A closely wound rectangular coil of 80 turns has dimensions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 43.0∘ with a magnetic field of 1.70 T to a position perpendicular to the field. The rotation takes 0.0600 s. Part A What is the average emf induced in the coil? Express your answer with the appropriate units.
A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as in the figure (Figure 1). Terminals a and b of winding A may be connected to a battery through a reversing switch. State whether the induced current in the resistor R is from left to right or from right to left in the following circumstances. Figure 1 of 1 Part A The current in winding A is from a to b and is increasing. from left to right from right to left Submit Request Answer Part B The current in winding A is from b to a and is decreasing. from left to right from right to left Submit Request Answer Part C The current in winding A is from b to a and is increasing. from left to right from right to left
In the figure (Figure 1) a conducting rod of length L = 30.0 cm moves in a magnetic field B→ of magnitude 0.490 T directed into the plane of the figure. The rod moves with speed v = 5.90 m/s in the direction shown. Figure 1 of 1 Part A What is the potential difference between the ends of the rod? Express your answer in volts. V = Submit Request Answer Part B Which point, a or b, is at higher potential? a b Part C When the charges in the rod are in equilibrium, what is the magnitude of the electric field within the rod? Express your answer in volts per meter. Submit Request Answer Part D What is the direction of the electric field within the rod? From b to a From a to b Part E When the charges in the rod are in equilibrium, which point, a or b, has an excess of positive charge? a b Submit Request Answer Part F What is the potential difference across the rod if it moves parallel to ab ? Express your answer in volts. V = Part G What is the potential difference across the rod if it moves directly out of the page? Express your answer in volts. V = Submit Request Answer
A rectangle measuring 30.0 cm by 40.0 cm is located inside a region of a spatially uniform magnetic field of 1.40 T, with the field perpendicular to the plane of the coil (Figure 1). The coil is pulled out at a steady rate of 2.00 cm/s traveling perpendicular to the field lines. The region of the field ends abruptly as shown. Figure 1 of 1 Part A Find the emf induced in this coil when it is all inside the field. Express your answer in volts. E = V Submit Request Answer Part B Find the emf induced in this coil when it is partly inside the field. Express your answer in volts. E = V Part C Find the emf induced in this coil when it is all outside the field. Express your answer in volts. E = V Submit Request Answer
The current in the long, straight wire AB shown in (Figure 1 )is upward and is increasing steadily at a rate di dt. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Emf and current induced in a loop. Figure 1 of 1 Part A At an instant when the current is i, what are the magnitude of the field B→ at a distance r to the right of the wire? Express your answer in terms of the variables i, r, and magnetic constant μ0. Submit Request Answer Part B At an instant when the current is i, what are the direction of the field B→ at a distance r to the right of the wire? into the page out of the page Submit Request Answer Part C What is the flux dΦB through the narrow shaded strip? Express your answer in terms of the variables i, L, r, dr, and magnetic constant μ0. Submit Request Answer Part D What is the total flux through the loop? Express your answer in terms of the variables i, L, a, b, and magnetic constant μ0. Submit Request Answer Part E What is the induced emf in the loop? Express your answer in terms of the variables di, dt, L, a, b, and magnetic constant μ0. Submit Request Answer Part F Evaluate the numerical value of the induced emf if a = 12.0 cm, b = 36.0 cm, L = 24.0 cm, and di/dt = 9.60 A/s. Express your answer in volts. E = V Submit Request Answer
A 0.300−m-long bar moves on parallel rails that are connected through a 5.60 Ω resistor, as shown in (Figure 1), so the apparatus makes a complete circuit. You can ignore the resistance of the bar and rails. The circuit is in a uniform magnetic field 1.60 T that is directed into the plane of the figure. Figure 1 of 1 Part A At an instant when the induced current in the circuit is counterclockwise and equal to 1.90 A, what is the magnitude of the velocity of the bar? Express your answer with the appropriate units. Submit Request Answer Part B What is the direction of the velocity of the bar? leftward rightward Submit Request Answer
A long, thin solenoid has 900 turns per meter and radius 2.50 cm. The current in the solenoid is increasing at a uniform rate of 42.0 A/s. Part A What is the magnitude of the induced electric field at a point near the center of the solenoid? Express your answer with the appropriate units. E = Value Units Submit Request Answer Part B What is the magnitude of the induced electric field at a point 0.500 cm from the axis of the solenoid? Express your answer with the appropriate units. Submit Request Answer Part C What is the magnitude of the induced electric field at a point 1.00 cm from the axis of the solenoid? Express your answer with the appropriate units.
