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physics
particle physics
Principles And Practice Of Physics 2nd Edition Eric Mazur - Solutions
Figure 21. 36 shows an ideal gas cycle consisting of two isotherms and two isochores. Complete the table by writing the algebraic signs of each of the terms \(\Delta E, W\), and \(Q\). If a term is zero, write zero.Data from Figure 21. 36 P AE WQ 1-2 2-3 3-4 4-1 V
Consider the device illustrated in Figure 21.3. A string is attached to a paddle wheel that is immersed in a viscous liquid in a container. As the string is pulled, the paddle wheel rotates at constant speed, increasing the temperature of the liquid from \(T_{i}\) to \(T_{f}\). (a) Draw an energy
Suppose the person pulling the string in Figure 21.13 does work \(W\) on the device immersed in a thermal reservoir \(\mathrm{R}\) at temperature \(T_{R}\).(a) Do the energy and entropy of the reservoir increase, decrease, or stay the same?(b) If the same experiment is repeated with the reservoir
A reversible heat engine converts energy taken from a thermal reservoir at temperature \(T_{\text {in }}\) by doing work on the environment and thermally transferring energy to a thermal reservoir at temperature \(T_{\text {out }}
For a set temperature \(T_{\text {in }}\) of a refrigerator interior, does the coefficient of performance of cooling increase, decrease, or stay the same as the temperature \(T_{\text {out }}\) of the room that contains the refrigerator increases? Assume the refrigerator is a reversible heat pump.
A steel bar transfers energy from a thermal reservoir at \(750 \mathrm{~K}\) to one at \(520 \mathrm{~K}\). If the bar transfers \(1.5 \times 10^{6} \mathrm{~J}\) of energy during a certain time interval over which the temperature distribution of the bar does not change, what is the entropy change
A power plant burns fossil fuel to produce steam at \(650 \mathrm{~K}\). The pressurized steam drives a steam turbine, where the steam condenses to water and is discarded at \(310 \mathrm{~K}\). What is the minimum quantity of energy discarded thermally by a 1.0-GW power plant to the environment
The thermal insulation in a refrigerator is never perfect. Typically energy is transferred thermally from the room to the refrigerator interior at a rate of \(60 \mathrm{~W}\) with the refrigerator door closed. Suppose the interior needs to be held at \(4.0^{\circ} \mathrm{C}\) and the temperature
In a reversible heat engine, \(6.02 \times 10^{23}\) molecules of nitrogen gas are used as the working substance. The gas undergoes a Carnot cycle as illustrated in Figure 21.43. The volume of the gas is \(6.00 \times 10^{-3} \mathrm{~m}^{3}\) in state 1 and \(14.0 \times 10^{-3} \mathrm{~m}^{3}\)
Consider a jet engine operating on the Brayton cycle. The working substance is air, which consists primarily of diatomic molecules. The air is drawn in at atmospheric pressure, \(1.01 \times 10^{5} \mathrm{~Pa}\), at \(288 \mathrm{~K}\). In the combustion chamber, the temperature of the air is
(a) Draw a free-body diagram for the pith ball in Figure 22.9a. Data from Figure 22.9(b) Two identical neutral pith balls A and B are suspended side by side from two vertical strings. After some charge is transferred from a charged rubber rod to \(A\), \(A\) and \(B\) interact. (B remains neutral
Compare the magnitudes of the gravitational and electric forces exerted by the nucleus of a hydrogen atom-a single proton \(\left(m_{\mathrm{p}}=1.7 \times 10^{-27} \mathrm{~kg}\right)\) - on an electron \(\left(m_{\mathrm{c}}=9.1 \times 10^{-31} \mathrm{~kg}\right)\) when the two are \(0.50 \times
You are given three charged particles. Particles 1 and 2 carry charge \(+q\) and particle 3 carries charge \(-4 q\). (a) Determine the relative values of the separation distances \(r_{12}\) and \(r_{13}\) when the three particles are arranged along a straight line in such a way that the vector sum
Consider four charged particles placed at the corners of a square whose sides have length \(d\). Particles 1,2 , and 4 carry identical positive charges. In order for the vector sum of the forces exerted on particle 1 to be zero, what charge must be given to particle 3 , which is in the corner
Consider the arrangement of charged particles shown in Figure 22.33. The charge magnitudes are the same in all three cases, but \(q_{1}\) and \(q_{2}\) are positive and \(q_{3}\) is negative. Sketch the trajectory of particle 1 if it is released while particles 2 and 3 are held fixed. Ignore any
You can use a positively charged object to charge a neutral object (i) by conduction (in the absence of grounding) or (ii) by induction (with grounding). For each process, which type of charge (positive, negative, or neither) does the neutral object acquire?
