A 5.0-kg block of aluminum is heated from 20°C to 90°C at atmospheric pressure. Find (a) The work done by the aluminum, (b) The amount of energy transferred to it by heat, and (c) The increase in its internal energy.
> Hydrothermal vents deep on the ocean floor spout water at temperatures as high as 570°C. This temperature is below the boiling point of water because of the immense pressure at that depth. Because the surrounding ocean temperature is at 4.0°C, an organis
> Suppose you spend 30.0 minutes on a stair- climbing machine, climbing at a rate of 90.0 steps per minute, with each step 8.00 inches high. If you weigh 150. lb and the machine reports that 600. kcal have been burned at the end of the workout, what effici
> Two moles of molecular hydrogen (H2) react with 1 mole of molecular oxygen (O2) to produce 2 moles of water (H2O) together with an energy release of 241.8 kJ/mole of water. Suppose a spherical vessel of radius 0.500 m contains 14.4 moles of H2 and 7.2 mo
> A cylinder containing 10.0 moles of a monatomic ideal gas expands from â’¶ to â’· along the path shown in Figure P12.71. (a) Find the temperature of the gas at point A and the temperature at point â’·.
> Every second at Niagara Falls, approximately 5.00 x 103 m3 of water falls a distance of 50.0 m. What is the increase in entropy per second due to the falling water? Assume the mass of the surroundings is so great that its temperature and that of the wate
> One mole of neon gas is heated from 300. K to 420. K at constant pressure. Calculate (a) The energy Q transferred to the gas, (b) The change in the internal energy of the gas, and (c) The work done on the gas. Note that neon has a molar specific heat of
> An ideal gas initially at pressure P0, volume V0, and temperature T0 is taken through the cycle described in Figure P12.68. (a) Find the net work done by the gas per cycle in terms of P0 and V0. (b) What is the net energy Q added to the system per cycle?
> A 1.0 x 102-kg steel support rod in a building has a length of 2.0 m at a temperature of 20.0°C. The rod supports a hanging load of 6.0 x 103 kg. Find (a) The work done on the rod as the temperature increases to 40.0°C, (b) The energy Q added to the rod
> When a gas follows path 123 on the PV diagram in Figure P12.66, 418 J of energy flows into the system by heat and -167 J of work is done on the gas. (a) What is the change in the internal energy of the system? (b) How much energy Q flows into the system
> If electrical power is transmitted over long distances, the resistance of the wires becomes significant. Why? Which mode of transmission would result in less energy loss: high current and low voltage or low current and high voltage? Discuss.
> A substance undergoes the cyclic process shown in Figure P12.65. Work output occurs along path AB while work input is required along path BC, and no work is involved in the constant volume process CA. Energy transfers by heat occur during each process in
> A Carnot engine operates between 100°C and 20°C. How much ice can the engine melt from its exhaust after it has done 5.0 x 104 J of work?
> A 1500-kW heat engine operates at 25% efficiency. The heat energy expelled at the low temperature is absorbed by a stream of water that enters the cooling coils at 20.°C. If 60. L flows across the coils per second, determine the increase in temperature o
> A Carnot engine operates between the temperatures Th = 1.00 x 102°C and Tc = 20.0°C. By what factor does the theoretical efficiency increase if the temperature of the hot reservoir is increased to 5.50 x 102°C?
> Suppose a highly trained athlete consumes oxygen at a rate of 70.0 mL/(min · kg) during a 30.0-min workout. If the athlete’s mass is 78.0 kg and their body functions as a heat engine with a 20.0% efficiency, calculate (a) Their metabolic rate in kcal/min
> A woman jogging has a metabolic rate of 625 W. (a) Calculate her volume rate of oxygen consumption in L/s. (b) Estimate her required respiratory rate in breaths/min if her lungs inhale 0.600 L of air in each breath and air is 20.9% oxygen.
> Sweating is one of the main mechanisms with which the body dissipates heat. Sweat evaporates with a latent heat of 2430 kJ/kg at body temperature, and the body can produce as much as 1.5 kg of sweat per hour. If sweating were the only heat dissipation me
> A weightlifter has a basal metabolic rate of 80.0 W. As he is working out, his metabolic rate increases by about 650 W. (a) How many hours does it take him to work off a 450-Calorie bagel if he stays in bed all day? (b) How long does it take him if he’s
> On a typical day, a 65-kg man sleeps for 8.0 h, does light chores for 3.0 h, walks slowly for 1.0 h, and jogs at moderate pace for 0.5 h. What is the change in his internal energy for all these activities?