A metal bar with length L, mass m, and resistance R is placed on frictionless metal rails that are inclined at an angle ϕ above the horizontal. The rails have negligible resistance. A uniform magnetic field of magnitude B is directed downward in the figure (Figure 1). The bar is released from rest and slides down the rails. Figure 1 of 1 Part A Is the direction of the current induced in the bar from a to b or from b to a ? from a to b from b to a Submit Request Answer Part B What is the terminal speed of the bar? Express your answer in terms some or all of of the variables R, m, ϕ, L, B, and acceleration due to gravity g. vt = Submit Request Answer Part C What is the induced current in the bar when the terminal speed has been reached? Express your answer in terms some or all of of the variables R, m, ϕ, L, B, and acceleration due to gravity g. Submit Request Answer Part D After the terminal speed has been reached, at what rate is electrical energy being converted to thermal energy in the resistance of the bar? Express your answer in terms some or all of of the variables R, m, ϕ, L, B, and acceleration due to gravity g. Part E After the terminal speed has been reached, at what rate is work being done on the bar by gravity? Express your answer in terms some or all of of the variables R, m, ϕ, L, B, and acceleration due to gravity g. Submit Request Answer
A parallel-plate, air-filled capacitor is being charged as in (Figure 1). The circular plates have radius 4.00 cm, and at a particular instant, the conduction current in the wires is 0.620 A. Figure 1 of 1 Part A What is the displacement current density jD in the air space between the plates? Express your answer with the appropriate units. Submit Request Answer Part B What is the rate at which the electric field between the plates is changing? Express your answer in volts per meter per second. dE dt V/m s Submit Request Answer Part C What is the induced magnetic field between the plates at a distance of 2.00 cm from the axis? Express your answer with the appropriate units. B = Value Units Submit Request Answer Part D What is the induced magnetic field between the plates at a distance of 1.00 cm from the axis? Express your answer with the appropriate units. B = Value Units Submit Request Answer
A uniform electric field is directed axially in a cylindrical region that includes a rectangular loop of wire with total resistance R. This loop has radially oriented width a and axially oriented length b, and sits tight against the cylinder axis, as shown in (Figure 1). The electric field is zero at time t = 0 and then increases in time according to E→ = ηt2k^, where η is a constant with units of V/(m⋅s2). Figure 1 of 1 Part A What is the magnitude of the displacement current through a circular loop centered on the cylinder axis with radius r ≤ a, at time t ? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part B Use Ampere's law to determine the magnitude of the magnetic field a distance r ≤ a from the cylinder axis at time t. Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part C What is the magnetic flux at time t through the rectangular wire loop? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part D What magnitude of current flows in the wire? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part E Does the current flow clockwise or counterclockwise from the perspective shown in the figure? clockwise counterclockwise Submit Request Answer
Part A What angle in radians is subtended by an arc of 1.57 m in length on the circumference of a circle of radius 2.58 m ? Express your answer in radians. θ = rad Submit Request Answer Part B What is this angle in degrees? Express your answer in degrees. θ = Part C An arc of length 13.3 cm on the circumference of a circle subtends an angle of 123∘. What is the radius of the circle? Express your answer in centimeters. r = cm Submit Request Answer Part D The angle between two radii of a circle with radius 1.48 m is 0.630 rad. What length of arc is intercepted on the circumference of the circle by the two radii? Express your answer in meters. L = m
A fan blade rotates with angular velocity given by ωz(t) = γ − βt2 Part A Calculate the angular acceleration as a function of time. Express your answer in terms of the variables β, γ, and t. αz(t) = Part B If γ = 5.15 rad/s and β = 0.790 rad/s3, calculate the instantaneous angular acceleration αz at t = 2.80 s. Express your answer in radians per second squared. αz = rad/s2 Submit Request Answer Part C If γ = 5.15 rad/s and β = 0.790 rad/s3, calculate the average angular acceleration αav−z for the time interval t = 0 to t = 2.80 s. Express your answer in radians per second squared. αav−z = rad/s2
An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 150 rev/min in 5.00 s. Part A Find the angular acceleration in rev/s2. Express your answer in revolutions per second squared. αz = rev/s2 Part B Find the number of revolutions made by the motor in the 5.00 s interval. Express your answer in revolutions. θ−θ0 = rev Submit Request Answer Part C How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part A? Express your answer in seconds. t = S
Spin cycles of washing machines remove water from clothes by producing a large radial acceleration at the rim of the cylindrical tub that holds the water and clothes. Suppose that the diameter of the tub in a typical home washing machine is 50 cm. Part A What is the rotation rate, in rev/min, of the tub during the spin cycle if the radial acceleration of points on the tub wall is 3g ? Express your answer in revolutions per minute. ω =rev/min Part B At this rotation rate, what is the tangential speed in m/s of a point on the tub wall? Express your answer in meters per second. v = m/s
Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by light rods (Figure 1) Figure 1 of 1 Part A Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an axis through point O in the figure). Express your answer in kilogram meters squared. I = kg⋅m2 Submit Request Answer Part B Find the moment of inertia of the system about an axis bisecting two opposite sides of the square (an axis along the line AB in the figure). Express your answer in kilogram meters squared. I = kg⋅m2 Part C Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O. Express your answer in kilogram meters squared. I = kg⋅m2
