Physics Fluids and Thermo Test

A block with mass mb sits at rest on a movable piston with mass mp that is fitted in the top of a cylindrical tank filled with a gas. When the block is removed, the piston accelerates upward. Free-body diagrams for the piston before and after the block is removed are shown above. Which of the following gives the correct expression for the acceleration of the piston at the instant after the block is removed?

(mb/mp)g Correct. Using Newton's second law before the block is removed gives ∑Fbefore=Fgas−(Wpiston+Wblock)=0, so Fgas=(mp+mb)g. Using Newton's second law after the block is removed gives ∑Fafter=Fgas−Wpiston=mpa, so a=Fgas−mpg/mp. Substituting for Fgas gives a=(mp+mb)g−mpg/mp=mb/mpg.

A gas enclosed in a cylinder has a pressure of 2.0×10^5Pa. The ends of the cylinder have a diameter of 0.40m and the cylinder has a height of 0.30m. The magnitude of the force exerted by the gas on the wall at one end of the cylinder is most nearly

2.5x10^4 N Correct. The force on one end wall is related to the pressure by F=PA=P(πr^2). Substituting values gives F=(2.0×10^5Pa)(π[0.40m/2]^2)=2.5×10^4N.

A gas is enclosed in a container. Figure 1 shows one gas molecule moving up and to the right toward a wall of the container. The molecule collides with the wall and afterward moves up and to the left. Figure 2 shows the average force exerted by the molecule on the wall. Which of the following best shows the average force exerted on the molecule during the collision? Gravity is negligible.

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A system consists of two containers containing different liquids. The system is insulated, and no thermal energy is lost to or gained from the environment. Liquid A has a density of 800kg/m^3 and an initial temperature of 60°C , while liquid B has a density of 1000kg/m^3 and an initial temperature of 20°C. Which of the following statements accurately predicts what will happen once the containers are put into thermal contact? Select two answers.

After a long time, the liquids will have the same temperature. Thermal energy will be transferred from liquid A to liquid B because liquid A has more internal energy per molecule. Correct. The internal energy per molecule is related to temperature, and thermal energy is transferred from the liquid with the higher temperature to the liquid with the lower temperature.

The small dots in the figure represent the molecules of a solid object, and the dashed lines represent the molecular bonds between them. The large dots represent the molecules of a liquid in which the object floats. Which of the following best describes the force that explains the interaction of the object and the liquid?

An electrical force that repels the electrons of the object's molecules from the electrons of the liquid's molecules Correct. The individual molecules of the liquid do not pass through the solid, and the individual molecules of the solid do not pass through the liquid, because the outer electrons repel each other.

An ideal gas is in a sealed cylinder with a moveable piston, as shown. In collisions between any two molecules of the gas, the linear momentum and the kinetic energy of the two-molecule system are the same before and after the collision. The gas is then heated until it reaches a certain temperature, and the heat source is removed. Which of the following claims correctly describes the linear momentum and kinetic energy in a collision between two gas molecules of the hotter gas?

Both the linear momentum and the kinetic energy have the same values before and after the collision. Correct. The fact that the gas is now hotter does not affect the application of conservation laws to the individual collisions.

A sample of an ideal gas is in a sealed cylinder with a movable piston and is initially in state A, as shown in the graph of pressure P as a function of volume V. The gas's temperature in state A is 300K. The gas can be taken from state A to state D via three separate paths, AD, ABD, or ABCD.

CD Correct. The only transfer of energy is by heating because the area under the curve is zero, and the energy is being transferred from the gas to the environment, since the temperature of the gas is decreasing.

A sphere of metal is placed in a liquid. The sphere sinks with an acceleration less than g due to the vertical buoyant force FB exerted by the liquid and the gravitational force Fg on the sphere. Which of the following best represents these two forces?

Correct. Since the sphere has a downward acceleration less than gg, the buoyant force must be opposite the gravitational force, and downward force of gravity must be greater than the upward buoyant force.

A sample of an ideal gas can be taken through the four thermodynamic processes, W, X, Y, and Z, shown in the four graphs of pressure P as a function of volume V. Processes W and X occur once every second while processes Y and Z occur twice every second. Which of the following correctly ranks the energy E transferred out of the gas in a given time interval?

EY>(EW=EZ)>EX Correct. The net amount of energy transferred per cycle is equal to the work done, which is the area of the graph bounded by the process. Graphs that bound a greater area indicate a larger net work for each iteration of the process. Processes W and Y have the same area, but process Y occurs twice per second and W only occurs once per second, so EY>EW. Process Z has half the area of process W, but it also occurs twice per second, so EW=EZ. Process X has the same area as process Z, but it only occurs once per second, so EZ>EX.

In an experiment, a student puts each of three objects, A, B, and C, in four different liquids and observes whether the objects float. The results are listed in the table. Which columns contain information that is most useful for estimating the density of object C?

Gasoline and Oil Correct. Upper and lower bounds on the density of object C are set by the least dense liquid that the object floats in and the most dense liquid that the object sinks in. Object C sinks only in the gasoline, so that is the only fluid that is less dense than the object. That sets the lower bound on the object's density. The object floats in the other three liquids, so it is less dense than all of them. The upper bound is set by the least dense of the liquids, which is oil.

A fountain in a park shoots a stream of water at an angle. Initially the stream reaches a height H and travels a horizontal distance D before hitting the ground. Over time, minerals in the water are deposited around the edges of the fountain opening, making it smaller. Which of the following describes the height and horizontal distance of the stream of water from the fountain at some later time?

Height: greater than H Horizontal Distance: greater than D Correct. According to the equation of continuity, a smaller opening means a greater exit speed. Both the vertical and horizontal components of the speed increase, so both the height and horizontal distance increase.

A student watches a soap bubble drift from inside a warm room, out an open window, and into the cold air outside. The student notices that the bubble gets smaller once it is outside. Assuming no air leaks out of the bubble, what conclusion could the student reasonably draw from this observation?

If the bubble were cooled even further, there is a temperature at which the volume of the bubble approaches zero. Correct. There is a temperature, absolute zero, at which the volume and pressure extrapolate to zero. At this temperature, all molecular motion stops, and a collection of gas atoms or molecules would have no motion and could not exert a pressure.

The graph shows pressure as a function of volume for a sample of an ideal gas in a cylinder. Which of the following is correct about the net work done by the gas during the cycle shown?

It is equal to the area enclosed by the cycle, because the net work is the work done by the gas during process X minus the work done on the gas during process Y . Correct. The net work is the sum of all the positive and negative amounts of work done by the gas.

Gases do not always behave ideally. Suppose one oxygen atom of a sample of gas is moving with speed v when it collides with and sticks to another oxygen atom that is momentarily at rest. Which of the following claims correctly describes the linear momentum and kinetic energy of the two-atom system after the collision compared to the linear momentum and kinetic energy before the collision?

Linear Momentum: the same Kinetic Energy:Less Correct. Linear momentum is conserved in all collisions where no external force is exerted on the system. The collision is inelastic, so kinetic energy is not conserved

A sample of gas X initially has a higher temperature than a sample of gas Y . The molecules of gas X have more mass than the molecules of gas Y . The samples are mixed together in an insulated container. Which of the following claims best describes the collisions between gas X and gas Y molecules?

Molecules of both gases will sometimes gain and sometimes lose momentum, and sometimes gain and sometimes lose kinetic energy. Correct. While the average speed of the gas X molecules is greater than the average speed of the gas Y molecules, the molecules of each gas have a variety of speeds. So the gas X molecule could have a greater speed or a smaller speed than the gas Y molecule. What happens in a collision depends on the relative speeds of the molecules.