> When a metal bar is temporarily connected between a hot reservoir at Th and a cold reservoir at Tc, the energy transferred by heat from the hot reservoir to the cold reservoir is Qh. In this irreversible process, find expressions for the change in entrop
> A short circuit is a circuit containing a path of very low resistance in parallel with some other part of the circuit. Discuss the effect of a short circuit on the portion of the circuit it parallels. Use a lamp with a frayed line cord as an example.
> Prepare a table for the following occurrence: You toss four coins into the air simultaneously and record all the possible results of the toss in terms of the numbers of heads and tails that can result. (For example, HHTH and HTHH are two possible ways in
> When an aluminum bar is temporarily connected between a hot reservoir at 725 K and a cold reservoir at 310 K, 2.50 kJ of energy is transferred by heat from the hot reservoir to the cold reservoir. In this irreversible process, calculate the change in ent
> The surface of the Sun is approximately at 5.70 x 103 K, and the temperature of the Earth’s surface is approximately 290. K. What entropy change occurs when 1.00 x 103 J of energy is transferred by heat from the Sun to the Earth?
> A sealed container holding 0.500 kg of liquid nitrogen at its boiling point of 77.3 K is placed in a large room at 21.0°C. Energy is transferred from the room to the nitrogen as the liquid nitrogen boils into a gas and then warms to the room’s temperatur
> A 70.0-kg log falls from a height of 25.0 m into a lake. If the log, the lake, and the air are all at 300. K, find the change in entropy of the Universe during this process.
> What is the change in entropy of 1.00 kg of liquid water at 100.°C as it changes to steam at 100.°C?
> A freezer is used to freeze 1.0 L of water completely into ice. The water and the freezer remain at a constant temperature of T = 0°C. Determine (a) The change in the entropy of the water and (b) The change in the entropy of the freezer.
> A 65-g ice cube is initially at 0.0°C. (a) Find the change in entropy of the cube after it melts completely at 0.0°C. (b) What is the change in entropy of the environment in this process? Hint: The latent heat of fusion for water is 3.33 x 105 J/kg.
> A Styrofoam cup holding 125 g of hot water at 1.00 x 102°C cools to room temperature, 20.0°C. What is the change in entropy of the room? (Neglect the specific heat of the cup and any change in temperature of the room.)
> A heat engine operates in a Carnot cycle between 80.0°C and 350°C. It absorbs 21000 J of energy per cycle from the hot reservoir. The duration of each cycle is 1.00 s. (a) What is the mechanical power output of this engine? (b) How much energy does it ex
> Given three light-bulbs and a battery, sketch as many different circuits as you can.
> A certain nuclear power plant has an electrical power output of 435 MW. The rate at which energy must be supplied to the plant is 1420 MW. (a) What is the thermal efficiency of the power plant? (b) At what rate is thermal energy expelled by the plant?
> A power plant has been proposed that would make use of the temperature gradient in the ocean. The system is to operate between 20.0°C (surface water temperature) and 5.00°C (water temperature at a depth of about 1 km). (a) What is the maximum efficiency
> In one cycle a heat engine absorbs 500 J from a high-temperature reservoir and expels 300 J to a low- temperature reservoir. If the efficiency of this engine is 60% of the efficiency of a Carnot engine, what is the ratio of the low temperature to the hig
> Two heat engines are operated in series so that part of the energy expelled from engine A is absorbed by engine B with |QhB| = 0.750|QcA|. Engines A and B have efficiencies eA = eB = 0.250 and engine A performs work WA = 275 J. Find the overall efficienc
> A freezer has a coefficient of performance of 6.30. The freezer is advertised as using 457 kW-h/y. (a) On average, how much energy does the freezer use in a single day? (b) On average, how much thermal energy is removed from the freezer each day? (c) Wha
> A heat pump has a coefficient of performance of 3.80 and operates with a power consumption of 7.03 x 103 W. (a) How much energy does the heat pump deliver into a home during 8.00 h of continuous operation? (b) How much energy does it extract from the out
> An engine absorbs 1.70 kJ from a hot reservoir at 277°C and expels 1.20 kJ to a cold reservoir at 27°C in each cycle. (a) What is the engine’s efficiency? (b) How much work is done by the engine in each cycle? (c) What is the power output of the engine i
> A lawnmower engine ejects 1.00 x 104 J each second while running with an efficiency of 0.200. Find the engine’s horsepower rating, using the conversion factor 1 hp = 746 W.