Three small blocks, each with mass m, are clamped at the ends and at the center of a rod of length L and negligible mass. Part A Compute the moment of inertia of the system about an axis perpendicular to the rod and passing through the center of the rod. Express your answer in terms of the variables m and L. I = Submit Request Answer Part B Compute the moment of inertia of the system about an axis perpendicular to the rod and passing through a point one-fourth of the length from one end. Express your answer in terms of the variables m and L. I =
A thin, rectangular sheet of metal has mass M and sides of length a and b. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Using the parallel-axis theorem. Part A Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet. Express your answer in terms of the variables M, a, and b. I = Submit Request Answer
The pulley in (Figure 1) has radius 0.160 m and moment of inertia 0.380 kg⋅m2. The rope does not slip on the pulley rim. Figure 1 of 1 Part A Use energy methods to calculate the speed of the 4.00 kg block just before it strikes the floor. Express your answer with the appropriate units. v = Submit Request Answer
For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Calculating gravitational force. Part A What is the ratio of the gravitational pull of the sun on the moon to that of the earth on the moon? (Assume the distance of the moon from the sun can be approximated by the distance of the earth from the sun.) Fsun Fearth =
The International Space Station makes 15.65 revolutions per day in its orbit around the earth. Part A Assuming a circular orbit, how high is this satellite above the surface of the earth? Express your answer in kilometers to three significant figures. h = km
You decide to visit Santa Claus at the north pole to put in a good word about your splendid behavior throughout the year. While there, you notice that the elf Sneezy, when hanging from a rope, produces a tension of 465.0 N in the rope. Part A If Sneezy hangs from a similar rope while delivering presents at the earth's equator, what will the tension in it be? (Recall that the earth is rotating about an axis through its north and south poles.) Express your answer to four significant figures and include the appropriate units.
An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and finds that it takes the rock 0.460 s to fall 1.90 m. Part A If the radius of the planet is 8.90×107 m, what is the mass of the planet? Express your answer with the appropriate units. mp =
You are exploring a distant planet. When your spaceship is in a circular orbit at a distance of 630 km above the planet's surface, the ship's orbital speed is 4600 m/s. By observing the planet, you determine its radius to be 4.48×106 m. You then land on the surface and, at a place where the ground is level, launch a small projectile with initial speed 14.6 m/s at an angle of 30.8∘ above the horizontal. Part A If resistance due to the planet's atmosphere is negligible, what is the horizontal range of the projectile? Express your answer with the appropriate units. d =
Astronomers have observed a small, massive object at the center of our Milky Way Galaxy. A ring of material orbits this massive object; the ring has a diameter of about 13 light-years and an orbital speed of about 210 km/s. For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Black hole calculations. Part A Determine the mass M of the massive object at the center of the Milky Way Galaxy. Give your answer in kilograms. Express your answer in kilograms. View Available Hint(s) M = kg Submit Part B Give your answer in solar masses (one solar mass is the mass of the sun). Express your answer in units of solar masses. View Available Hint(s)
Three forces are applied to a wheel of radius 0.350 m, as shown in the figure (Figure 1). One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.0∘ angle with the radius. Figure 1 of 1 Part A What is the magnitude of the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center? Express your answer in newton-meters. τ = N⋅m Submit Request Answer Part B What is the direction of the net torque in part (A)? into the page out of the page Submit Request Answer
A machine part has the shape of a solid uniform sphere of mass 245 g and diameter 2.90 cm. It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of An unwinding cable ii. Part A Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation. Express your answer in radians per second squared. α = rad/s2 Submit Request Answer Part B How long will it take to decrease its rotational speed by 23.0 rad/s ? Express your answer in seconds. t = s
Two uniform solid balls are rolling without slipping at a constant speed. Ball 1 has twice the diameter, half the mass, and one-third the speed of ball 2 . The kinetic energy of ball 2 is 25.0 J. Part A What is the kinetic energy of ball 1 ? Express your answer with the appropriate units. K1 =
The engine of an aircraft propeller delivers an amount of power 176 hp to the propeller at a rotational velocity of 2500 rev/min. Part A How much torque does the aircraft engine provide? Express your answer in newton-meters. τ = N⋅m Submit Request Answer Part B How much work does the engine do in one revolution of the propeller? Express your answer in joules. W = J
A woman with mass 50 kg is standing on the rim of a large horizontal disk that is rotating at 0.80 rev/s about an axis through its center. The disk has mass 110 kg and radius 3.9 m. Part A Calculate the magnitude of the total angular momentum of the woman-disk system. (Assume that you can treat the woman as a point.) Express your answer with the appropriate units. ? L =
The Hubble Space Telescope is stabilized to within an angle of about 2 millionths of a degree by means of a series of gyroscopes that spin at 19, 200 rpm. Although the structure of these gyroscopes is actually quite complex, we can model each of the gyroscopes as a thin-walled cylinder of mass 2.00 kg and diameter 5.00 cm, spinning about its central axis. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of A precessing gyroscope. Part A How large a torque would it take to cause these gyroscopes to precess through an angle of 1.10×10−6 degree during a 6.0 hour exposure of a galaxy? Express your answer in newton-meters.