A student has a sample of gas in an insulated cylindrical container with a movable piston. The student compresses the gas by increasing the force exerted on the piston and measures the pressure and volume of the gas. The student needs to determine the work done on the gas. Which of the following describes a correct analysis of information from the graph that will determine the work?

Multiply the total change in pressure by the total change in volume. Divide the result by two. Add to this the product of the final pressure and the total change in volume. Correct. The work done on the system is the area under the best-fit line to the data on the graph. This can be found by adding the triangular area defined by the data points to the rectangular area below this.

In the figure, water flows from a section of pipe with a smaller radius to a section of pipe with a larger radius. How do the pressure and velocity in the wider pipe compare to those in the narrower pipe?

Pressure: Greater Velocity: Less Correct. According to the equation of continuity, the velocity of the water in the wider pipe is less than in the narrower pipe. According to Bernoulli's equation, when water does not change vertical position, a lesser velocity corresponds to a greater pressure.

Which of the following correctly explain why the pressure of a gas in a rigid container increases with increasing temperature? Select two answers.

The average molecular kinetic energy increases with temperature, so the molecules exert a larger average force on the walls of the container when they collide with the walls of the container. The average molecular speed increases with temperature, so the molecules collide with the walls of the container more frequently. Correct. The pressure of a gas is the force it exerts on the walls of the container divided by the area of the walls. If the molecules on average are moving faster because of increased temperature, then they collide with the walls more frequently, increasing the average force exerted on the walls.

A solid cube is submerged in a container of water of density ρw . The cube has mass M , volume Vc , and density ρw2 . The water exerts an upward buoyant force on the cube of magnitude ρwVcg . A solid sphere with unknown mass and twice the volume of the cube is submerged and then released. The sphere is observed to have the same acceleration immediately after release as the original cube. Which of the following claims can be made about the density of the sphere?

The density of the sphere must be the same as that of the cube because in order to have the same acceleration, the sphere's mass must be twice the mass of the cube. Correct. To have the same acceleration as the cube, the sphere's mass-to-volume ratio must be the same as that of the cube, so the mass of the sphere must also be twice the mass of the cube. Hence, the density is the same.

A block is submerged in a container of fluid. Which of the following describes the microscopic cause of the force exerted on the bottom of the block by the fluid being greater than the force exerted on the top of the block by the fluid?

The electrostatic force between the electrons in the molecules of the block and the electrons in the molecules of the fluid is greater at the bottom than at the top. Correct. Contact forces are due to interatomic electric forces. The electrons of the molecules on the surface of the materials in contact repel each other.

The figure shows a sample of an ideal gas enclosed within a cylinder that has been fitted with a movable piston. The piston and the sides of the cylinder are thermally insulated. The bottom of the cylinder is in contact with a thermal reservoir. The gas is compressed isothermally while thermal equilibrium is maintained with the reservoir. The piston, gas, and reservoir form a closed, isolated system. True statements about entropy for this reversible situation include which of the following? Select two answers.

The entropy of the gas decreases because work is done on the gas while its temperature remains constant. The entropy of the reservoir increases because thermal energy is transferred to it from the gas. Correct. The temperature is constant, so the change in entropy is proportional to the change in thermal energy. Since thermal energy is being transferred from the gas to the reservoir, the thermal energy of the reservoir, and hence the entropy, is increasing.

The temperature of an ideal gas is held constant as its volume is slowly decreased. Which of the following claims correctly describes the cause of the increase in the force exerted by the gas on the walls of the container?

The gas molecules strike the walls more frequently.

The figure shows a top view of three connected, horizontal pipes. Water moves from left to right in pipe A and then divides when it reaches the junction with pipes B and C. Pipes B and C have the same diameter, which is less than half the diameter of pipe A. Which of the following are correct statements about properties of the water? Select two answers.

The gravitational potential energy of the water-Earth system is the same in all three pipes because they are at the same height The kinetic energy of the water is the same in pipes B and C because they have the same diameter. Correct. Applying the equation of continuity yields Aava=Abvb+Acvc. The diameters of B and C, and thus their areas, are the same. So the speeds, and thus the kinetic energies, are also the same.

An ideal gas is confined in a container with a moveable piston. The graph of pressure as a function of volume shows four different processes in which the gas is compressed. Which of the following correctly ranks the magnitude of the work W done on the gas in the four processes?

W2> W1> (W3=W4) Correct. In this case, the line on the PV diagram that describes process 2 has the most area under it. The area under process 2 is greater than the area under process 1 which is greater than the area under process 3 or 4.

The figure shows a horizontal pipe with sections with different cross-sectional areas. Small tubes extend from the top of each section. The cross-sectional area of the pipe at location C is half that at A, and the areas at A and D are the same. Water flows in the pipe from left to right. Which of the following correctly ranks the height h of the water in the tubes above the labeled locations?

(ha=hd)> hb> hc Correct. According to Bernoulli's equation, the pressure is less in a liquid that is moving faster. The speed of liquid is inversely proportional to the cross-sectional area it moves through. So the narrowest part of the pipe has the highest speed and the lowest pressure, and it will support the shortest column of water.

A 1.0m by 2.0m by 3.0m rectangular block has a uniform density of 600kg/m^3and is completely submerged and held stationary in a deep pool of water. The water exerts an upward buoyant force on the block of 6×10^4N . The block is released and, after rising a short distance toward the surface, experiences a drag force of 2×10^4N. The magnitude of the acceleration of the block at this instant is most nearly

1.11 m/s^2 Correct. The mass of the block can be determined using the relation m=ρV=(600kg/m^3)(6m^3)=3.6×10^3 kg. Thus the force of gravity on the block is FGblock=ma=(3.6×10^3kg)(10m/s^2)=3.6×10^4 N. From a free-body diagram we find that the net force on the block is ΣF=Fbouyant−FGblock−Fdrag Substituting values gives ΣF=6×10^4 −3.6×10^4 −2×10^4N = 0.4×10^4N Thus, the acceleration of the block can be found using Newton's second law: a=ΣF/m=0.4×10^4N/3.6×10^3kg=1.11 m/s^2

Water with density 1000kg/m^3 is moving at 0.50m/s through a cylindrical tube with a diameter of 0.10m. The tube then narrows to a diameter of 0.05m. The mass flow rate in the narrow section of pipe is most nearly

3.9 kg/s Correct. The mass flow rate is the same throughout the pipe, so it can be calculated at the point where all the necessary data are given: fluid velocity (v) and diameter (d). Thus, massflowrate=ρvA=(10^3kg/m3)(0.5ms)(π(0.05m)^2)=3.9kg/m^3

An ideal fluid flows from left to right in the horizontal pipe shown in the figure. The fluid enters the left side of the pipe with speed v, where the diameter of the pipe is d. The pipe then narrows to a diameter of d/2. What is the speed of the fluid in the narrow section of the pipe with diameter d/2?

4v Correct. The mass flow rate must be the same in both sections of pipe, given by A1v1=A2v2. Therefore π(d/2)^2v=π(d/4)^2V, and (d^2/4)v=(d^2/16)V, resulting in a final answer V=4v

A quantity of an ideal gas, initially at zero degrees Celsius, is placed in a container of unknown fixed volume. The gas is heated, and the temperature and pressure are measured, resulting in the graph shown. Which of the following quantities can be determined from a best-fit line to the data?

