A 0.50 kg block of iron [c = 0.44 kJ/(kg·K)] at 20.0°C is in contact with a 0.50 kg block of aluminum [c = 0.900 kJ/(kg·K)] at a temperature of 20.0°C. The system is completely isolated from the rest of the universe. Suppose heat flows from the iron into the aluminum until the temperature of the aluminum is 22.0°C. (a) From the first law, calculate the final temperature of the iron. (b) Estimate the entropy change of the system. (c) Explain how the result of part (b) shows that this process is impossible. [Hint: Since the system is isolated, ΔSsystem = ΔSuniverse.]
> An astronaut in top physical condition has an average resting pulse on Earth of about 52 beats per minute. Suppose the astronaut is in a spaceship traveling at 0.87c (γ = 2) with respect to Earth when he takes his own resting pulse. Does he measure about
> A proton (mass 1.67 × 10−27 kg, charge +e) is fired directly at a lithium nucleus (mass 1.16 × 10−26 kg, charge +3e). If the proton's velocity is 5.24 × 105 m/s when it is far from the nucleus, how far apart will the two particles be when the proton is a
> A particle with nonzero mass m can never move faster than the speed of light. Is there also a maximum momentum that the particle can have? A maximum kinetic energy? Explain.
> As you talk on a cell phone, does the mass of the phone's battery change at all? If so, does it increase or decrease?
> An electron is moving at nearly light speed. A constant force of magnitude F is acting on the electron in the direction of its motion. Is the acceleration of the electron less than, equal to, or greater in magnitude than F/m? Explain.
> A quasar is a bright center in a far distant galaxy where some energetic action is taking place (probably due to energy being released as matter falls into a black hole at the center of the galaxy). Through her telescope Mavis observes a quasar 12 × 109
> Does a stretched spring have the same mass as when it is relaxed? Explain.
> A cylindrical brass container with a base of 75.0 cm2 and height of 20.0 cm is filled to the brim with water when the system is at 25.0°C. How much water overflows when the temperature of the water and the container is raised to 95.0°C?
> Explain why it is impossible for a particle with mass to move faster than the speed of light.
> When the spring on a toy gun is compressed by a distance x, it will shoot a rubber ball straight up to a height of h. Ignoring air resistance, how high will the gun shoot the same rubber ball if the spring is compressed by an amount 2x? Assume x ≪ h.
> A particle with charge +e has a total energy of 0.638 MeV when it is moving at 0.600c. If this particle then enters a linear accelerator, what is its speed after it has been accelerated through a 2.6 MV potential difference?
> A friend argues with you that relativity is absurd: “It's obvious that moving clocks don't run slow and that moving objects aren't shorter than when they're at rest.” How would you reply?
> The drawing shows a snapshot of a transverse wave traveling along a string at 10.0 m/s. The equation for the wave is y(x, t) = A cos (ωt + kx). (a) Is the wave moving to the right or to the left? (b) What are the numerical values of A, Ï
> In a double-slit experiment, what is the linear distance on the screen between adjacent maxima if the wavelength is 546 nm, the slit separation is 0.100 mm, and the slit-screen separation is 20.0 cm?
> A spherical rain drop of radius 1.0 mm has a charge of +2.0 nC. The electric field in the vicinity is 2.0 kN/C downward. The terminal speed of an identical but uncharged drop is 6.5 m/s. The drag force is related to the drop’s speed by
> In an experiment to measure the Coulomb constant, a tiny sphere with charge +7.0 nC is suspended from a spring. When two other tiny charged spheres, each with a charge of −4.0 µC, are placed in the positions shown in the figure, the spring stretches 0.50
> The graph shows the position x of a switch engine in a rail yard as a function of time t. At which of the labeled times t0 to t7 is (a) ax 0, (d) vx = 0, (e) the speed decreasing?