A certain gyroscope precesses at a rate of 0.40 rad/s when used on earth. Part A If it were taken to a lunar base, where the acceleration due to gravity is 0.165 g, what would be its precession rate? Express your answer in radians per second. Ω = rad/s
Two coils have mutual inductance of M = 3.30×10−4 H. The current i1 in the first coil increases at a uniform rate of 830 A/s. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Emf due to mutual inductance. Part A What is the magnitude of the induced emf in the second coil? Express your answer in volts. Submit Request Answer Part B Suppose that the current described is in the second coil rather than the first. What is the magnitude of the induced emf in the first coil? Express your answer in volts.
It has been proposed to use large inductors as energy storage devices. Part A How much electrical energy is converted to light and thermal energy by a 170 W light bulb in one day? Express your answer with the appropriate units. E = Submit Request Answer Part B If the amount of energy calculated in part A is stored in an inductor in which the current is 80.0 A, what is the inductance? Express your answer with the appropriate units. L =
One solenoid is centered inside another. The outer one has a length of 47.0 cm and contains 6800 coils, while the coaxial inner solenoid is 5.0 cm long and 0.130 cm in diameter and contains 22 coils. The current in the outer solenoid is changing at 38.0 A/s. Part A What is the mutual inductance of these solenoids? M = μH Submit Request Answer Part B Find the emf induced in the inner solenoid. Ein = V
In (Figure 1), R = 11.0 Ω and the battery emf is 6.30 V. With switch S2 open, switch S1 is closed. After several minutes, S1 is opened and S2 is closed. Figure 1 of 1 Part A At 2.20 ms after S1 is opened, the current has decayed to 0.200 A. Calculate the inductance of the coil. Express your answer with the appropriate units. L = Submit Request Answer Part B How long after S1 is opened will the current reach 1.00% of its original value? Express your answer with the appropriate units. t =
In an L−C circuit, C = 3.23 μF and L = 85.0 mH. During the oscillations the maximum current in the inductor is 0.852 mA. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of An oscillating circuit. Part A What is the maximum charge on the capacitor? Express your answer in coulombs. Qmax C Submit Request Answer Part B What is the magnitude of the charge on the capacitor at an instant when the current in the inductor has magnitude 0.507 mA ? Express your answer in coulombs. q = C
The minimum capacitance of a variable capacitor in a radio is 4.15 pF. Part A What is the inductance of a coil connected to this capacitor if the oscillation frequency of the L−C circuit is 1.70 MHz, corresponding to one end of the AM radio broadcast band, when the capacitor is set to its minimum capacitance? Express your answer in henries. L = H Part B The frequency at the other end of the broadcast band is 0.539 MHz. What is the maximum capacitance of the capacitor if the oscillation frequency is adjustable over the range of the broadcast band? Express your answer in farads. C = F
Your latest invention is a car alarm that produces sound at a particularly annoying frequency of 3.60×103 Hz. To do this, the car alarm circuitry must produce an alternating electric current of the same frequency. That's why your design includes an inductor and capacitor in series. The maximum voltage across the capacitor is to be 12.0 V. To produce a sufficiently loud sound, the capacitor must store an amount of energy equal to 1.60×10−2 J Part A What value of capacitance should you choose for your car alarm circuit? Express your answer in farads. C = F Submit Request Answer Part B What value of inductance should you choose for your car alarm circuit? Express your answer in henries. L = H
In the circuit shown in (Figure 1), neither the battery nor the inductors have any appreciable resistance, the capacitors are initially uncharged, and the switch S has been in position 1 for a very long time. Figure 1 of 1 Part A What is the current in the circuit? Express your answer in amperes. I = A Submit Request Answer Part B The switch is now suddenly flipped to position 2 . Find the maximum charge that the 25.0 μF capacitor will receive. Express your answer in coulombs. q = C Submit Part C The switch is now suddenly flipped to position 2. Find the maximum charge that the 35.0 μF capacitor will receive. Express your answer in coulombs. q = C Submit Request Answer Part D How much time after the switch is flipped will it take the capacitors to acquire this charge? Express your answer in seconds. t = s