Because we observe two types of electric interactions, attractive and repulsive, we postulate two types of charge. Do you think there are also two types of mass? Why do you think this? Do you think there are two types of magnetic pole? Why do you think this?
Is the statement A plastic comb that has been passed through the hair a few times carries a negative charge a physical law or a definition? What are some of the differences between a law and a definition?
A balloon rubbed in your hair or on your clothes sticks to a wall. If you place the rubbed side of the balloon against the wall, it sticks to the wall immediately. Try this, however: After rubbing the balloon in your hair, place the side of the balloon you did not rub against the wall and notice
Air can act as both an insulator and a conductor. Consider reaching for a metal doorknob after scuffing your feet over a carpet. As your hand approaches the knob, a spark jumps between your hand and the knob. Explain how air acts as both insulator and conductor in this situation.
Masons use a hose open at both ends and filled with water to ensure that the blocks they lay remain level (Figure 18. 37). How does such a hose help them do this?Data from Figure 18. 37
(a) Imagine a rock and a balloon of the same volume completely submerged in water. How do the buoyant forces exerted on them compare? (b) How do the buoyant forces compare when the balloon volume is half the rock volume? (c) Which object floats and which sinks in part \(a\) and in part \(b\) ?
For a thrown ball to rise, what type of spin should the thrower place on it?
(a) Draw a free-body diagram analogous to Figure 18.32 for a gas-liquid-solid boundary at which the contact angle is \(90^{\circ}\). Make your solid surface horizontal. (b) How do the magnitudes and directions of the adhesive and cohesive forces exerted on your particle compare? (c) How does the
(a) Imagine a capillary tube placed in a nonwetting liquid (as opposed to the wetting-liquid situation of Figure 18.35). How does the pressure at a point \(\mathrm{P}\) just below the now convex surface compare with atmospheric pressure? (b) How does the level in the tube compare with the level of
Consider a cylindrical container that has a radius of \(30.0 \mathrm{~mm}\) and is filled with water to a height of \(0.150 \mathrm{~m}\). If the container is at sea level, what is the pressure \((a)\) at the water surface and ( \(b\) ) at the bottom of the container?(c) How far above the water
When a piece of cork floats in water, three-quarters of its volume is above the water surface. How does the mass density of cork compare with the mass density of water?
When air is blown downward into the narrow opening of a funnel (Figure 18.22), a lightweight ball initially positioned below the wide opening is pulled up into the funnel and held in place. Explain how the ball can be pulled upward even though the airflow and gravity are both directed downward.Data
Suppose surface tension increases in direct proportion to surface area (an oversimplification!). How does the ratio of surface tension to the force of gravity exerted on a drop change as the drop diameter increases tenfold?
Airplane cabins are pressurized to prevent passengers from developing altitude sickness during flight. Your altimeter watch, which uses pressure to determine altitude, indicates a cabin altitude of \(2500 \mathrm{~m}\) even though the captain has just announced that the airplane is flying at an
A dam of horizontal length \(\ell\) holds water of mass density \(ho\) to a height \(h\). What is the magnitude of the force exerted by the water on the dam?
In Figure 18.47, the top tank, which is open to the atmosphere, contains water \(\left(ho_{\text {water }}=1.0 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\right)\) and the bottom tank contains oil \(\left(ho_{\text {oil }}=0.92 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\right)\) covered by a
Suppose a load is placed on the large piston in Figure 18.50 and we wish to raise that load by a certain distance. How does the work done on the small piston compare with the work required to raise the load? Ignore the masses of the pistons.Data from Figure 18.50 area A, area A, h P, F/A, 2 1 and 3
Water leaks out of a small hole in the side of a bucket. The hole is a distance \(d\) below the surface of the water, and the cross section of the hole is much smaller than the diameter of the bucket. At what speed does the water emerge from the hole?