> Humans cool off by perspiring; the evaporating sweat removes heat from the body. If the skin temperature is 35.0°C and the air temperature is 28.0°C, what is the entropy change of the universe due to the evaporation of 150 mL of sweat? Take the latent he
> In gel electrophoresis, the mobility μ of a molecule in a particular gel matrix is defined as μ = v1/E, where v1 is the terminal speed of the molecule and E is the applied electric field strength. In one case, a molecule has mobility 3.0 × 10−8 C·m/(N·s)
> A student eats 2000 kcal per day. (a) Assuming that all of the food energy is released as heat, what is the rate of heat released (in watts)? (b) What is the rate of change of entropy of the surroundings if all of the heat is released into air at room t
> The Bohr model of the hydrogen atom proposed that the electron orbits around the proton in a circle of radius 5.3 × 10−11 m. The electric force is responsible for the radial acceleration of the electron. What is the speed of the electron in this model?
> (a) Which has the larger buoyant force acting on it when immersed in water, 1.0 kg of lead or 1.0 kg of aluminum? Explain. (b) Which has the larger buoyant force acting on it, 1.0 kg of steel that is sinking to the bottom of a lake or 1.0 kg of wood with
> Within an insulated system, 418.6 kJ of heat is conducted through a copper rod from a hot reservoir at +200.0°C to a cold reservoir at +100.0°C. (The reservoirs are so big that this heat exchange does not change their temperatures appreciably.) What is t
> A very small charged block with a mass of 2.35 g is placed on an insulated, frictionless plane inclined at an angle of 17.0° with respect to the horizontal. The block does not slide down the plane because of a 465 N/C uniform electric field th
> Rank these in order of increasing entropy: (a) 1 mol of water at 20°C and 1 mol of ethanol at 20°C in separate containers; (b) a mixture of 1 mol of water at 20°C and 1 mol of ethanol at 20°C; (c) 0.5 mol of water at 20°C and 0.5 mol of ethanol at 20°
> The energy-time uncertainty principle allows for the creation of virtual particles that appear from a vacuum for a very brief period of time Δt, then disappear again. This can happen as long as ΔE Δt = ħ/2, where ΔE is the rest energy of the particle. (
> (a) Write an expression for the magnitude of the electric field at a point (x, 0) on a line perpendicular to the dipole axis. State the direction of the field for x > 0 and for x < 0. (b) Show that when x ≫ d, E ≈ kqd/x3. (c) The field is inversely pro
> Rank these in order of increasing entropy: (a) 0.5 kg of ice and 0.5 kg of (liquid) water at 0°C; (b) 1 kg of ice at 0°C; (c) 1 kg of (liquid) water at 0°C; (d) 1 kg of water at 20°C.
> A pilot wants to fly from Dallas to Oklahoma City, a distance of 330 km at an angle of 10.0° west of north. The pilot heads directly toward Oklahoma City with an airspeed of 200 km/h. After flying for 1.0 h, the pilot finds that he is 15 km off course to
> (a) Write an expression for the electric field at a point (0, y) on the dipole axis for y > d/2. What is the direction of the field? (b) Show that when y ≫ d, E ≈ 2kqd/y3. [Hint: Use the binomial approximation from Appendix A.9.] (c) The field is inverse
> Show that the coefficient of performance for a reversible refrigerator is 1/[(TH/TC) − 1].
> A thin wire with positive charge Q evenly spread along its length is shaped into a semicircle of radius R. (a). What is the direction of the electric field at the center of curvature of the semicircle? Explain. (b) Is the magnitude of the field at the
> The gauge pressure of the air in an automobile tire is 32 lb/in2. Convert this to (a) Pa, (b) mmHg, (c) atm.
> Show that the coefficient of performance for a reversible heat pump is 1/(1 − TC/TH).
> In a cathode ray tube, electrons initially at rest are accelerated by a uniform electric field of magnitude 4.0 × 105 N/C during the first 5.0 cm of the tube’s length; then they move at essentially constant velocity another 45 cm before hitting the scree
> An engine operates between temperatures of 650 K and 350 K at 65.0% of its maximum possible efficiency. (a) What is the efficiency of this engine? (b) If 6.3 × 103 J is exhausted to the low temperature reservoir, how much work does the engine do?