In the circuit shown in (Figure 1), find the readings in the following meters just after switch S is closed. Figure 1 of 1 Part A Find the reading in the voltmeter V1. Express your answer in volts. V1 = V Submit Request Answer Part B Find the reading in the voltmeter V2. Express your answer in volts. V2 = V Part C Find the reading in the voltmeter V3. Express your answer in volts. V3 = V Submit Request Answer Part D Find the reading in the voltmeter V4. Express your answer in volts. V4 = V Part E Find the reading in the ammeter A1. Express your answer in amperes. I1 = A Submit Request Answer Part F Find the reading in the ammeter A2. Express your answer in amperes. I2 = A Part G Find the reading in the ammeter A3. Express your answer in amperes. I3 = A Submit Request Answer Now find the readings of the following voltmeters and ammeters after S has been closed a very long time. Part H Find the reading of the voltmeter V1. Express your answer in volts. V1 = V Submit Request Answer Part I Find the reading of the voltmeter V2. Express your answer in volts. V2 = V Part J Find the reading of the voltmeter V3. Express your answer in volts. V3 = V Submit Request Answer Part K Find the reading of the voltmeter V4. Express your answer in volts. V4 = Part L Find the reading in the ammeter A1. Express your answer in amperes. I1 = A Submit Request Answer Part M Find the reading in the ammeter A2. Express your answer in amperes. I2 = Part N Find the reading in the ammeter A3. Express your answer in amperes. I3 =
In the circuit shown in (Figure 1), E = 55.0 V, R1 = 38.0 Ω, R2 = 23.0 Ω, and L = 0.300 H. Figure 1 of 1 Part A Switch S is closed. At some time t afterward the current in the inductor is increasing at a rate of di/dt = 50.0 A/s. At this instant, what is the current i1 through R1 ? Express your answer in amperes. Submit Request Answer Part B Switch S is closed. At some time t afterward the current in the inductor is increasing at a rate of di/dt = 50.0 A/s. At this instant, what is the current i2 through R2 ? Express your answer in amperes. Submit Part C After the switch has been closed a long time, it is opened again. Just after it is opened, what is the current through R1 ? Express your answer in amperes. i = A
A 61-kg woman eats a 447 Calorie ( 447 kcal ) jelly doughnut for breakfast. (a) How many joules of energy are the equivalent of one jelly doughnut? J (b) How many steps must the woman climb on a very tall stairway to change the gravitational potential energy of the woman-Earth system by a value equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is 15 cm. stairs (c) If the human body is only 20% efficient in converting chemical potential energy to mechanical energy, how many steps must the woman climb to work off her breakfast? stairs
The temperature of an object is changed when heat is added to or extracted from it. Determine the final temperature (in ∘C ) of a 85.0 g mass of lead initially at 76.0∘C if 1,150 J of heat energy is extracted from it. The specific heat of lead is 128 J/(kg⋅∘C). ∘C
Steam at 100∘C is condensed into a 38.0 g copper calorimeter cup containing 200 g of water at 25.0∘C. Determine the amount of steam (in g) needed for the system to reach a final temperature of 40.0∘C. The specific heat of copper is 387 J/(kg⋅∘C). g
Determine the amount of work done on an ideal gas as it is heated in an enclosed thermally isolated cylinder topped with a freely moving piston. The cylinder contains of n moles of the gas and the temperature is raised from T1 to T2. The piston has a mass m and a cross sectional area A. (Use any variable or symbol stated above along with the following as necessary: R.) W =
Why is the following situation impossible? An ideal gas undergoes a process with the following parameters: Q = 10.0 J, W = 12.0 J, and ΔT = −2.00∘C. This answer has not been graded yet.