Blood flows through an artery that has a radius of \(3.0 \mathrm{~mm}\). What is the maximum flow speed if the volume flow rate through the artery is \(2.0 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{s}\) ?
The pressure difference across the wall of a blood vessel is called transmural pressure. Suppose an aorta of radius \(11 \mathrm{~mm}\) has a transmural pressure of \(12 \mathrm{kPa}\) and a capillary of radius \(4.0 \mu \mathrm{m}\) has a transmural pressure of \(5.0 \mathrm{kPa}\). Which blood
With a standard deck of 52 playing cards, what is the probability of randomly picking(a) any card numbered 8 and \((b)\) any king, queen, jack, or ace?
When two standard dice are thrown, what is the probability that the sum of the dots on the two top faces will be 7 ?
Particles in a closed container move around and collide with one another and with the walls of the container. There are \(5.00 \times 10^{13}\) basic states possible for this system, and the recurrence time is 365 days. How long is the average time interval between collisions?
A bag holds 10 black jellybeans, 12 green ones, 3 orange ones, and 20 blue ones. If you reach in and grab one randomly, what is the probability of picking sequentially (a) a black one, \((b)\) an orange one, and (c) a blue one?
A manufacturer sells three types of motorcycles-call them types A, B, and C-each available in yellow, red, glossy black, or matte black and each offered with cither a 600 -cc motor or an 850 -cc motor. (a) How many configurations are available? \((b)\) If each motorcycle is available with 26
When three standard dice are thrown, what is the probability that the sum of the dots on the three top faces will be 4?
A pendulum is in a container that has been evacuated so that there are only two atoms A and B in the container with the pendulum. If the pendulum initially has six units of energy and the two atoms have none, what is the probability that all six energy units will leave the pendulum and be absorbed
A pendulum is released from an elevation of \(1.15 \mathrm{~m}\) and allowed to swing in a room filled with \(1.50 \times 10^{21}\) nitrogen molecules having an average speed of \(550 \mathrm{~m} / \mathrm{s}\). If the energy of the pendulum is equal to the energy distributed over all the nitrogen
(a) When a coin is tossed five times, which sequence of outcomes is more likely: HHHHH or HTHTH? (b) Without regard to order, which is more likely: that in five tosses the coin lands heads-up five times or lands headsup three times?
Some musical instruments have valves that can be either opened or closed to produce different tones. How many tones can be produced by a horn that has \((a)\) two valves,(b) three valves, and(c) six valves?(d) Some trumpet players do something called half-valve work, where they play a valve that
Six particles in a container can move in only one of six directions: up, down, left, right, forward, and backward. If the particles move randomly such that each collides and changes direction every \(1.0 \times 10^{-6} \mathrm{~s}\), for how many seconds during a \(24-\mathrm{h}\) day are all six
An adsorbing filter allows gas particles to stick to locations on the filter surface. Once a particle sticks to a location, that location is filled. The filter can no longer remove gas particles when all locations are filled. Each \(1.0 \mathrm{~nm}^{2}\) of the filter surface has six adsorbing
A system contains three particles-A, B, and C-and three units of thermal energy. Determine the probability of any one particle having all the energy.
In a system of three particles-A, B, and C-that share nine units of energy, which energy distribution is more likely at a given instant: particle \(\mathrm{A}\) has two units of energy or particle \(A\) has three units of energy?
The air in a room held at a steady temperature \(T\) is made up largely of nitrogen molecules \(\left(m_{\mathrm{N}_{2}}=4.652 \times 10^{-26} \mathrm{~kg}\right.\) ) and oxygen molecules \(\left(m_{\mathrm{O}_{3}}=5.3135 \times 10^{-26} \mathrm{~kg}\right)\). At equilibrium, what is the ratio of
A closed container initially holds 50 monatomic A particles that have a combined energy of 120 units. After 100 monatomic \(B\) particles with a combined energy of 180 units are added to the container, the system is allowed to come to thermal equilibrium. (a) At equilibrium, how many energy units
In a system that contains four distinguishable particles and five units of energy, what is the probability that one particle has all the energy?