Absolute zero Correct. The ideal gas law is PV=nRT. The equation for the best-fit line to the data can be written as P=nRVT+T0. Absolute zero is the temperature where all atomic and molecular motion stops, so the pressure of the gas is zero. Therefore, the line can be extrapolated to zero pressure to determine absolute zero.

Which of the following graphs best represents the absolute pressure Pabs at a point in a liquid near Earth's surface as a function of the depth h of the point below the surface of the liquid?

Correct. The relationship between Pabs and atmospheric pressure Patm is Pabs=Patm+ρgh. This is a linear relationship because ρ and g are constants, with a y-intercept equal to Patm

A plastic bowl is floating in a sink full of water. Which of the following describes the microscopic cause of the buoyant force exerted on the bowl by the water?

Electrostatic repulsion between the electrons in the molecules in the bowl and the electrons in the molecules of the water Correct. Contact forces are due to interatomic electric forces. The electrons of the molecules on the surface of the materials in contact repel each other.

A cylindrical container with a movable piston contains a fixed amount of ideal gas. Initially, it is in thermal equilibrium with an ice-water bath. The diagram shows the forces exerted on the piston. The cylinder is then removed from the ice water and placed into a hot-water bath. The system slowly comes to thermal equilibrium with its surroundings. The forces exerted on the piston once the system reaches equilibrium are shown in the figure. What is the relationship among the forces exerted on the piston?

Fgas=(Fatm+mg) Correct. At equilibrium, the net force on the piston is zero and the upward force equals the sum of the downward forces

In an experiment, a student releases an object from rest in four different liquids and observes whether it floats. The results are listed in the table. Which of the following is true about the density of the object?

It is between the density of distilled water and the density of salt water. Correct. The object floats in salt water, so its density is less than that of the salt water. The object sinks in distilled water, which has the next greatest density, so its density is greater than that of distilled water.

A sample of an ideal gas is in a sealed cylinder with a movable piston and is initially in state A, as shown in the graph of pressure P as a function of volume V. The gas's temperature in state A is 300K. The gas can be taken from state A to state D via three separate paths, AD, ABD, or ABCD.

None; the change in internal energy is the same for all three paths. Correct. All processes start at the same temperature and end at the same temperature, so the change in internal energy is the same for all processes.

Disk 1 of mass m is initially fixed inside a cylinder of cross-sectional area A . One end of the cylinder is closed, as shown in the figure, and the space between the closed end and disk 1 contains a gas that is maintained at gauge pressure P . Disk 1 is then released and accelerates through a distance d as it is pushed by the gas. After exiting the cylinder, disk 1 is surrounded by air of pressure P0 . It then collides with and sticks to disk 2 of mass 3m that is at rest. If friction is negligible, what is the final kinetic energy of the two-disk system?

PAd/4 Correct. The work done on disk 1 by the gas equals its kinetic energy as it leaves the cylinder. W=Fd=PAd=1/2mvi^2. The disks stick together, so they have the same final speed vf. Conserving momentum yields vf in terms of vi: mvi=4mvf so vf=vi/4. The final kinetic energy is 1/2(4m)vf^2=1/2(4m)vi^2/16=1/4(1/2mvi^2)=PAd/4

To launch a rocket, fuel in its engines is ignited, and the combustion produces gases at high pressure. As the combustion gases escape downward from one end of the rocket, the rocket is accelerated upward. Which of the following claims correctly describes forces in this situation?

The combustion gases are pushed out of the rocket because the pressure inside the engine is greater than the pressure outside the rocket. The rocket exerts a net downward force on the gases, which means the gases exert a net upward force on the rocket. Correct. According to Newton's third law, there will be a pair of forces acting between the rocket and the combustion gases. Because the gases are under pressure, the rocket exerts a force on the gases and the gases exert a force on the rocket.

Water is poured into a U-shaped tube and allowed to come to rest, as shown in the figure. Which of the following can help explain why the water in the left and right sides of the tube reaches the same height? Select two answers.

The force exerted by the atmosphere on the surface of the water is the same on both sides. The weight of water in the left and right halves of the tube is the same. Correct. The equilibrium water levels occurs when the net force is the same on both sides. Determining the net force includes accounting for the weight of fluid in each half of the tube. Since both ends of the tube are open to the air, the atmospheric force is the same on both of them. Since the atmospheric force is the same, the weight of liquid in each half must be the same. With only one liquid, this occurs when the same amount of liquid is in each half

A sphere made of gold is moving downward through liquid mercury at an increasing speed. The mercury exerts a net buoyant force in the upward direction on the gold sphere. Which of the following describes a Newton's-third-law pair for this force?

The gold sphere exerts a force on the mercury with magnitude equal to the buoyant force. Correct. The third-law counterpart to the buoyant force exerted by the mercury on the gold sphere will be the force exerted by the gold sphere on the mercury. In addition it will have magnitude equal to that of the buoyant force.

A wooden cube is floating at rest on the surface of a liquid. Which of the following is an action-reaction pair of forces that can explain why the force exerted by the liquid on the bottom of the container is greater with the floating cube than without it?

The liquid exerts a net upward force on the cube, and the cube exerts a contact force on the liquid. Correct. The force the cube exerts on the liquid is equivalent to increasing the force the air exerts on the liquid. The result is an increase in the force exerted by the liquid.

A sphere of radius R is filled with n moles of helium gas at a constant temperature T. A second sphere of radius 2R is filled with the same amount of helium gas at the same temperature. Which of the following is a reason why the pressure in the second sphere is less than that in the first sphere?

The molecules in the second sphere have to go travel a longer distance between collisions with the walls of the sphere than the molecules in the first sphere do Correct. The second sphere is larger, and because the molecules have the same temperature, they have the same average speed. So, it takes a molecule longer to travel across the diameter of the sphere, and it hits the sphere wall less frequently than it would in the first sphere. That means less force; thus, less pressure is exerted on the second sphere.

The figure shows a container filled with water to a depth d. The container has a hole a distance y above its bottom, allowing water to exit with an initially horizontal velocity. Which of the following correctly predicts and explains how the speed of the water as it exits the hole would change if the distance y above the bottom of the container increased?

The speed would decrease because the water pressure at the depth of the hole would decrease. Correct. The pressure increase in the container with depth is given by ρgΔh, where Δh is the distance below the surface of the water. According to Bernoulli's equation, the square of the speed of the water is proportional to the water pressure ρgΔh, which is decreasing because Δh decreases as y increases.

The figure shows a cylinder that has a movable piston and contains an ideal gas initially in state 1 at room temperature. The cylinder is sealed. Blocks of known mass can be added to or removed from the top of the piston. The gas is taken through the process represented by the graph of pressure P as a function of volume V. Which of the following energy bar charts could represent the process as the gas is taken from state 1 to state 2, where U1 represents the initial internal energy of the N molecules of gas, Q represents the energy transferred to the gas by heating, W represents the work done on the gas, and U2 represents the final internal energy of the gas?

U1- positive Q- negative W- small positive U2- small positive Correct. During the process, the gas loses thermal energy, and positive work is done on the gas. By the first law of thermodynamics, the sum of the change in thermal energy and the work done on the gas is equal to the change in the internal energy.

The figure shows a horizontal pipe with sections with different cross-sectional areas. The cross-sectional area of the pipe at location C is half that at A, and the cross-sectional areas at A and D are the same. Water flows in the pipe from left to right. Which of the following correctly ranks the mass flow rate f in the four sections of pipe?

fa=fb=fc=fd Correct. The mass flow rate is the mass of a substance that passes per unit of time. Although speed varies with cross-sectional area, the mass flow rate does not. No water is added or removed from the pipe between points A and B, so the mass flow rate must be equal at each point.