A thermodynamic system undergoes a process in which its internal energy decreases by 525 J. Over the same time interval, 180 J of work is done on the system. Find the energy transferred from it by heat. J
The surface temperature of the star Vega is 10,000 K, its radius is 1.74×109 m, and its emissivity is 0.970. Determine the total energy radiated by this star each second (in W). w
A 19th century lab technician is testing possible metals for bulb filaments. A platinum filament with a surface area of 0.450 mm2 and an emissivity of 0.979 radiates 0.30 W of light. Determine the filament's temperature (in K). The melting point for platinum is 2045 K. K
(a) How many atoms of helium gas fill a spherical balloon of diameter 31.0 cm at 22.0∘C and 1.00 atm? atoms (b) What is the average kinetic energy of the helium atoms? J (c) What is the rms speed of the helium atoms? km/s
A container is filled with an ideal diatomic gas to a pressure and volume of P1 and V1, respectively. The gas is then warmed in a two-step process that increases the pressure by a factor of four and the volume by a factor of three. Determine the amount of energy transferred to the gas by heat if the first step is carried out at constant volume and the second step at constant pressure. (Use any variable or symbol stated above as necessary.) Q =
You and your younger brother are designing an air rifle that will shoot a lead pellet with mass m = 1.00 g and cross-sectional area A = 0.0350 cm2. The rifle works by allowing high-pressure air to expand, propelling the pellet down the rifle barrel. Because this process happens very quickly, no appreciable thermal conduction occurs and the expansion is essentially adiabatic. Your design is such that, once the pressure begins pushing on the pellet, it moves a distance of L = 55.0 cm before leaving the open end of the rifle at your desired speed of v = 130 m/s. Your design also includes a chamber of volume V = 10.0 cm3 in which the high-pressure air is stored until it is released. Your brother reminds you that you need to purchase a pump to pressurize the chamber. To determine what kind of pump to buy, you need to find what the pressure of the air must be in the chamber (in Pa) to achieve your desired muzzle speed. Ignore the effects of the air in front of the bullet and friction with the inside walls of the barrel. (Assume that air is diatomic. ) Pa
A diatomic molecule is rotating about its center of mass with an angular speed of 2.40×1012 rad/s. Determine the rotational kinetic energy (in J) of one molecule, if the gas is oxygen which has a bond length of 1.21 Å and a molecular molar mass of 32.0 g/mole. J
An efficiency consultant is studying the power stroke of a four-stroke engine and determines the following: As the piston is forced down, the mixture of combustion products and air undergoes an adiabatic expansion. The engine is running at 2,900 cycles/min. The gauge pressure immediately before the expansion is 27.0 atm. The volumes of the mixture immediately before and after the expansion are 50.0 cm3 and 400 cm3, respectively (figure below). The time interval for the expansion is one-fourth the period of the cycle. The mixture behaves like an ideal diatomic gas with a specific heat ratio of 1.40 . Determine the average power (in kW) generated during the power stroke. Before After (i) kW
Air in a thundercloud expands as it rises. If its initial temperature is 302 K and no energy is lost by thermal conduction on expansion, what is its temperature when the initial volume has doubled? K
(a) The liquid and gaseous state of chlorine are in thermal equilibrium at 239 K. Even though it is on the point of condensation, model the gas as ideal and determine the most probable speed of the molecules (in m/s). m/s (b) What If? At what temperature (in K) would an atom of radon in a canister of radon gas have the same most probable speed as the chlorine in thermal equilibrium at 239 K? K
Fifteen identical particles have various speeds: one has a speed of 2.00 m/s, two have speeds of 3.00 m/s, three have speeds of 5.00 m/s, four have speeds of 8.00 m/s, three have speeds of 9.00 m/s, and two have speeds of 14.0 m/s. (a) Find the average speed (in m/s). m/s (b) Find the rms speed (in m/s). m/s (c) Find the most probable speed of these particles (in m/s). m/s (d) What If? How many additional particles with a speed of 14.0 m/s must be added to the original fifteen particles for the average speed to become 10.0 m/s ? (Round your answer to at least the nearest integer.) particles (e) What would be the rms speed of the original plus additional particles (in m/s)? m/s
A technician is testing vacuum pumps. The pumps are connected to a vacuum chamber with a volume of 1.50 m3, allowed to run for a set period of time, and the temperature and pressured measured. For a particular pump, the final chamber temperature and pressure are respectively measured to be 310 K and 3.50×10−10 Torr (where 1 Torr = 133 Pa). Determine the number of molecules in the chamber at the end of the pumping time. You may treat the contents of the vacuum chamber as an ideal gas. molecules