A \(0.10-\mathrm{kg}\) pendulum swings inside a box that contains \(1.0 \times 10^{23}\) nitrogen molecules. The initial speed of the pendulum is \(0.80 \mathrm{~m} / \mathrm{s}\), and it comes to rest in \(5.0 \mathrm{~min}\). When the number of nitrogen molecules in the box is increased to \(2.5
If the thermal (incoherent kinetic) energy of a system made up of \(1.00 \mathrm{~mol}\) of argon atoms \(\left(6.02 \times 10^{23}\right.\) atoms) is \(498 \mathrm{~J}\), what is the average speed of each atom? The mass of an argon atom is \(6.63 \times 10^{-26} \mathrm{~kg}\).
To a vessel that contains \(1.00 \mathrm{~mol}\) of monatomic ideal gas \(\mathrm{A}\) is added \(0.100 \mathrm{~mol}\) of monatomic ideal gas \(\mathrm{B}\). The mass of each atom of gas A is \(3.35 \times 10^{-26} \mathrm{~kg}\), and the mass of each atom of gas B is \(1.39 \times 10^{-25}
Inside a box, a \(1.00-\mathrm{kg}\) ball is gently dropped from a height of \(1.00 \mathrm{~m}\) (Figure P19.21). The box contains \(1.00 \mathrm{~mol}\) of argon atoms, each having a mass of \(6.63 \times 10^{-26} \mathrm{~kg}\) and moving at an average speed of \(100 \mathrm{~m} / \mathrm{s}\)
A spherical balloon that has a diameter of \(0.500 \mathrm{~m}\) and contains \(1.00 \mathrm{~mol}\) of helium gas is left in the Sun for \(10.0 \mathrm{~min}\). During that interval, the Sun irradiates the balloon with an average intensity of \(1120 \mathrm{~W} / \mathrm{m}^{2}\), all of which is
A cube can be envisioned as an assembly of identical octants (numbered 1-8 in no particular order). The cube contains three identical particles. How many basic states in this system yield a macrostate \((a)\) in which all three particles are in octant 1 and \((b)\) in which two particles are in
A box sitting in a room occupies \(1 / 64\) of the room volume. When the box is opened, two identical particles are released into the room. What is the probability that at any instant after they are released, the two particles \((a)\) return to the box simultaneously and \((b)\) occupy the same \(1
Three particles are released into a box that can be thought of as a set of four identical quadrants. How many basic states are possible if the particles are \((a)\) indistinguishable from one another and \((b)\) distinguishable from one another?
Four distinguishable particles move freely in a room divided into octants (there are no actual partitions). Let the basic states be given by specifying the octant in which each particle is located. (a) Give an example of a macrostate for this system. (b) How many basic states are there? (c) The
You have six identical particles in a box divided into four quadrants. For a certain experiment, you need to have a certain number of particles in the upper left quadrant. You observe that in a given day, the distribution of particles you need occurs for \(51.43 \mathrm{~min}\). How many particles
A cube that has a volume of \(1.00 \mathrm{~m}^{3}\) contains \(N\) distinguishable particles. Determine the probability that all the particles are in a smaller volume \(V\) of the cube if(a) \(N=1, V=0.500 \mathrm{~m}^{3}\);(b) \(N=1, V=0.250 \mathrm{~m}^{3}\);(c) \(N=1, V=0.0100
A space probe measures the number density of particles of interstellar gas by enclosing \(1.00 \mathrm{~m}^{3}\) of space and measuring the number of atoms that pass from that volume through a detector in the shape of a cylinder \(15.0 \mathrm{~mm}\) in diameter and \(5.00 \mathrm{~mm}\) long. In
A box divided into four quadrants can hold a maximum of 30 particles in each quadrant. (a) If 114 particles are placed in the box, how many basic states and macrostates are possible, if the macrostates are defined as the number of particles in the upper left quadrant? (b) What is the most probable
A box divided into compartments \(A\) and \(B\) contains 14 particles in \(A\) and 6 in \(B\). The separating partition allows energy exchange between compartments as the particles collide with the partition. Table 19. 2 (page 656) lists the numbers of basic states possible when 10 energy units are
In how many ways can you distribute 10 indistinguishable energy units over 14 distinguishable particles?