A solid cube is submerged in a container of water of density ρw . The cube has mass M , volume Vc , and density ρw/2 . The water exerts an upward buoyant force on the cube of magnitude ρwVcg . The cube is released and allowed to rise. What is the magnitude of the acceleration of the cube immediately after release?

g Correct. The forces exerted on the cube are the downward force of gravity and the upward buoyant force. Applying Newton's second law with the buoyant force ρwVc ggives Ma=ρwVc g−Mg. The mass of the cube is M=ρwVc/2. Substituting for the mass and solving gives a=g

The table lists experimental data related to the conduction of energy by three slabs of metal. The slabs have identical dimensions but are made of different metals. Which of the following correctly ranks the metals' thermal conductivities k ?

k1>k2>k3

Gas molecule A is moving to the right with speed v, as shown in the figure, when it collides with identical gas molecule B, which is at rest. After the collision, molecule A is moving directly toward the top of the page with the same speed v. Which of the following best represents the net force on molecule A during the collision?

up and to the left Correct. This force will reduce the horizontal speed of molecule AA to zero and give it a speed toward the top of the page. The horizontal and vertical components of the force are the same, so it will create the same change in speed in each direction.

An incompressible fluid is flowing in a pipe from point A to point B, as shown in the figure. The pipe is circular with a radius of 2cm at point A and a radius of 1cm at point B . The speed of the fluid at point A is vA . Which of the following best describes the speed vB of the fluid at point B ?

vb is greater than va by a factor of 4, which is the ratio of the cross-sectional area at point A to the cross-sectional area at point B Correct. According to the continuity equation, vA should be multiplied by the ratio of the cross-sectional area at point A to the cross-sectional area at point B

A sample of an ideal gas is contained in a cylinder with a moveable piston. The gas expands, doing work W on the piston and absorbing thermal energy Q from its surroundings. Which of the following identifies and justifies the correct form of the first law of thermodynamics during this process?

ΔU=Q−W , because thermal energy is transferred to the gas and work is done by the gas. Correct. Energy is transferred to the gas by heating, which acts to increase the internal energy, and work is done by the gas, which acts to decrease the internal energy.

A submarine of mass 3.6×106kg is submerged in water and at equilibrium. Inside of the submarine are ballast tanks filled with water. Some of the water in the ballast tanks is then ejected, decreasing the density of the submarine. The free-body diagram in the figure shows the magnitude and direction of the forces acting on the submarine after the water is ejected. The acceleration of the submarine is most nearly

1.1m/s^2 Correct. The acceleration is the net force divided by the object's mass. The net force is the buoyancy force (4.0×10^7) minus the weight of the object (3.6×10^7). This gives 4×10^6N and, when divided by the mass of the object (3.6×10^6), yields 1.1m/s^2

A positive gas ion with mass 1.66×10^−27kg is traveling with speed 150m/s in the +x -direction when it collides head-on with a negative gas ion with mass 2.32×10^−27kg traveling with speed 150m/s in the −x -direction. The ions stick together. What is the total kinetic energy of the two-ion system immediately after the collision?

1.2x10^-24J Correct. Using conservation of momentum, the final speed of the two-ion system can be determined: m+v+m−(−v)=(m++m−)vf so vf=m+v−m−v/m++m−= m+−m−/m++m−v. The kinetic energy can then be calculated. K=1/2(m++m−)v2f=1/2(m++m−)(m+−m−/m++m−v)2, and substituting gives K=1/2(1.66×10−27kg−2.32×10^−27kg)^2/1.66×10^−27kg+2.32×10^−27kg(150m/s)^2=1.2×10^−24J.

A container filled with gas is sealed on the top by a piston of negligible mass and area 0.005m^2. The container and gas are allowed to reach thermal equilibrium with the surrounding air, and a block on top of the piston keeps the piston in place. If the pressure inside the container is 3×10^5Pa, what is the total downward force exerted on the piston?

1500N Correct. The downward force on the piston must be equal in magnitude to the upward force exerted by the gas. The force exerted by the gas has magnitude PA=(3×10^5Pa)(0.005m^2)=1500N.

A cylinder is fitted with a low-friction, movable piston and filled with air at room temperature and atmospheric pressure, as shown in the left figure. The initial volume of the cylinder is 0.20m^3. The bottom of the cylinder is placed in an ice water bath, as shown in the right figure, causing the volume to decrease to 0.15m^3. The atmospheric pressure is 1.0×10^5Pa. What is the work done on the air inside the cylinder during this process?

5.0x10^3 J Correct. The work done on a gas at constant pressure is W=−PΔV. Since the volume of the gas decreased, positive work is done on the air in the piston: W=−(1.0×10^5Pa)(0.15m^3−0.20m^3)= 5×10^3J.

An ideal gas is sealed in a cylindrical container with an open top and a moveable piston, as shown in the figure. The piston has a mass of 10kg and a radius of 10cm. At the instant shown, the pressure of the gas in the cylinder is 105,000Pa. The free-body diagram shows the forces acting on the piston at this instant, which are the force FGas exerted by the ideal gas in the container, the force FAir exerted by the air above the piston, and the force Fg due to gravity. The magnitude of the acceleration of the piston is most nearly

5.7m/s^2 Correct. Applying Newton's second law to the three forces in the free-body diagram and using consistent signs for the directions allows one to solve for the acceleration: ma=FGas−FAir−Fg, a=FGas−FAir−Fg/m =PGasA−PAirA−Fg/m. Substituting the given values: a=(1.05×10^5Pa)(π0.1^2)−(1.0×10^5Pa)(π0.1^2)−(10kg)(10m/s^2)/ 10kg =5.7m/s^2.

In the system shown, a movable piston is initially at rest inside a cylindrical vacuum chamber. The piston has area 0.050m^2 and mass 0.50kg . An explosion just above the piston produces a pressure of 60,000Pa on the piston, causing it to rapidly accelerate downward . The free-body diagram of the piston just after the explosion is shown. What is the magnitude of the piston's acceleration at this instant?

6010m/s^2 Correct. Both the force of the explosion and the weight of the piston will add to the acceleration. To calculate the force exerted on the piston by the explosion, the relationship between pressure and force is used: F=PA=(60,000Pa)(0.050m^2)=3000N. Applying Newton's second law allows the acceleration to be determined: Fexplosion=mg+ma, a=Fexplosion/m+g=300N/0.50kg+10m/s^2=6010m/s^2.

A small submarine is underwater and moving horizontally at the same constant speed as the northward current in a straight, level section of a river. It releases a sensor that will float in the water. If resistance is negligible, what is the shape of the path followed by the sensor?

A parabolic path toward the north and curving upward Correct. If the sensor will float in the water, it will move upward. It is already going at the same speed as the water, so there is no horizontal force on it. The sensor follows a parabolic path like a projectile in air, but one that curves upward.

A sphere is moving vertically in a liquid. The free-body diagram shows the magnitudes and directions of the forces exerted on the sphere at a particular instant. What is the magnitude of the sphere's acceleration and the direction of the sphere's motion?

Acceleration: .07m/s^2 Downward Correct. The net force on the sphere is the weight minus the sum of the drag and buoyant forces, or 4.0N+5.2N−8.6N=0.6N. The acceleration is the net force divided by the mass, which can be determined from the weight. W=mg m=W/g=8.6N/10m/s^2 =0.86kg Therefore, the acceleration is Fnet/m =0.6N/0.86kg=0.7m/s^2. The direction of motion is downward because the drag force is upward and opposes the sphere's motion.

