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 p 0 . 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
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 p 0 . 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
Solution Summary: The author explains the absolute pressure of gas trapped below the piston when in equilibrium.
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?
A sealed cubical container 23.0 cm on a side contains a gas with three times Avogadro's number of neon atoms at a temperature of 29.0°C.
HINT
(a)
Find the internal energy (in J) of the gas.
J
(b)
The total translational kinetic energy (in J) of the gas.
J
(c)
Calculate the average kinetic energy (in J) per atom.
J
(d)
Use
P =
2
3
N
V
1
2
mv2
to calculate the gas pressure (in Pa).
Pa
(e)
Calculate the gas pressure (in Pa) using the ideal gas law
(PV = nRT).
Pa
A frictionless gas-filled cylinder is fitted with a movable piston. The block resting on the top of the piston determines the constant pressure that the gas has. The height h is 0.112 m when the temperature is 273 K and increases as the temperature increases. What is the value of h when the temperature reaches 330 K?
A sealed cubical container 19.0 cm on a side contains a gas with five times Avogadro's number of krypton atoms at a temperature of 15.0°C.
HINT
(a)
Find the internal energy (in J) of the gas.
J
(b)
The total translational kinetic energy (in J) of the gas.
J
(c)
Calculate the average kinetic energy (in J) per atom.
J
(d)
Use
P =
2
3
N
V
1
2
mv2
to calculate the gas pressure (in Pa).
Pa
(e)
Calculate the gas pressure (in Pa) using the ideal gas law
(PV = nRT).
Pa
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