> A charge of 63.0 nC is located at a distance of 3.40 cm from a charge of −47.0 nC. What are the x- and y-components of the electric field at a point P that is directly above the 63.0 nC charge at a distance of 1.40 cm? Point P and the t
> (a) For a reversible engine, will you obtain a better efficiency by increasing the high-temperature reservoir by an amount ΔT or decreasing the low-temperature reservoir by the same amount ΔT? Explain. (b) To illustrate your answer to this question, cal
> The main energy expenditure involved in running is the work done by the muscles to accelerate the legs. When a foot strikes the ground, it is momentarily brought to rest while the remainder of the animal’s body continues to move forward
> (a) What is the maximum temperature of the gas? (b) What would be the efficiency of an ideal engine with reservoirs at the maximum and minimum temperatures of this engine? Compare this to the actual efficiency, 0.444.
> A sample in a centrifuge moves in a circle of radius 8.0 cm at a constant speed of 500 m/s. (a) How much time does it take for the velocity’s direction to change by 45° (1/8 of a revolution)? (b) What is the magnitude of the average acceleration during
> A reversible refrigerator has a coefficient of performance of 3.0. How much work must be done to freeze 1.0 kg of liquid water initially at 0°C?
> (a) How much net work does this engine do per cycle? (b) Assuming that the efficiency of the engine is 0.444, what is the heat input into the gas per cycle? (c) How much heat is exhausted per cycle? (d) It takes 3.0 s for the engine to go through each
> A woman’s systolic blood pressure when resting is 160 mmHg. What is this pressure in (a) Pa, (b) lb/in2, and (c) atm?
> A heat engine uses the warm air at the ground as the hot reservoir and the cooler air at an altitude of several thousand meters as the cold reservoir. If the warm air is at 37°C and the cold air is at 25°C, what is the maximum possible efficiency for the
> A power plant burns coal to produce pressurized steam at 535 K. The steam then condenses back into water at a temperature of 323 K. (a) What is the maximum possible efficiency of this plant? (b) If the plant operates at 50.0% of its maximum efficiency
> An inventor proposes a heat engine to propel a ship, using the temperature difference between the water at the surface and the water 10 m below the surface as the two reservoirs. If these temperatures are 15.0°C and 10.0°C, respectively, what is the maxi
> The efficiency of a muscle during weight lifting is equal to the work done in lifting the weight divided by the total energy output of the muscle (work done plus internal energy dissipated in the muscle). Determine the efficiency of a muscle that lifts a
> An oil-burning electric power plant uses steam at 773 K to drive a turbine, after which the steam is expelled at 373 K. The engine has an efficiency of 0.40. What is the theoretical maximum efficiency possible at those temperatures?
> An electric power station generates steam at 500.0°C and condenses it with river water at 27°C. By how much would its theoretical maximum efficiency decrease if it had to switch to cooling towers that condense the steam at 47°C?
> A magnesium ion Mg2+ is accelerated through a potential difference of 22 kV. What is the de Broglie wavelength of this ion?
> A motorcycle is speeding on a straight, level highway at constant speed. At t = 0, the motorcycle passes a police car that is initially at rest. The officer gives chase, but the motorcyclist doesn’t notice and keeps moving at constant s
> An engine has a 30.0% efficiency. The engine raises a 5.00 kg crate from rest to a vertical height of 10.0 m, at which point the crate has a speed of 4.00 m/s. How much heat input is required for this engine?
> How many grams of carbohydrate does a person of mass 74 kg need to metabolize to climb five flights of stairs (15 m height increase)? Each gram of carbohydrate provides 17.6 kJ of energy. Assume 10.0% efficiency—that is, 10.0% of the available chemical e
> In Problem 6, what is the pile driver’s speed just before it strikes the pile?
> Two engines operate between the same two temperatures of 750 K and 350 K, and have the same rate of heat input. One of the engines is a reversible engine with a power output of 23 kW. The second engine has an efficiency of 42%. What is the power output o
> A certain engine can propel a 1800 kg car from rest to a speed of 27 m/s in 9.5 s with an efficiency of 27%. What are the rate of heat flow into the engine at the high temperature and the rate of heat flow out of the engine at the low temperature?