Oxygen molecules are in a closed container. One such molecule is traveling at 400m/s when it collides perpendicularly with the wall of the container. The mass of an oxygen molecule is 5.3×10^−26 kg. The molecule can be treated as if it were a spherical particle, and the gas can be treated as ideal. What are the magnitudes of the change in the momentum and the change in the kinetic energy of the oxygen molecule due to the collision?

Change in Momentum: 4.2x10^-23 kgm/s Change in kinetic energy: 0J Correct. The collision with the wall is elastic according to the model of ideal gases. Therefore, there is no change in kinetic energy due to the collision. The molecule bounces off the wall and reverses direction: Δp=mvf−mvo=(5.3×10^−26 kg)(−400−400)m/s=4.2×10^−23kg⋅ms.

A gas is in a sealed cylinder fitted with a movable piston, as shown in the figure, so that none of the gas escapes. The cylinder and piston are made of an insulating material. The cylinder is fitted with pressure and temperature sensors, and the volume of the confined gas can be measured from markings on the side of the cylinder. The gas is initially in a state with pressure Pi, temperature Ti, and volume Vi. The piston is slowly compressed and data are recorded until the gas reaches a final state with pressure Pf, temperature Tf, and volume Vf. A graph of the pressure as a function of volume is shown, with dotted lines indicating isotherms. Which of the following describes the energy transfer process that the insulation prevents?

Collisions of gas molecules with the inner surface of the cylinder cause disturbances of molecules of the insulating material that travel through the cylinder, transferring energy to air molecules that hit the outer surface of the cylinder Correct. The insulation prevents energy loss by conduction.

A solid cube is submerged in a container of water of density ρw . The cube has mass M , volume Vc , and density ρw2 . The water exerts an upward buoyant force on the cube of magnitude ρwVcg . Which of the diagrams is the best representation of the forces exerted by the water on the cube?

Correct. The pressure of the water increases with depth; thus, the force on the cube also increases with depth. The magnitude of the force exerted on the top face of the cube is less than that exerted on the bottom face. The average force exerted on each side of the cube has a magnitude between the forces exerted on the top and bottom.

A physics teacher gives a solid object to each student in her class. The objects are each made of the same material but have different shapes and sizes. The teacher asks the students to measure the mass and volume of their object and to work together to determine the density of the material from which the objects are made. Which of the following methods will give the best estimate of the material's density?

Each student shares the mass and volume of their object with the class. The class then creates a graph plotting mass as a function of volume, draws a best-fit line through the data, and uses the slope of the best-fit line as the density of the material. Correct. This procedure utilizes a line that comes closest to all of the data points. The slope of this line gives the ratio of mass divided by volume, which is density.

A block of weight W is floating in water, and one-third of the block is above the surface of the water. Which of the following correctly describes the magnitude F of the force that the block exerts on the water and explains why F has that value?

F=W. The block is at rest, so the net force on it must be zero. The water must exert an upward force of magnitude F on the block to make this so. The block then exerts a force of equal magnitude on the water Correct. By Newton's second law, the net force on the stationary block must be zero. So the water must be exerting a force equal to the block's weight on the block. By Newton's third law, the block must be exerting a force of magnitude W on the water.

In the lab, a student is given a glass beaker filled with water with an ice cube of mass m and volume Vc floating in it. The downward force of gravity on the ice cube has magnitude Fg . The student pushes down on the ice cube with a force of magnitude FP so that the cube is totally submerged. The water then exerts an upward buoyant force on the ice cube of magnitude FB . Which of the following is an expression for the magnitude of the acceleration of the ice cube when it is released?

FB−Fg/m Correct. Once the cube is released, the only forces are the upward buoyant force and gravity downward. Since the object floated, the buoyant force is greater than gravity, so the latter should be subtracted from the former.

A student conducts an experiment to measure the universal gas constant R using the apparatus shown. A cylinder with volume markings is filled with 0.45mol of helium gas at room temperature and pressure. The piston is connected to a lever system, as shown in Figure 1, with a pivot that is connected to a fixed support and moving hinges that allow the lever to push the rod and piston down. The student pushes on the lever and moves the piston down, as shown in Figure 2, to compress the gas as slowly and steadily as possible while the pressure, volume, and temperature of the gas are measured. The graph on the left shows pressure as a function of volume for this process. The graph on the right shows PV/nT as a function of time, which should show that R is constant. The student suspects that there is a problem with the experimental apparatus that caused the variation in data between 1 and 2 atm pressure. Which of the following issues with the apparatus would most likely have caused the anomalous data?

Hinges that stick and cause uneven motion of the lever. Correct. Any sudden motion of the lever can create conditions in the gas that are far from equilibrium so that the ideal gas law is not applicable.

A sphere with density ρs and volume V is submerged in a fluid with density ρf , which exerts a buoyant force of magnitude ρfVg on the sphere. Immediately after being released from rest, the sphere moves upward with an acceleration of magnitude a . Which of the following changes would result in an acceleration with greater magnitude immediately after release?

Increasing the density of the fluid Correct. The acceleration increases with increasing fluid density. This can be shown by applying Newton's second law to the sphere, expressing the sphere mass in terms of density and volume, and solving for the acceleration: ma=Fnet=Fbuoyant−mg, ρsVa=ρfVg−ρsVg, a=(ρf/ρs−1)g.

A gas is in a sealed cylinder fitted with a movable piston, as shown in the figure, so that none of the gas escapes. The cylinder and piston are made of an insulating material. The cylinder is fitted with pressure and temperature sensors, and the volume of the confined gas can be measured from markings on the side of the cylinder. The gas is initially in a state with pressure Pi, temperature Ti, and volume Vi. The piston is slowly compressed and data are recorded until the gas reaches a final state with pressure Pf, temperature Tf, and volume Vf. A graph of the pressure as a function of volume is shown, with dotted lines indicating isotherms. Which of the following claims identifies the change in internal energy of the gas between its initial and final states and describes the corresponding changes in energy due to work and heating?

Internal energy increases. Energy is added to the gas via work and none is lost by heating. Correct. The internal energy of a gas is proportional to its temperature. In this case, the temperature of the gas increased so the internal energy increased. The gas is insulated, so no energy was transferred by heating.

Students want to investigate the inverse relationship between the pressure and volume of an ideal gas as predicted by the ideal gas law. Their plan is to use a gas-filled cylinder with a movable piston on one end and compress the piston. The students will then measure the volume and pressure of the gas when the piston is in various positions. Which of the following additions to this procedure will allow the students to observe the predicted relationship between pressure and volume? Select two answers.

Maintain a constant gas temperature by surrounding the cylinder in a constant temperature water bath. Ensure the piston and cylinder walls don't allow gas in or out of the cylinder. Correct. Keeping the number of moles in the cylinder constant is required so only the relationship between pressure and volume is considered when using PV=nRT .

A student has four square plates. The two large plates are the same size but made of materials with different thermal conductivity, and are initially at thermal equilibrium with their surroundings. The two identical small square plates are initially heated to a temperature greater than that of the surroundings. Each small plate is placed in contact with one of the large plates in the configuration shown. For each configuration, the student will measure the time it takes for the temperature to begin to rise at one or both of the labeled points. A shorter time means a higher thermal conductivity. Measurement at which of the points gives the best information for determining which material has higher thermal conductivity?