A system has the numbers of macrostates and basic states shown in Table P19.33. (a) In which macrostate is the system in equilibrium? (b) Which macrostates are least likely? (c) How many basic states are possible for the system? (d) What is the probability that the system occupies macrostate
A box divided into identical compartments \(\mathrm{A}\) and \(\mathrm{B}\) contains 25 distinguishable particles in \(\mathrm{A}\) and 20 distinguishable particles in B. There are nine energy units in the box, initially distributed only among the particles in B. The system is closed, but the
\(\mathrm{A}\) box divided into identical compartments \(\mathrm{A}\) and \(\mathrm{B}\) contains two distinguishable particles in A and three distinguishable particles in \(B\). There are five energy units in the box, initially shared by the two particles in \(A\). The system is closed, but
A box like the one in Problem 31 has two particles in compartment A, two particles in compartment B, and four energy units to be distributed. (a) Construct a table like Table 19. 2 (page 656) for this setup. (b) Does equipartition of energy take place even with such a small number of particles?Data
System 1 is in equilibrium, and a separate system 2 is also in equilibrium. The systems are independent of each other but have an equal probability of being in equilibrium. The number of basic states possible in system 1 is 3422 times greater than the number possible in system 2 . In system 2, the
A system has three macrostates. Macrostates 1 and 3 are least likely and have one basic state each. Macrostate 2 is the equilibrium state and is six times more likely to occur than either of the other two macrostates. (a) What is the probability that the equilibrium state 2 occurs? (b) What is the
A cylindrical box is divided into three equal-volume, pieshaped regions-A, B, and C-by vertical partitions that allow the transfer of energy but not of particles from one region to another. Each region shares a partition with the other two. Each region contains 13 particles, and the system contains
What is the entropy of a closed system in which 25 distinguishable grains of sand are distributed among 1000 distinguishable equal-sized compartments?
A number of distinguishable spherical beads, each having a radius of \(15.0 \mathrm{~mm}\), are placed into individual compartments in a \(1.00-\mathrm{m}^{3}\) container. The same number of beads, each having a radius of \(20.0 \mathrm{~mm}\), are placed into different compartments in a container
You have 80 particles moving randomly in a closed container, and the system contains 80 energy units. Which is less likely: that a single particle has all 80 energy units, or that each particle has one energy unit?
The volume of a cylindrical chamber is controlled by a movable piston. A sample of gas is placed in the chamber, and the volume is allowed to change from \(0.0100 \mathrm{~m}^{3}\) to \(0.100 \mathrm{~m}^{3}\) at a constant temperature. If the entropy of the system increases by \(6.91 \times
A closed box contains 20 particles, 10 on each side of a movable partition. The particles in the left compartment are small and occupy a volume \(\delta V_{\text {left. }}\). Those in the right compartment are larger and occupy a volume \(\delta V_{\text {right }}=8 \delta V_{\text {left }}\).(a)
Rank the following systems according to their entropy, lowest first:A. 1,000,000 different colors that can be assigned to each of the \(70 \times 10^{21}\) stars in the observable universe B. The particles in \(1 \mathrm{~mol}\) of an ideal gas that can be adsorbed (one particle per site) at any of
Figure P19.46 shows a device consisting of two units, A and B. Each unit has a volume \(V\), and at one end a partition separates off a small compartment that has volume \(V / 3\), as shown in part \(a\). Initially, unit \(A\) has \(3 \mathrm{~mol}\) of a gas in its smaller compartment, and unit B
Suppose each of 50 distinguishable objects has a volume of \(1.00 \times 10^{-9} \mathrm{~mm}^{3}\) and are initially in a box that has a volume of \(1.00 \times 10^{-6} \mathrm{~m}^{3}\). If the volume of the box is doubled, (a) by what factor does the number of basic states change and \((b)\) by
A box of volume \(V\) has a movable partition separating it into two compartments. The left compartment contains 3000 particles, the right one contains 1000 particles, and initially the partition is in the middle so that the compartments are of equal volume. The partition is released and slides
A change in the volume occupied by a set of distinguishable particles increases the number of basic states by a factor of 6633 and increases the entropy per particle by a factor of 1. 10. How many distinguishable particles are there in the system?