> The human body could potentially serve as a very good thermal reservoir, as its internal temperature remains quite constant at around 37°C and is stabilized by continual intake of food. Suppose an inventor designed microscopic engines that could be impla
> A model steam engine of 1.00 kg mass pulls eight cars of 1.00 kg mass each. The cars start at rest and reach a velocity of 3.00 m/s in a time of 3.00 s while moving a distance of 4.50 m. During that time, the net heat input is 135 J. What is the change i
> A new organic semiconductor device is able to generate electricity (which can be used to charge a battery or light an LED) using the warmth of human skin. If your skin temperature is maintained by your body at 35°C and the temperature of the surroundings
> (a) Find the heat flow into or out of the gas during each step, (b) Find the entropy change of the gas during the isothermal step. (c) What is the entropy change of the gas for a complete cycle? Is it equal in magnitude to the entropy change of the envir
> The motor that drives a refrigerator produces 148 W of useful power. The hot and cold temperatures of the heat reservoirs are 20.0°C and −5.0°C. What is the maximum possible amount of ice it can produce in 2.0 h from water that is initially at 8.0°C?
> (a) Calculate the work done by the engine during each step and the net work done per cycle. (b) If the heat input per cycle is 58.3 kJ, what is the efficiency?
> The outdoor temperature on a winter's day is −4°C. If you use 1.0 kJ of electric energy to run a heat pump, how much heat does that put into your house at 21°C? Assume that the heat pump is ideal.
> A crate of oranges weighing 180 N rests on a flatbed truck 2.0 m from the back of the truck. The coefficients of friction between the crate and the bed are μs = 0.30 and μk = 0.20. The truck drives on a straight, level highway at a constant 8.0 m/s. (a)
> Estimate the average blood pressure in a person’s foot if the foot is 1.37 m below the aorta, where the average blood pressure is 104 mmHg. For the purposes of this estimate, assume the blood isn’t flowing.
> You need to move a heavy crate by sliding it across a smooth floor. The coefficient of sliding friction is 0.2. You can either push the crate horizontally or pull the crate using an attached rope. When you pull on the rope, it makes a 30° angle with the
> Draw a PV diagram to illustrate the cycle for this engine. Label the axes with numerical values.
> An ideal refrigerator keeps its contents at 0.0°C and exhausts heat into the kitchen at 40.0°C. For every 1.0 kJ of work done, (a) how much heat is exhausted? (b) How much heat is removed from the contents?
> (a) Find the heat flow into or out of the gas during each of the four steps. (b) What is the net heat flow into the gas per cycle? (c) Calculate the change in entropy of the cold reservoir (not of the gas) in steps B and C and the change in entropy of
> At a tea party, a coffeepot and a teapot are placed on the serving table. The coffeepot is a shiny silver-plated pot with emissivity of 0.12; the teapot is ceramic and has an emissivity of 0.65. Both pots hold 1.00 L of liquid at 98°C when the party begi
> Find the change in internal energy of the gas during each of the four steps.
> A black wood stove has a surface area of 1.20 m2 and a surface temperature of 175°C. What is the net rate at which heat is radiated into the room? The room temperature is 20°C.
> (a) Find the work done by the engine during each of the four steps and the net work done for the cycle. (b) If the heat input per cycle is 2770 J, what is the efficiency of the engine? (c) Compare the efficiency to that of an ideal engine using the sam
> If the maximum intensity of radiation for a blackbody is found at 2.65 um, what is the temperature of the blackbody?
> A fish at a pressure of 1.1 atm has its swim bladder inflated to an initial volume of 8.16 mL. If the fish starts swimming horizontally, its temperature increases from 20.0°C to 22.0°C as a result of the exertion. (a) Since the fish is still at the same
> An IV is connected to a patient’s vein. The blood in the vein has a gauge pressure of 12 mmHg. At least how far above the vein must the IV bag be hung in order for fluid to flow into the vein? Assume the fluid in the IV has the same density as blood.
> In a movie, a stuntman places himself on the vertical front of a truck as the truck accelerates. The coefficient of friction between the stuntman and the truck is 0.65. The stuntman is not standing on anything but can “stick” to the front of the truck as
> An incandescent lightbulb radiates at a rate of 60.0 W when the temperature of its filament is 2820 K. During a brownout (temporary drop in line voltage), the power radiated drops to 58.0 W. What is the temperature of the filament? Ignore changes in the
> Mitch drops a 2.0 g coin into a 3.0 m deep wishing well. What is the de Broglie wavelength of the coin just before it hits the bottom of the well?