Measurement at either point A or point B , because the relative times for either point will give sufficient information. Correct. The time measured at either point AA or point BB will be less for the plate made from the material with higher thermal conductivity.

Two types of gas atoms are mixed in an insulated container. The atoms collide and stick together, forming a gas of a new substance. The temperature of the new gas is higher than the temperatures of either of the original gases. Suppose the speeds of two colliding atoms of the original gases are known, and the speed of the resulting new gas molecule is determined using conservation of momentum. Can this new speed be used to determine the change in kinetic energy of the two-atom system as a result of the collision?

No, because kinetic energy is lost in inelastic collisions and the kinetic energy of the new gas increases, meaning the reaction that produced the new gas must have released energy. Correct. The calculation described would be useful if there were no other source of energy. However, this is an inelastic collision because the atoms stick together, and kinetic energy is lost in inelastic collisions. Since the temperature of the new gas is greater than the temperatures of the original gases, there must have been some other source of energy. The container is insulated, so the source must be the reaction that formed the new substance. Information about the amount of additional energy is needed to determine the change in kinetic energy.

A sample of ideal gas is in a sealed rectangular container that has sides of different sizes. Side A has an area of 80cm^2 and side B has an area of 100cm^2. Which of the following correctly compares the pressure P exerted on sides A and B of the container and explains the relationship in terms of net force and molecular collisions with the side

PB=PA . The pressure is the same on both sides because although the average force exerted by the individual molecules as they collide with the sides is the same, the net force and area are both proportionally greater for side B . Correct. Pressure is the ratio of force to area. The force is proportional to the rate of collisions per unit area with each side and the area of the side. Therefore, pressure is proportional to the rate of collisions per unit area, which is constant for a sample of gas.

A student has a sample of gas with a known temperature and volume in an insulated cylinder with a piston and wants to investigate the relationship between temperature and volume. The student quickly pushes on the piston to reduce the volume a small amount and measures the new temperature and volume of the gas. This procedure is repeated to get measurements for increasingly smaller volumes of the gas. The data show that as the volume of the gas decreases, its temperature increases, which appears to contradict the ideal gas law. Which of the following modifications to the experiment would demonstrate the relationship between temperature and volume in the ideal gas law?

Perform a new experiment with hot gas that uses an object on top of the piston to keep the pressure of the gas constant while the gas is allowed to cool. Correct. The flaw in the investigation was that the pressure was not held constant. This new procedure will allow the student to determine the relationship between volume and temperature.

tudents perform an experiment to determine the number of moles in a sample of an ideal gas. The students place the sample in a container with a movable piston. A thermometer and a pressure sensor are attached to the container. The gas is initially at a temperature of 293K. The students cool the gas to 273K in an ice bath, recording the temperature and pressure at regular intervals during the process. The students are surprised to find that the pressure remains constant as the temperature decreases. How could the students refine their experiment to determine the number of moles of gas present in the sample?

Perform the same experiment with the piston held in place so that the volume is constant. Correct. The students are investigating how temperature affects pressure, so any other variables should be kept constant. The piston is movable. As the temperature decreases, the volume of the gas decreases because the piston can move. This introduces another variable into the experiment. Fixing the piston in place would keep the volume that the gas occupies constant and allow students to determine a value for the number of moles from the ideal gas law PV=nRT. For instance, plotting P versus 1/V would give a linear graph. The slope could be used to find n, the number of moles of the gas.

Students are given a solid rod made of an unknown material and are asked to determine the thermal conductivity k of the rod. The rod is initially at room temperature. They measure the length L and the cross-sectional area A of the rod. Which of the following procedures would provide the most reliable estimate of k ?

Place one end of the rod in a water bath at 100°C . At regular time intervals, measure the temperature at the other end of the rod and the amount of energy needed to keep the water bath at 100°C . Correct. The equation that relates thermal conductivity to the dimensions of the rod is Q/Δt=kAΔT/L. The amount of energy needed to keep the water bath at 100°C is the amount of energy transferred to the rod. This procedure provides data on all the needed quantities.

The figure shows a cylinder that has a movable piston and contains an ideal gas initially in state 1 at room temperature. The cylinder is sealed. Blocks of known mass can be added to or removed from the top of the piston. The gas is taken through the process represented by the graph of pressure P as a function of volume V.

Placing the cylinder on a block of ice while keeping the mass on the piston constant Correct. The piston would exert a constant pressure on the gas, but the gas will lose thermal energy due to contact with the ice. Therefore the gas would contract, as predicted by the ideal gas law.

Two gas particles collide. Particle A has mass MA, and particle B has mass MB. When they collide, they exert forces on each other as shown in the diagrams, and particle A has an acceleration with magnitude aA and particle B has an acceleration with magnitude aB. Which of the following correctly indicates the ratio aA/aB and whether the accelerations are in the same or the opposite directions?

Ratio aA/aB: MB/MA Direction: opposite Correct. In a collision, a force is exerted on each object. The magnitude of that force is the same for both objects, but the direction of the force is different. According to Newton's second law, the force is equal to the mass of the object times its acceleration. Therefore aA=FB-A/MA, aB=FA-B/MB, and because FB-A=FA-B, the ratio aA/aB=MB/MA .

Students are investigating the change in the density of water as the temperature of the water increases. The students measure the mass and the volume of a quantity of water and then heat the water to various temperatures in the range using a thermometer to measure the temperature. They then attempt to determine the density of the water at the different temperatures. Assume any changes of equipment or measuring tools due to temperature changes are negligible. Which of the following methods would allow the students to obtain data from which they could determine the change in density of the water at different temperatures?

Record the temperature of the water and precise measurements of the volume of the water. Correct. Because the water's mass does not change, measuring the volume at different temperatures would allow students to be able to determine how the water's temperature effects its density.

An object is placed on the moveable piston of a cylinder filled with a gas. The object exerts a downward force F on the piston that accelerates the piston downward, compressing the gas. Which of the following is a correct description of the magnitude of the upward force exerted by the piston on the object?

The force exerted by the piston on the object is equal to F. Correct. By Newton's third law, the piston exerts an equal and opposite force on the object.

An ideal gas is confined within a rigid container with a fixed lid. The container is placed on a heat source. Which of the following correctly compares the force exerted on the lid by the ideal gas and the force exerted on the ideal gas by the lid, and correctly relates the force to pressure?

The force of the ideal gas on the lid is equal to the force of the lid on the ideal gas, but the force is increasing because of the increased kinetic energy of the ideal gas, leading to an increase in pressure. Correct. The force of the ideal gas on the container is the same as the force of the container on the ideal gas as described by Newton's third law, since they are the two sides of the same interaction. There is a heat source, so the kinetic energy of the ideal gas will increase, thus increasing the change in speed of the ideal gas molecules when they collide with the walls of the container. The impulse-momentum theorem states that the greater change in speed comes from a larger force of the container on the ideal gas, and this larger force is equal and opposite to the force of the ideal gas on the container and leads to a greater pressure on the container.

A cube submerged in a rectangular tank of liquid is at rest. Which of the following is a Newton's third law pair of forces in this situation?

The force that the liquid exerts on a side of the tank and the force the side of the tank exerts on the liquid Correct. An interacting force pair involves the forces that two objects exert on each other.

A block is submerged in a container of water and remains at rest with the only forces exerted on it being gravity and forces exerted by the water. The force exerted by the water on the bottom of the block is greater than the force exerted by the water on the top of the block. Which of the following is an explanation of the microscopic cause of the difference in the forces?

