Solved: (II) The specific heat at constant volume of a

What happens to the work done on a jar of orange juice when it is vigorously shaken?

When a hot object warms a cooler object, does temperature flow between them? Are the temperature changes of the two objects equal? Explain.

(a) If two objects of different temperature are placed in contact, will heat naturally flow from the object with higher internal energy to the object with lower internal energy? (b) Is it possible for heat to flow even if the internal energies of the two objects are the same? Explain.

In warm regions where tropical plants grow but the temperature may drop below freezing a few times in the winter, the destruction of sensitive plants due to freezing can be reduced by watering them in the evening. Explain.

The specific heat of water is quite large. Explain why this fact makes water particularly good for heating systems (that is, hot-water radiators).

Why does water in a canteen stay cooler if the cloth jacket surrounding the canteen is kept moist?

Explain why burns caused by steam at 100C on the skin are often more severe than burns caused by water at 100C.

Explain why water cools (its temperature drops) when it evaporates, using the concepts of latent heat and internal energy

Will potatoes cook faster if the water is boiling more vigorously?

Very high in the Earths atmosphere the temperature can be 700C. Yet an animal there would freeze to death rather than roast. Explain.

What happens to the internal energy of water vapor in the air that condenses on the outside of a cold glass of water? Is work done or heat exchanged? Explain.

Use the conservation of energy to explain why the temperature of a well-insulated gas increases when it is compressedsay, by pushing down on a pistonwhereas the temperature decreases when the gas expands.

In an isothermal process, 3700 J of work is done by an ideal gas. Is this enough information to tell how much heat has been added to the system? If so, how much?

Explorers on failed Arctic expeditions have survived by covering themselves with snow. Why would they do that?

Why is wet sand at the beach cooler to walk on than dry sand?

When hot-air furnaces are used to heat a house, why is it important that there be a vent for air to return to the furnace? What happens if this vent is blocked by a bookcase?

Is it possible for the temperature of a system to remain constant even though heat flows into or out of it? Tf so. oive

Discuss how the first law of thermodynamics can apply to metabolism in humans. In particular, note that a person does work W, but very little heat Q is added to the body (rather, it tends to flow out). Why then doesnt the internal energy drop drastically in time?

Explain in words why Cp is greater than Cy.

Explain why the temperature of a gas increases when it is adiabatically compressed.

An ideal monatomic gas is allowed to expand slowly to twice its volume (1) isothermally; (2) adiabatically; (3) isobarically. Plot each on a PV diagram. In which process is Aint the greatest, and in which is Ajnt the least? In which is W the greatest and the least? In which is Q the greatest and the least?

Ceiling fans are sometimes reversible, so that they drive the air down in one season and pull it up in another season. Which way should you set the fan for summer? For winter?

Goose down sleeping bags and parkas are often specified as so many inches or centimeters of loft, the actual thickness of the garment when it is fluffed up. Explain.

Microprocessor chips nowadays have a heat sink glued on top that looks like a series of fins. Why is it shaped like that?

Sea breezes are often encountered on sunny days at the shore of a large body of water. Explain, assuming the temperature of the land rises more rapidly than that of the nearby water.

The Earth cools off at night much more quickly when the weather is clear than when cloudy. Why?

Explain why air-temperature readings are always taken with the thermometer in the shade.

A premature baby in an incubator can be dangerously cooled even when the air temperature in the incubator is warm. Explain.

The floor of a house on a foundation under which the air can flow is often cooler than a floor that rests directly on the ground (such as a concrete slab foundation). Explain.

Why is the liner of a thermos bottle silvered (Fig. 19-27), and why does it have a vacuum between its two walls?

A 22C day is warm, while a swimming pool at 22C feels cool. Why?

In the Northern Hemisphere the amount of heat required to heat a room where the windows face north is much higher than that required where the windows face south. Explain.

Heat loss occurs through windows by the following processes: (1) ventilation around edges; (2) through the frame, particularly if it is metal; (3) through the glass panes; and (4) radia tion. (a) For the first three, what is (are) the mechanisms conduction, convection, or radiation? (b) Heavy curtains reduce which of these heat losses? Explain in detail.

Early in the day, after the Sun has reached the slope of a mountain, there tends to be a gentle upward movement of air. Later, after a slope goes into shadow, there is a gentle downdraft. Explain.