> Three types of sigma baryons can be created in accelerator collisions. Their quark contents are given by uus, uds, and dds, respectively. What are the electric charges of each of these sigma particles, respectively?
> A reversible heat engine has an efficiency of 33.3%, removing heat from a hot reservoir and rejecting heat to a cold reservoir at 0°C. If the engine now operates in reverse, how long would it take to freeze 1.0 kg of water at 0°C, if it operates on a pow
> A lizard of mass 3.0 g is warming itself in the bright sunlight. It casts a shadow of 1.6 cm2 on a piece of paper held perpendicularly to the Sun's rays. The intensity of sunlight at Earth is 1.4 × 103 W/m2, but only half of this energy penetrates the at
> A container holding 1.20 kg of water at 20.0°C is placed in a freezer that is kept at −20.0°C. The water freezes and comes to thermal equilibrium with the interior of the freezer. What is the minimum amount of electrical energy required by the freezer to
> Consider the net rate of heat loss by radiation from exposed skin on a cold day. By what factor does the rate for an outdoor temperature of 0°C exceed the rate at 5°C? Assume an initial skin temperature of 35°C.
> For a more realistic estimate of the maximum coefficient of performance of a heat pump, assume that a heat pump takes in heat from the outdoors at 10°C below the ambient outdoor temperature, to account for the temperature difference across its heat excha
> It is often argued that the head is the most important part of the body to cover when out in cold weather. Estimate the total energy loss by radiation if a person's head is uncovered for 15 min on a very cold, −15°C day, assuming he is bald, his skin tem
> A manometer using oil (density 0.90 g/cm3) as a fluid is connected to an air tank. Suddenly the pressure in the tank increases by 7.4 mmHg. (a) By how much does the fluid level rise in the side of the manometer that is open to the atmosphere? (b) What
> Estimate the entropy change of 850 g of water when it is heated from 20.0°C to 50.0°C. [Hint: Assume that the heat flows into the water at an average temperature of 35.0°C.]
> A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 320 km from Athens in the direction 20.0° north of east. The pilot heads directly for Sparta and flies at an airspeed of 160 km/h. After flying for 2.0 h, the pilot expec
> A student in a lecture hall has 0.25 m2 of skin (arms, hands, and head) exposed. The skin is at 34°C and has an emissivity of 0.97. The temperature of the room is 20°C (air, walls, ceiling, and floor all at the same temperature). (a) At what rate does t
> (a) What is the entropy change of 1.00 mol of H2O when it changes from ice to water at 0.0°C? (b) If the ice is in contact with an environment at a temperature of 10.0°C, what is the entropy change of the universe when the ice melts?
> A student wants to lose some weight. He knows that rigorous aerobic activity uses about 700 kcal/h (2900 kJ/h) and that it takes about 2000 kcal per day (8400 kJ) just to support necessary biological functions, including keeping the body warm. He decides
> An object moves in a circle. Is the total work done on the object by external forces necessarily zero? Explain.
> On a hot day, you are in a sealed, insulated room. The room contains a refrigerator, operated by an electric motor. The motor does work at the rate of 250 W when it is running. The refrigerator removes heat from the food storage space at a rate of 450 W
> A person of surface area 1.80 m2 is lying out in the sunlight to get a tan. If the intensity of the incident sunlight is 7.00 × 102 W/m2, at what rate must heat be lost by the person in order to maintain a constant body temperature? (Assume the effective
> Suppose you inhale 0.50 L of air initially at 20°C and 100 kPa pressure. While holding your breath, this air is warmed at constant pressure to 37°C. Treating the air as an ideal diatomic gas, how much heat flows from the body into the air?
> A sphere with a diameter of 80 cm is initially at a temperature of 250°C. If the intensity of the radiation detected at a distance of 2.0 m from the sphere's center is 102 W/m2, what is the emissivity of the sphere?
> An experiment to determine the specific heat of a gas (Chapter 14) makes use of a water manometer attached to a flask. Initially the two columns of water are even. Atmospheric pressure is 1.0 × 105 Pa. After heating the gas, the water levels
> A balloon contains 160 L of nitrogen gas at 25°C and 1.0 atm. How much energy must be added to raise the temperature of the nitrogen to 45°C while allowing the balloon to expand at atmospheric pressure?