The molecules of water hitting the bottom of the block have a greater average speed than those hitting the top of the block, and thus they exert a greater force. Correct. This is a description that correctly indicates the microscopic difference in the interactions at the two surfaces.

An oxygen atom (of mass m ) has a speed of 2v0 collides with another oxygen atom that has a speed of v0 in the same direction. As a result, the two atoms exert forces on each other and form an oxygen molecule. Assume that the two-atom system is completely isolated and no energy is released. Which of the following correctly predicts the resulting changes in the momentum and kinetic energy of the two-atom system as the atoms form a molecule?

The momentum does not change. The kinetic energy decreases. Correct. The system is isolated, so the system's momentum is constant. The atoms stick together to form a molecule, so the collision is inelastic. Therefore, the kinetic energy is not conserved. Kinetic energy decreases in an inelastic collision.

A sphere of mass 0.5kg is dropped into a column of oil. At the instant the sphere becomes completely submerged in the oil, the sphere is moving downward at 8m/s, the buoyancy force on the sphere is 4.0N, and the fluid frictional force is 4.0N. Which of the following describes the motion of the sphere at this instant?

The sphere's speed is decreasing while the sphere continues to move downward. Correct. The net force acting on the sphere is 4.9N down from gravity, 4N up from the buoyant force, and 4Nup from the frictional force. This results in a net force of 3.1N up and therefore a net acceleration upward. Since the sphere is moving downward, its speed will be decreasing.

Four cubes with equal volumes are at rest in a container of water, as shown in the figure. A student claims that cube D is experiencing a greater number of water molecule collisions per second with its bottom surface than the other cubes. Which of the following indicates whether or not the student is correct and provides evidence?

The student is correct, because the bottom surface of cube DD is deepest, which means the pressure is greatest. Correct. The macroscopic pressure is caused by the net impulse exerted on the surface by collisions with water molecules. Since pressure increases with depth, so does the rate of collisions.

The figure shows an experimental setup with two thermal reservoirs connected by a uniform solid cylindrical bar. The experiment is performed twice, once with bar X and then with bar Y . The graph shows the amount of energy Q transferred through each bar as a function of time t . If there is only one difference between the experimental situations, which of the following could account for the differences in the lines on the graph for each bar? Select two answers.

The thermal conductivity of bar X is greater than that of bar Y. The length of bar X is less than that of bar Y . Correct. The equation for thermal conductivity Q/Δt=kA ΔT/L indicates that the rate of energy transfer (which is equal to the slope of the line) is inversely proportional to the length L. Since the graph for X is less than that for Y, it may have a smaller length.

Two metal cylinders of equal density and volume are submerged in water and remain at rest with their top surfaces at the same height, as shown. Cylinder A has a smaller height and a larger cross-sectional area than cylinder B. Which of the following explains why the force exerted on the top of cylinder A is greater than the force exerted on the top of cylinder B?

The water molecules striking the top surface of cylinder A have the same average speed as the water molecules striking the top surface of cylinder B, but more water molecules strike the top surface of cylinder A than the top surface of cylinder B Correct. Since cylinder A has a greater area, more molecules strike its top surface than cylinder B 's top surface. This results in a larger force even though the average molecular speed is the same.

The figure shows a block of wood floating in a beaker of water. Which of the following is true of the force exerted by the wood on the water?

The wood exerts a downward force on the water that is equal in magnitude to the weight of the wood. Correct. Since the block is not moving, the water must be exerting an upward force on it that equals its weight. By Newton's third law, the block must be exerting a force of equal magnitude on the water in the opposite direction.

The figure shows the movement of a fluid through an automobile engine and a radiator. The system is designed to prevent overheating of the engine. Which of the following claims correctly describe the energy transfer processes involved? Select two answers.

Thermal energy is transferred out of the hot fluid in the radiator, and the resulting cooler fluid is then used to cool the engine. The hot engine adds thermal energy to the cool fluid, which reduces the temperature of the engine and raises the temperature of the cool fluid. Correct. When the cool fluid comes in contact with the engine, it will take thermal energy away from the engine. This will cool the engine and warm the cool fluid in the process, making the fluid hotter.

A rigid container holds an ideal gas. A gas molecule of mass mm moving at speed v collides with a container wall. The molecule's velocity is perpendicular to the wall before the collision. What type of collision occurs when the molecule strikes the wall, and what is the change in momentum of the molecule?

Type of Collision: elastic Change in Momentum: 2mv Correct. Energy and momentum must be conserved in these types of collisions or the temperature (internal energy) of the gas will change; this means that the molecules have an elastic collision with the walls of the container. Since the molecules strike the stationary walls with a momentum of mv, they will rebound back at a speed of mv since momentum is conserved. As momentum is a vector quantity, this means that the change in momentum is 2mv.

The water coming out of a water fountain initially makes a 45°angle to the horizontal. Which of the following changes, if any, could result in the water reaching the ground farther from the fountain without changing the water pressure in the fountain pipe, and why?

Using a smaller nozzle on the end of the fountain, because the smaller area of the opening will lead to a higher speed for the water. Correct. The equation of continuity indicates that A1v1=A2v2 , where AA is the area of the nozzle opening and v is the speed of the water. There are a fixed number of cubic meters of water per second exiting the nozzle. By decreasing the area of the nozzle, the velocity of the water will increase.

A student wants to determine whether the density of a solid cube of copper will decrease as its temperature is increased without melting the cube. Graphing which of the following will allow the student to study this question?

Volume as a function of temperature Correct. Density is mass divided by volume. Since the cube does not melt, no mass is lost and the cube's density depends only on the volume. Therefore, any change in volume will correspond to a change in density, so graphing volume as a function of temperature will show if the density changes with temperature.

In the lab, a student is given a glass beaker filled with water with an ice cube of mass m and volume Vc floating in it. The ice cube displaces a volume Vd of water as it floats. The density of the water is ρw , and the density of the ice is ρi . The water exerts an upward buoyant force of magnitude ρwVdg on the ice cube. Which of the following is equal to the magnitude of the force that the ice cube exerts on the water?

ρwVd g Correct. The force the ice cube exerts on the water has the same magnitude and is in the opposite direction to the buoyant force the water exerts on the ice cube.

A gas contains two types of charged particles. Negatively charged particle X− has mass m and velocity +v0 , as shown in the figure. It collides head-on with positively charged particle Y+ that has mass 8m and velocity −v0 . Electrostatic force then holds the particles together. What is the final velocity of the two-particle system?

-7/9v0 Correct. The system's momentum before the collision is the same as the momentum after the collision: mv0−8mv0=(m+8m)vf , so vf=−7/9v0 .

Compressed air in a vertical cylinder with a piston of radius 0.30m is used to lift a crate. The minimum pressure of the air in the cylinder needed for the piston to lift the crate is 1.61×10^5N/m^2, and the pressure in the room outside the piston is 1.01×10^5N/m^2. If the mass of the piston is negligible, the weight of the crate is most nearly

1.7x10^4 N Correct. Pressure and force are related by P=F/A. The difference in pressure between the gas inside the cylinder and the outside air causes an upward force. The force exerted by the pressure difference is F=ΔP⋅A=(1.61×10^5N/m^2−1.01×10^5N/m^2)(π)(0.3m)^2=1.7×10^4N.

A sample of an ideal gas is in a sealed cylinder with a movable piston and is initially in state A, as shown in the graph of pressure P as a function of volume V. The gas's temperature in state A is 300K. The gas can be taken from state A to state D via three separate paths, AD, ABD, or ABCD.