> One of the most efficient engines ever built is a coal-fired steam turbine engine in the Ohio River valley, driving an electric generator as it operates between 1870°C and 430°C. (a) What is its maximum theoretical efficiency? (b) Its actual efficiency i
> In each cycle of its operation, a heat engine expels 2400 J of energy and performs 1800 J of mechanical work. (a) How much thermal energy must be added to the engine in each cycle? (b) Find the thermal efficiency of the engine.
> Why is it dangerous to turn on a light when you are in a bathtub?
> The work done by an engine equals one-fourth the energy it absorbs from a reservoir. (a) What is its thermal efficiency? (b) What fraction of the energy absorbed is expelled to the cold reservoir?
> A heat engine is being designed to have a Carnot efficiency of 65% when operating between two heat reservoirs. (a) If the temperature of the cold reservoir is 20°C, what must be the temperature of the hot reservoir? (b) Can the actual efficiency of the e
> A heat engine operates between a reservoir at 25°C and one at 375°C. What is the maximum efficiency possible for this engine?
> An ideal gas expands at a constant pressure of 6.00 x 105 Pa from a volume of 1.00 m3 to a volume of 4.00 m3 and then is compressed to one-third that pressure and a volume of 2.50 m3 as shown in Figure P12.32 before returning to its initial state. How mu
> A gas increases in pressure from 2.00 atm to 6.00 atm at a constant volume of 1.00 m3 and then expands at constant pressure to a volume of 3.00 m3 before returning to its initial state as shown in Figure P12.31. How much work is done in one cycle? Figur
> One mole of gas initially at a pressure of 2.00 atm and a volume of 0.300 L has an internal energy equal to 91.0 J. In its final state, the gas is at a pressure of 1.50 atm and a volume of 0.800 L, and its internal energy equals 182 J. For the paths IAF,
> Consider the cyclic process described by Figure P12.28. If Q is negative for the process BC and ΔU is negative for the process CA, determine the signs of Q, W, and ΔU associated with each process. Figure P12.28:
> An ideal monatomic gas is contained in a vessel of constant volume 0.200 m3. The initial temperature and pressure of the gas are 300. K and 5.00 atm, respectively. The goal of this problem is to find the temperature and pressure of the gas after 16.0 kJ
> An ideal diatomic gas expands adiabatically from 0.750 m3 to 1.50 m3. If the initial pressure and temperature are 1.50 x 105 Pa and 325 K, respectively, find (a) The number of moles in the gas, (b) The final gas pressure, (c) The final gas temperature, a
> A ski resort consists of a few chairlifts and several interconnected downhill runs on the side of a mountain, with a lodge at the bottom. The lifts are analogous to batteries, and the runs are analogous to resistors. Describe how two runs can be in serie
> An ideal monatomic gas contracts in an isobaric process from 1.25 m3 to 0.500 m3 at a constant pressure of 1.50 x 105 Pa. If the initial temperature is 425 K, find (a) The work done on the gas, (b) The change in internal energy, (c) The energy transfer Q
> An ideal gas expands at constant pressure. (a) Show that PΔV = nRΔT. (b) If the gas is monatomic, start from the definition of internal energy and show that ΔU = 3/2Wenv, where Wenv is the work done by the gas on its environment. (c) For the same monatom
> An ideal monatomic gas expands isothermally from 0.500 m3 to 1.25 m3 at a constant temperature of 675 K. If the initial pressure is 1.00 x 105 Pa, find (a) The work done on the gas, (b) The thermal energy transfer Q, and (c) The change in the internal en
> A system consisting of 0.0256 moles of a diatomic ideal gas is taken from state A to state C along the path in Figure P12.22. (a) How much work is done on the gas during this process? (b) What is the lowest temperature of the gas during this process, and
> An ideal gas is compressed from a volume of Vi = 5.00 L to a volume of Vf = 3.00 L while in thermal contact with a heat reservoir at T = 295 K as in Figure P12.21. During the compression process, the piston moves down a distance of d = 0.130 m under the
> A monatomic ideal gas undergoes the thermodynamic process shown in the PV diagram of Figure P12.20. Determine whether each of the values ΔU, Q, and W for the gas is positive, negative, or zero. Hint: The internal energy of a monatomic ideal g
> A gas is enclosed in a container fitted with a piston of cross-sectional area 0.150 m2. The pressure of the gas is maintained at 6.00 x 103 Pa as the piston moves inward 20.0 cm. (a) Calculate the work done by the gas. (b) If the internal energy of the g
> A quantity of a monatomic ideal gas undergoes a process in which both its pressure and volume are doubled as shown in Figure P12.18. What is the energy absorbed by heat into the gas during this process? Hint: The internal energy of a monatomic ideal gas
> A gas is compressed at a constant pressure of 0.800 atm from 9.00 L to 2.00 L. In the process, 400. J of energy leaves the gas by heat. (a) What is the work done on the gas? (b) What is the change in its internal energy?