A piece of wood lying in the Sun absorbs more heat than a piece of shiny metal. Yet the metal feels hotter than the wood when you pick it up. Explain.

An emergency blanket is a thin shiny (metal-coated) plastic foil. Explain how it can help to keep an immobile person warm.

Explain why cities situated by the ocean tend to have less extreme temperatures than inland cities at the same latitude.

(II) When a gas is taken from a to c along the curved path in Fig. 19-32, the work done by the gas is W = -35 J and the heat added to the gas is Q = -63 J. Along path abc, the work done is W = 54 J. (a) What is Q for path abc? (b) If PC = \P\), what is W for path cda? (c) What is Q for path cda? (d) What is Eint>a ~~ Eint, c? (e) If Eint, d Eint, c = 12 J, what is Q for path da?

(Ill) In the process of taking a gas from state a to state c along the curved path shown in Fig. 19-32, 85 J of heat leaves the system and 55 J of work is done on the system. (a) Determine the change in internal energy, Ejnt a Ejnt c. (b) When the gas is taken along the path cda, the work done by the gas is W = 38 J. How much heat Q is added to the gas in the process cda? (c) If Pa = 22P&, how much work is done by the gas in the process abc? (d) What is Q for path abc? (e) If Eintj a - Eint; b = 15 J, what is Q for the process be? Here is a summary of what is given: Qa-c = 85 J Wa_>c = -55 J Wcda = 38 J Eint, a E^t, b 15 J Pa = 2.2 Pd.

(Ill) Suppose a gas is taken clockwise around the rectangular cycle shown in Fig. 19-32, starting at b, then to a, to d, to c, and returning to b. Using the values given in Problem 39, (a) describe each leg of the process, and then calculate (b) the net work done during the cycle, (c) the total internal energy change during the cycle, and (d) the net heat flow during the cycle. (e) What percentage of the intake heat was turned into usable work: i.e., how efficient is this rectangular cycle (give as a percentage)?

(Ill) Determine the work done by 1.00 mol of a van der Waals gas (Section 18-5) when it expands from volume V\ to V2 isothermally.

(I) What is the internal energy of 4.50 mol of an ideal diatomic gas at 645 K, assuming all degrees of freedom are active?

(I) If a heater supplies 1.8 X 106J/h to a room 3.5 m X 4.6 m X 3.0 m containing air at 20C and 1.0 atm, by how much will the temperature rise in one hour, assum ing n n losses n f h e a t n r a ir mass tn th e n n ts id e ?

(I) Show that if the molecules of a gas have n degrees of freedom, then theory predicts C y = \nR and Cp = \ {n + 2 )i?

(II) A certain monatomic gas has specific heat cv = 0.0356 kcal/kg *C, which changes little over a wide temperature range. What is the atomic mass of this gas? What gas is it?

(II) Show that the work done by n moles of an ideal gas when it expands adiabatically is W = nCv (T\ - T2), where T\ and T2 are the initial and final temperatures, and C y is the molar specific heat at constant volume.

(II) An audience of 1800 fills a concert hall of volume 22.000 m3. If there were no ventilation, by how much would the temperature of the air rise over a period of 2.0 h due to the metabolism of the people (70 W/person)?

(II) The specific heat at constant volume of a particular gas is 0.182 kcal/kg K at room temperature, and its molecular mass is 34. (a) What is its specific heat at constant pressure? (b) What do you think is the molecular structure of this gas?

(II) A 2.00 mole sample of N2 gas at 0C is heated to 150C at constant pressure (1.00 atm). Determine (a) the change in internal energy, (b) the work the gas does, and (c) the heat added to it.

(Ill) A 1.00-mol sample of an ideal diatomic gas at a pressure of 1.00 atm and temperature of 420 K undergoes a process in which its pressure increases linearly with temperature. The final temperature and pressure are 720 K and 1.60 atm. Determine (a) the change in internal energy, (b) the work done by the gas, and (c) the heat added to the gas. (Assume five active degrees of freedom.)

(I) A 1.00-mol sample of an ideal diatomic gas, originally at 1.00 atm and 20C, expands adiabatically to 1.75 times its initial volume. What are the final pressure and temperature for the gas? (Assume no molecular vibration.)

(II) Show, using Eqs. 19-6 and 19-15, that the work done by a gas that slowly expands adiabatically from pressure Pi and volume Vl5 to P2 and V2, is given by w = (PtVi - p2v2)/(y - l).