600K Correct. The ideal gas law can be used to relate the pressure, volume, and temperature of the gas in states A and B: PAVA=nRTA and PBVB=nRTB. Combining these equations and solving for the temperature in state B gives TB=(PBVB/PAVA)TA=(2PAVA/PAVA)TA=2(300K)=600K.

When water boils, bubbles of water vapor form in the liquid and travel to the surface of the water. At the surface the bubbles burst, and the water vapor molecules collide with the surrounding air, which is at room temperature. Which of the following claims best describes the flow of energy between the water vapor molecules and the air molecules and the resulting change in temperature of the air and water vapor?

Energy flows into the air. The temperature of the air increases, and the temperature of the water vapor decreases. Correct. The water vapor is at a higher temperature than the air. As the molecules collide, energy is transferred from the higher-energy water vapor to the lower-energy air. So the temperature of the water vapor decreases, and the temperature of the air increases.

When a room-temperature spoon is placed in a cold bowl of ice cream, some of the ice cream quickly melts where it comes into contact with the spoon. Which of the following is the best explanation for why the ice cream melts?

Energy is transferred to the ice cream molecules and increases their average speed, because the higher-energy molecules in the spoon are vibrating and colliding with the lower-energy molecules of the ice cream. Correct. The kinetic theory says that molecules will move and collide and the higher-energy molecules (of the spoon) will collide with the lower-energy molecules (of the ice cream.) These collisions will, on the average, transfer energy from the spoon to the ice cream. This increases the average speed of the ice cream molecules near the spoon, increasing their temperature and allowing some of the ice cream to melt.

Which of the following describes the microscopic difference between the change in entropy of a gas during reversible processes (which are theoretical) and irreversible processes (which actually occur)?

Reversible Processes: The number of combinations of microscopic states that can combine to create the macroscopic state of the gas remains the same. Irreversible processes: The number of combinations of microscopic states that can combine to create the macroscopic state of the gas increases. Correct. Entropy is a measure of how many different microscopic ways a system may be arranged to give the same measurable macroscopic system quantities, such as volume, pressure, and temperature. Thus, entropy is often described as a measure of the disorder of a system.

The graph shows pressure as a function of volume for a sample of an ideal gas that is confined in a cylinder. A moveable piston sits on top of the gas, and the piston can move vertically with negligible friction. The weight of the piston is significantly less than the force exerted by the gas on the piston during the process shown. Which of the following is true of the acceleration of the piston during the process?

The acceleration stays the same since the net force on the piston stays the same. Correct. The pressure stays the same throughout the process, so the force the gas exerts on the piston is constant. This means a constant net force is exerted on the piston, which produces a constant acceleration.

Two identical samples of helium gas are in identical sealed flasks at room temperature. One flask is just sitting in the room, and the other is inside a large, insulated vacuum container. Both flasks are opened and the samples are released, so the helium in one flask spreads throughout the room and the helium in the other flask spreads in the sealed container, as shown in the figures. Which of the following is true of the change in entropy that occurs in each case when the flasks are opened?

The entropy increases in both cases because each system is now in a more disordered state. Correct. The helium that mixed with the air and the helium that spread out into the container are both more disordered than they were in their original states.

A student is sitting on the ground a few meters away from a campfire on a cool, windless night. The student feels noticeably warm on the side facing toward the fire, and noticeably cool on the side facing away from the fire. Which of the following models describes the primary method by which the side of the student facing toward the fire is warmed?

The fire emits electromagnetic radiation. Some of the radiation is absorbed by the student and is converted to thermal energy. Correct. Energy is transferred by radiation and absorbed by the student.

A block of mass M is floating in a container of liquid and is partially submerged. The block is then replaced by a block of mass 2M. Which of the following describes two forces that are a Newton's-third-law force pair whose magnitudes are the same for the two situations?

The gravitational force Earth exerts on the liquid and the gravitational force the liquid exerts on Earth Correct. The mass of the liquid does not change, so the gravitational force on it remains the same.

The figure shows a horizontal metal bar with the left end in thermal contact with a constant temperature reservoir that is much hotter than the initial temperature of the bar. The reservoir-bar system is thermally isolated from the surroundings. The atoms of the metal bar are represented by the black dots. Which of the following provides the best reasoning for how the system reaches thermal equilibrium?

The hotter atoms on the left are vibrating faster than the colder atoms on the right and collide with the colder atoms, transferring kinetic energy until the bar reaches thermal equilibrium with the reservoir. Correct. This choice is the closest definition of thermal conductivity, where the hotter atoms are vibrating faster and (on the average) transfer their kinetic energy in collisions to the colder, slower-moving atoms.

A metal block with temperature 90°C is placed in a container. Water with temperature 10°C is then poured into the container. Which of the following explains how the temperature of the block changes?

The temperature of the block decreases continuously as particles in the block collide with particles in the water until the temperatures of the block and water become equal at a temperature between 10°C and 90°C. Correct. Energy is transferred from the block to the water when particles in the block collide with particles in the water. Since energy is conserved during these particle collisions, the temperature of the water increases as the temperature of the block decreases, resulting in a final temperature between the initial temperatures of the block and water.

A gas is in a sealed cylinder fitted with a movable piston, as shown in the figure, so that none of the gas escapes. The cylinder and piston are made of an insulating material. The cylinder is fitted with pressure and temperature sensors, and the volume of the confined gas can be measured from markings on the side of the cylinder. The gas is initially in a state with pressure Pi, temperature Ti, and volume Vi. The piston is slowly compressed and data are recorded until the gas reaches a final state with pressure Pf, temperature Tf, and volume Vf. A graph of the pressure as a function of volume is shown, with dotted lines indicating isotherms. Which of the following claims correctly indicates the changes in the collisions between gas molecules and the cylinder wall that contribute to the change in pressure of the gas as it goes from its initial to its final state?

The volume decreases, so the number of collisions per unit time increases. The average speed of the molecules increases, so the average impulse of the collisions increases. Correct. The smaller volume means that on average, the molecules have less distance to travel before colliding with a side of the container. Because the temperature increases, the average kinetic energy, and therefore speed, of the molecules increases.

An ideal fluid flows from left to right in the horizontal pipe shown in the figure. The fluid enters the left side of the pipe with speed v, where the diameter of the pipe is d. The pipe then narrows to a diameter of d/2. Does the pressure of the fluid change as the pipe becomes narrower, and why or why not?

Yes, because the kinetic energy of the fluid changes but the total gravitational potential energy of the fluid-Earth system is constant. Correct. Applying Bernoulli's equation, P1+ρgy1+1/2ρv1^2=P2+ρgy2+1/2ρv2^2, the potential energy terms cancel because the height of the fluid does not change. So P1+1/2ρv1^2=P2+1/2ρv2^2 If the speed changes as the pipe becomes narrower, then the pressure does also.

A room with length L, width W, and height H is filled with n moles of an ideal gas at temperature T, as represented by the figure. Which of the following indicates the magnitude and direction of the average force exerted on the gas by wall X ?

nRT/W, into the page Correct. The wall exerts a force on the gas that is equal in magnitude and opposite in direction to the force exerted by the gas on the wall. The relevant quantities are related by the ideal gas law, P=nRTV. The volume is LWH, pressure is F/A, and the area of wall X is LH. So F/LH=nRT/LWH, giving F=nRT/W. The force exerted by the gas is directed out of the page, so the force exerted on the gas is into the page.