For a cylinder of hydrogen (H2) gas, you have been informed that the rms speed of the molecules is 585 m/s. Determine the temperature of the gas in degrees K. Use 2.0159×10−3 kg as the mass of a mole of hydrogen molecules. K
Calculate the change in internal energy of 3.45 mol of helium gas when its temperature is increased by 2.00 K. J
A 1.00−L insulated bottle is full of tea at 94.5∘C. You pour out a mug of tea and immediately screw the stopper back on the bottle. Find the change in temperature of the tea remaining in the bottle that results from the admission of air at room temperature. (Let the room temperature be 20.0∘C and assume that you poured out 195 cm3 of tea. Take the molar mass of air as 28.9 g/mol and ρair = 1.20×10−3 g/cm3. Here we define a "monatomic ideal gas" to have molar specific heats CV = 32 R and CP = 52 R, and a "diatomic ideal gas" to have CV = 52 R and CP = 72 R.) ∘C
You are visiting your relatives in the Los Angeles basin on a warm day in late September. Everyone is talking about how windy and warm it is because of the Santa Ana conditions. In these conditions, winds that normally blow from west to east reverse direction, so that air comes westward over the mountains that surround Los Angeles and down into the basin. As a packet of air descends from a location in the mountains into the basin, it is compressed adiabatically, causing it to become hotter. Suddenly, the conversation stops when someone remembers you are taking physics, and everyone turns to look at you. Your uncle asks you on behalf of the rest of your family to show them a calculation that explains why the Santa Ana winds are so warm. He says that he has been to the Cajon Pass, with an elevation of 1,151 m. Every time he has been there, he has noticed strong winds, especially during Santa Ana conditions, when the air to the east and north of southern California pours westward through the passes. Your aunt is looking on her smartphone and tells you that the atmospheric pressure varies with elevation nearly linearly between sea level and low mountain altitudes, with a reduction of 12 Pa for each meter of increased elevation. Your uncle says that the air temperature was 67.3∘F when he was in the Cajon Pass. Everyone starts clamoring and begging you for a calculation that would show the temperature of the air in a Santa Ana wind on that day in the Los Angeles basin. What temperature do you calculate (in ∘F) ? (Assume air is a diatomic gas and that the Los Angeles basin has a pressure of 1 atm. ) ∘F
A certain molecule has f degrees of freedom. Show that an ideal gas consisting of such molecules has the following properties. (Submit a file with a maximum size of 1 MB. ) (a) Its total internal energy is fnRT 2. (b) Its molar specific heat at constant volume is fR2. (c) Its molar specific heat at constant pressure is (f+2)R 2. (d) Its specific heat ratio is γ = Cp CV = (f+2) f. Choose File No file chosen This answer has not been graded yet.
One cubic meter of atomic hydrogen at 0∘C at atmospheric pressure contains approximately 2.70×1025 atoms. The first excited state of the hydrogen atom has an energy of 10.2 eV above the lowest state, called the ground state. Use the Boltzmann factor to find the following. (a) the number of atoms in the first excited state at 0∘C (b) the number of atoms in the first excited state at (8.00×103)∘C (Do not round the numbers in your calculation.)
Determine the following speeds (in m/s) for molecules of the diatomic gas bromine at a temperature of 840 K. Use 160×10−3 kg/mole as the molar mass for bromine molecules. (a) root mean square speed m/s (b) average speed m/s (c) most probable speed m/s
At what temperature would the average speed of helium atoms equal the following value? Note: The mass of a helium atom is 6.64×10−27 kg (a) the escape speed from Mars, 5.05×103 m/s K (b) the escape speed from Saturn, 3.62×104 m/s K
Consider a sample containing 1.85 mol of an ideal diatomic gas. (a) Assuming the molecules rotate but do not vibrate, find the total heat capacity of the sample at constant volume. nCv = J/K (b) Assuming the molecules rotate but do not vibrate, find the total heat capacity of the sample at constant pressure. nCp = J/K (c) Assuming the molecules both rotate and vibrate, find the total heat capacity of the sample at constant volume. nCv = J/K Assuming the molecules both rotate and vibrate, find the total heat capacity of the sample at constant pressure. nCp = J/K
A large garage with well-insulated walls and containing 650 m3 of air at 285 K is heated at constant pressure (atmospheric). Consider air to be an ideal diatomic gas. (a) Determine the energy (in kJ ) required to increase the temperature of the air in the building by 2.30∘C. kJ (b) Determine the mass (in kg ) this amount of energy could lift through a height 1.90 m. kg
A cylinder contains a mixture of helium and argon gas in equilibrium at 140∘C. (a) What is the average kinetic energy for each type of gas molecule? helium J argon J (b) What is the rms speed of each type of molecule? helium km/s argon m/s