> In a running event, a sprinter does 4.8 x 105 J of work and her internal energy decreases by 7.5 x 105 J. (a) Determine the heat transferred between her body and surroundings during this event. (b) What does the sign of your answer to part (a) indicate?
> An uncharged series RC circuit is to be connected across a battery. For each of the following changes, determine whether the time for the capacitor to reach 90% of its final charge would increase, decrease, or remain unchanged. Indicate your answers with
> A gas expands from I to F in Figure P12.5. The energy added to the gas by heat is 418 J when the gas goes from I to F along the diagonal path. (a) What is the change in internal energy of the gas? (b) How much energy must be added to the gas by heat for
> A cylinder of volume 0.300 m3 contains 10.0 mol of neon gas at 20.0°C. Assume neon behaves as an ideal gas. (a) What is the pressure of the gas? (b) Find the internal energy of the gas. (c) Suppose the gas expands at constant pressure to a volume of 1.00
> The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. Using the results from the discussion of kinetic theory in Section 10.5, show that the internal energy of a monatomic ideal gas at pressure P and occ
> A chemical reaction transfers 1250 J of thermal energy into an ideal gas while the system expands by 2.00 x 10-2 m3 at a constant pressure of 1.50 x 105 Pa. Find the change in the internal energy.
> One mole of an ideal gas initially at a temperature of Ti = 0°C undergoes an expansion at a constant pressure of 1.00 atm to four times its original volume. (a) Calculate the new temperature Tf of the gas. (b) Calculate the work done on the gas during th
> (a) Find the work done by an ideal gas as it expands from point A to point B along the path shown in Figure P12.8. (b) How much work is done by the gas if it compressed from B to A along the same path? Figure P12.8:
> A sample of helium behaves as an ideal gas as it is heated at constant pressure from 273 K to 373 K. If 20.0 J of work is done by the gas during this process, what is the mass of helium present?
> A gas follows the PV diagram in Figure P12.6. Find the work done on the gas along the paths (a) AB, (b) BC, (c) CD, (d) DA, and (e) ABCDA. Figure P12.6:
> A gas expands from I to F along the three paths indicated in Figure P12.5. Calculate the work done on the gas along paths (a) IAF, (b) IF, and (c) IBF. Figure P12.5:
> Find the numeric value of the work done on the gas in (a) Figure P12.4a and (b) Figure P12.4b. Figure P12.4:
> There is an old admonition given to experimenters to “keep one hand in the pocket” when working around high voltages. Why is this warning a good idea?
> Gas in a container is at a pressure of 1.5 atm and a volume of 4.0 m3. What is the work done on the gas (a) If it expands at constant pressure to twice its initial volume, and (b) If it is compressed at constant pressure to one-quarter its initial volum
> Sketch a PV diagram and find the work done by the gas during the following stages. (a) A gas is expanded from a volume of 1.0 L to 3.0 L at a constant pressure of 3.0 atm. (b) The gas is then cooled at constant volume until the pressure falls to 2.0 atm.
> A balloon holding 5.00 moles of helium gas absorbs 925 J of thermal energy while doing 102 J of work expanding to a larger volume. (a) Find the change in the balloon’s internal energy. (b) Calculate the change in temperature of the gas.