A box that is \(1.00 \mathrm{~m}\) long measured from left to right has a sliding partition that separates it into two compartments. The left compartment contains 10 particles, the right one contains 60 particles, and initially the partition is \(0.750 \mathrm{~m}\) from the left wall of the box.
A container holds \(1.0 \mathrm{~mol}\) of an ideal monatomic gas at \(72 \mathrm{~K}\), and then \(0.50 \mathrm{~mol}\) of another monatomic ideal gas at \(126 \mathrm{~K}\) is added. What is the equilibrium temperature?
Initially, \(1.00 \mathrm{~mol}\) of an ideal monatomic gas has \(75.0 \mathrm{~J}\) of thermal energy. If this energy is increased by \(25.0 \mathrm{~J}\), what is the change in entropy?
A theory predicts a reaction that produces ideal monatomic gas particles that have the following speeds: \(6.2 \mathrm{~m} / \mathrm{s}, 7. 4 \mathrm{~m} / \mathrm{s}, 7. 4 \mathrm{~m} / \mathrm{s}, 7. 8 \mathrm{~m} / \mathrm{s}, 8. 3 \mathrm{~m} / \mathrm{s}, 12. 6 \mathrm{~m} / \mathrm{s}\),
What is the root-mean-square speed of four monatomic ideal gas particles that have the following velocities (written in component form \():(4.0,6.0,2.0) \mathrm{m} / \mathrm{s},(8.0,-3.0,8.0) \mathrm{m} / \mathrm{s}\), (7.0,1.0,6.0) m / s, (8.0,9.0,5.0) m / s ?
An ideal monatomic gas is at \(125^{\circ} \mathrm{C}\). If you increase the thermal energy of the gas and the root-mean-square speed of the gas particles triples, by what factor does the absolute temperature change?
The rate of change of entropy with respect to thermal energy is \(1.81 \times 10^{20}\) in a system at \(400 \mathrm{~K}\). At what absolute temperature is the rate of change twice this value?
The entropy for a certain monatomic gas has been empirically determined to be given by the expression \(S=\frac{7}{2} N \ln E_{\mathrm{th}}+N E_{\mathrm{th}}^{2} / 15\). Express the factor \(1 / k_{\mathrm{B}} T\) for this gas in terms of \(N\) and \(E_{\mathrm{ch}}\).
In \((x, y, z)\) notation, four ideal monatomic gas particles have the velocities \(\vec{v}_{1}=(-6.0,5.0,1.0) \mathrm{m} / \mathrm{s}, \vec{v}_{2}=\) \((4.0,5.0,-2.0 \mathrm{~m} / \mathrm{s}), \vec{v}_{3}=(7.0,0,8.0) \mathrm{m} / \mathrm{s}\), and \(\vec{v}_{4}=\) \((-4.0,-9.0,-6.0) \mathrm{m} /
A box is divided into four equal-sized quadrants. Each quadrant contains gaseous hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\), which we treat as monatomic. The partition that separates the quadrants allows energy to be exchanged, but not particles. However, there is a tiny hole in the
At \(24.0^{\circ} \mathrm{C}\), what is the average speed of atoms of helium gas? The mass of each atom is \(6.646 \times 10^{-27} \mathrm{~kg}\).
What is the root-mean-square speed of helium atoms (mass \(6.646 \times 10^{-27} \mathrm{~kg}\) ) in a star where the temperature is \(1.8 \times 10^{4} \mathrm{~K}\) ?
A cubical box measuring \(1.25 \mathrm{~m}\) on each side contains a monatomic ideal gas at a pressure of \(2.0 \mathrm{~atm}\). (a) How much thermal energy do the particles of this gas contain? (b) If half the thermal energy of the particles were converted to the kinetic energy of a
An empty \(2.00-\mathrm{L}\) soft drink bottle is filled with \(0.0100 \mathrm{~mol}\) of a monatomic ideal gas at atmospheric pressure \(\left(1.01 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\right)\). (a) What is the average kinetic energy of each gas particle in the bottle? (b) Compare the value
A particle accelerator exerts a force on particles that are initially at rest. Each of the particles has a mass of \(1.6726 \times 10^{-27} \mathrm{~kg}\), and the point of application of the force is along the entire \(100-\mathrm{m}\) length of the accelerator. The particles traverse this
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