A heat engine takes in 330 J of energy from a hot reservoir and performs 26.0 J of work in each cycle. (a) Find the efficiency of the engine. % (b) Find the energy expelled to the cold reservoir in each cycle. J
A firearm can be modeled as a kind of heat engine, where the projectile acts as a piston that separates from the rest of the system during expansion. Consider a gun with a 1.60 kg barrel made of iron [specific heat = 448 J/(kg⋅∘C)]. The gun fires a 3.40 g bullet that exits the barrel with a speed of 340 m/s. When the propellant is ignited, 1.10% of the energy released goes into propelling the bullet (this is the thermal efficiency of the "engine"). The other 98.9% can be approximated as being entirely absorbed by the barrel, which increases in temperature uniformly for a short time before this energy is dissipated into the surroundings. What is this temperature increase (in ∘C)? (Round your answer to at least one decimal place.) ∘C
A refrigerator has a coefficient of performance equal to 6.00 . The refrigerator takes in 110 J of energy from a cold reservoir in each cycle. (a) Find the work required in each cycle. J (b) Find the energy expelled to the hot reservoir. J
A Carnot engine has a power output of 130 kW. The engine operates between two reservoirs at 20∘C and 540∘C. (a) How much energy enters the engine by heat per hour? MJ (b) How much energy is exhausted by heat per hour? MJ
A gasoline engine has a compression ratio of 7.00 and uses a gas for which γ = 1.40. (a) What is the efficiency of the engine if it operates in an idealized Otto cycle? % (b) If the actual efficiency is 17.0%, what fraction of the fuel is wasted as a result of friction and energy losses by heat that could by avoided in a reversible engine? (Assume complete combustion of the air-fuel mixture.) %
You toss two six-sided dice. What is the total number of ways in which you can obtain the following? (a) a 7 (b) a 9 What If? If you now rolled three six-sided dice, what would be the number of ways in which you can obtain the following? (c) a 12 (d) a 9
An ice tray contains 410 g of liquid water at 0∘C. Calculate the change in entropy of the water as it freezes slowly and completely at 0∘C. J/K
The temperature at the surface of the Sun is approximately 5,850 K, and the temperature at the surface of the Earth is approximately 285 K. What entropy change of the Universe occurs when 6.00×103 J of energy is transferred by radiation from the Sun to the Earth? J/K
(a) A freezer maintains an interior temperature inside of −26.0∘C and has a coefficient of performance of 3.00 . The freezer sits in a room with a temperature of 21.0∘C. The freezer is able to completely convert 32.0 g of liquid water at 21.0∘C to ice at −26.0∘C in one minute. What input power (in watts) does the freezer require? (The specific heat of liquid water is 4.186 J/(g⋅∘C), the specific heat of ice is 2.090 J/(g⋅∘C), and the latent heat of fusion of water is 334 J/g. ) W (b) What If? In reality, only part of the power consumption of a freezer is used to make ice. The remainder is used to maintain the temperature of the rest of the freezer. Suppose, however, that 100% of a freezer's typical power consumption of 160 W is available to make ice. The freezer has the same coefficient of performance as given above. How many grams per minute of water at 21.0∘C could this freezer convert to ice at −26.0∘C? g/min
What is the maximum possible efficiency of a heat engine operating between a reservoir at 24.0∘C and one at 370∘C? (Enter a number as a fraction or decimal.) eC =
Suppose you have a bag of 100 marbles of which 50 are red and 50 are green. You are allowed to draw three marbles from the bag according to the following rules. Draw one marble, record its color, and return it to the bag. Shake the bag and then draw another marble. Continue this process until you have drawn and returned three marbles. (Submit a file with a maximum size of 1 MB. ) (a) List the possible macrostates and microstates resulting from this procedure. (b) Prepare a second list for the case in which you draw five marbles rather than three. Choose File No file chosen This answer has not been graded yet.
A block made of iron with a mass of 0.80 kg is heated to 800∘C, then dropped into 5.00 kg of water at 10∘C. What is the total change in entropy (in J/K ) of the block-water system, assuming no energy is lost by heat from this system to the surroundings? The specific heat of iron is 448 J/(kg⋅K), and the specific heat of water is 4,186 J/(kg⋅K). (Hint: note that dQ = mcdT.) J/K
When an aluminum bar is connected between a hot reservoir at 620 K and a cold reservoir at 358 K, 2.00 kJ of energy is transferred by heat from the hot reservoir to the cold reservoir. (a) In this irreversible process, calculate the change in entropy of the hot reservoir. J/K (b) In this irreversible process, calculate the change in entropy of the cold reservoir. J/K (c) In this irreversible process, calculate the change in entropy of the Universe, neglecting any change in entropy of the aluminum rod. J/K