> (a) Determine the work done on a fluid that expands from i to f as indicated in Figure P12.10. (b) How much work is done on the fluid if it is compressed from f to i along the same path? Figure P12.10:
> An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of 8.00 x 103 g and an area of 5.00 cm2 and is free to slide up and down, keeping the pressure of the gas constant. (a) How much work is done on the gas as t
> Lake Erie contains roughly 4.00 x 1011 m3 of water. (a) How much energy is required to raise the temperature of that volume of water from 11.0°C to 12.0°C? (b) How many years would it take to supply this amount of energy by using the 1.00 x 104-MW exhaus
> An aluminum rod is 20.0 cm long at 20.0°C and has a mass of 0.350 kg. If 1.00 x 104 J of energy is added to the rod by heat, what is the change in length of the rod?
> The highest recorded waterfall in the world is found at Angel Falls in Venezuela. Its longest single waterfall has a height of 807 m. If water at the top of the falls is at 15.0°C, what is the maximum temperature of the water at the bottom of the falls?
> A wood stove is used to heat a single room. The stove is cylindrical in shape, with a diameter of 40.0 cm and a length of 50.0 cm, and operates at a temperature of 400.°F. (a) If the temperature of the room is 70.0°F, determine the amount of radiant ener
> Earth’s surface absorbs an average of about 960. W/m2 from the Sun’s irradiance. The power absorbed is Pabs = (960. W/m2) (Adisc), where Adisc = πR2E is Earth’s projected area. An equal amount of power is radiated so that Earth remains in thermal equilib
> Two light-bulbs are each connected to a voltage of 120 V. One has a power of 25 W, the other 100 W. (a) Which light-bulb has the higher resistance? (b) Which light-bulb carries more current?
> If you were asked to design a capacitor in which small size and large capacitance were required, what would be the two most important factors in your design?
> Two astronauts (Fig. P8.80), each having a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particle
> A uniform ladder of length L and weight w is leaning against a vertical wall. The coefficient of static friction between the ladder and the floor is the same as that between the ladder and the wall. If this coefficient of static friction is μs = 0.500, d
> An object of mass M = 12.0 kg is attached to a cord that is wrapped around a wheel of radius r = 10.0 cm (Fig. P8.78). The acceleration of the object down the frictionless incline is measured to be a = 2.00 m/s2 and the incline makes an angle Î&ced
> A 40.0-kg child stands at one end of a 70.0-kg boat that is 4.00 m long (Fig. P8.77). The boat is initially 3.00 m from the pier. The child notices a turtle on a rock beyond the far end of the boat and proceeds to walk to that end to catch the turtle. (a
> Figure P8.76 shows a clawhammer as it is being used to pull a nail out of a horizontal board. If a force of magnitude 150 N is exerted horizontally as shown, find (a) The force exerted by the hammer claws on the nail and (b) The force exerted by the surf
> A 0.50-kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane, with the cord making a 30° angle with the vertical. (See Fig. P7.75.) (a) Determine the ball’s speed. (b) If, instead, the ball i
> A massless spring of constant k = 78.4 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance d, as in Figure P7.74. The block (initially at rest) is then released and travel
> In a popular amusement park ride, a rotating cylinder of radius 3.00 m is set in rotation at an angular speed of 5.00 rad/s, as in Figure P7.73. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum
> The maximum lift force on a bat is proportional to the square of its flying speed v. For the hoary bat (Lasiurus cinereus), the magnitude of the lift force is given by The bat can fly in a horizontal circle by “bankingâ€
> (a) A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 20.0° with the horizontal. A 30.0-kg piece of luggage i
> Blood pressure is normally measured with the cuff of the sphygmomanometer around the arm. Suppose the blood pressure is measured with the cuff around the calf of the leg of a standing person. Would the reading of the blood pressure be (a) The same here a
> A 0.275-kg object is swung in a vertical circular path on a string 0.850 m long as in Figure P7.70. (a) What are the forces acting on the ball at any point along this path? (b) Draw free-body diagrams for the ball when it is at the bottom of the circle a
> A 4.00-kg object is attached to a vertical rod by two strings as shown in Figure P7.69. The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension in (a) The upper string and (b) The lower string. Figure P7.69:
