Warm winds called Chinooks (a Native-American term...
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- 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_forwardAn ideal gas is contained in a vessel at 300 K. The temperature of the gas is then increased to 900 K. (i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of 3, (d) a factor of 1, or (e) a factor of 13? Using the same choices as in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a collision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas?arrow_forward(a) Show that the density of an ideal gas occupying a volume V is given by = PM/KT, where M is the molar mass. (b) Determine the density of oxygen gas at atmospheric pressure and 20.0C.arrow_forward
- A gas is at 200 K. If we wish to double the rms speed of the molecules of the gas, to what value must we raise its temperature? (a) 283 K (b) 400 K (c) 566 K (d) 800 K (e) 1 130 Karrow_forwardThe mass of a single hydrogen molecule is approximately 3.32 1027 kg. There are 5.64 1023 hydrogen molecules in a box with square walls of area 49.0 cm2. If the rms speed of the molecules is 2.72 103 m/s, calculate the pressure exerted by the gas.arrow_forwardOne cylinder contains helium gas and another contains krypton gas at the same temperature. Mark each of these statements true, false, or impossible to determine from the given information. (a) The rms speeds of atoms in the two gases are the same. (b) The average kinetic energies of atoms in the two gases are the same. (c) The internal energies of 1 mole of gas in each cylinder are the same. (d) The pressures in the two cylinders ale the same.arrow_forward
- A cylinder that has a 40.0-cm radius and is 50.0 cm deep is filled with air at 20.0C and 1.00 atm (Fig. P10.74a). A 20.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi (Fig. P16.74b). Finally, a 25.0-kg dog stands on the piston, further compressing the air, which remains at 20C (Fig. P16.74c). (a) How far down (h) does the piston move when the dog steps onto it? (b) To what temperature should the gas be warmed to raise the piston and dog back to hi?arrow_forwardOn a hot summer day, the density of air at atmospheric pressure at 35.0C is 1.1455 kg/m3. a. What is the number of moles contained in 1.00 m3 of an ideal gas at this temperature and pressure? b. Avogadros number of air molecules has a mass of 2.85 102 kg. What is the mass of 1.00 m3 of air? c. Does the value calculated in part (b) agree with the stated density of air at this temperature?arrow_forwardA 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_forward
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