(II) A 3.65-mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.1210 m3 to 0.750 m3. Initially the pressure was 1.00 atm. Determine: (a) the initial and final temperatures; (b) the change in internal energy; (c) the heat lost by the gas; (d) the work done on the gas. (Assume no molecular vibration.)

(II) An ideal monatomic gas, consisting of 2.8 mol of volume 0.086 m3, expands adiabatically. The initial and final temperatures are 25C and 68C. What is the final volume of the gas?

(Ill) A 1.00-mol sample of an ideal monatomic gas, originally at a pressure of 1.00 atm, undergoes a three-step process: (1) it is expanded adiabatically from 7i = 588 K to T2 = 389 K; (2) it is compressed at constant pressure until its temperature reaches T3; (3) it then returns to its original pressure and temperature by a constant-volume process, (a) Plot these processes on a PV diagram, (b) Determine T3. (c) Calculate the change in internal energy, the work done hv the pas. and the heat added tn the pas fnr each nrncess.

(Ill) Consider a parcel of air moving to a different altitude y in the Earths atmosphere (Fig. 19-33). As the parcel changes altitude it acquires the pressure P of the surrounding air. From Eq. 13-4 we have dP dy = ~ P g where p is the parcels altitude-dependent mass density.Problem 56. During this motion, the parcels volume will change and, because air is a poor heat conductor, we assume this expansion or contraction will take place adiabatically. (a) Starting with Eq. 19-15, PV7 = constant, show that for an ideal gas undergoing an adiabatic process, p l yT y = constant. Then show that the parcels pressure and temperature are related by ,d P P d T ^ - 7^ + y T ^ = and thus x/ x P d T (i - y)(-pg) + y = - (b) Use the ideal gas law with the result from part (a) to show that the change in the parcels temperature with change in altitude is given by dT dy 1 - 7 mg 7 k where m is the average mass of an air molecule and k is the Boltzmann constant, (c) Given that air is a diatomic gas with an average molecular mass of 29, show that dT/dy = 9.8C/km. This value is called the adiabatic lapse rate for dry air. (d) In California, the prevailing westerly winds descend from one of the highest elevations (the 4000-m Sierra Nevada mountains) to one of the lowest elevations (Death Valley, -100 m) in the continental United States. If a dry wind has a temperature of 5C at the top of the Sierra Nevada, what is the winds temperature after it has descended to Death Valley?

(I) (a) How much power is radiated by a tungsten sphere (emissivity e = 0.35 ) of radius 16 cm at a temperature of 25 C? (b) If the sphere is enclosed in a room whose walls are k en t at 5C w h a t is th e n e t flow ra te o f en e r o v nut n f

(I) One end of a 45-cm-long copper rod with a diameter of 2.0 cm is kept at 460 C, and the other is immersed in water at 22C. Calculate the heat conduction rate along the rod.

(II) How long does it take the Sun to melt a block of ice at 0C with a flat horizontal area 1.0 m2 and thickness 1.0 cm? Assume that the Suns rays make an angle of 35 with the vertical and that the emissivity of ice is 0.050.

(II) Heat conduction to skin. Suppose 150 W of heat flows by conduction from the blood capillaries beneath the skin to the bodys surface area of 1.5 m2. If the temperature difference is 0.50 C, estimate the average distance of capillaries below the skin surface.

(II) A ceramic teapot (e = 0.70) and a shiny one (e = 0.10) each hold 0.55 L of tea at 95C. (a) Estimate the rate of heat loss from each, and (b) estimate the temperature drop after 30 min for each. Consider only radiation, and assume the surroundings are at 20 C.

(II) A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 19-34). The copper end is placed in a furnace maintained at a constant temperature of 225C. The aluminum end is placed in an ice bath held at constant temperature of 0.0C. Calculate the temperature at the point where the two rods are joined.

(II) (a) Using the solar constant, estimate the rate at which the whole Earth receives energy from the Sun. (b) Assume the Earth radiates an equal amount back into space (that is, the Earth is in equilibrium). Then, assuming the Earth is a perfect emitter (e = 1.0), estimate its average surface temperature. [Hint: Use area A = 4t7t| , and state why.]

(II) A 100-W lightbulb generates 95 W of heat, which is dissipated through a glass bulb that has a radius of 3.0 cm and is 0.50 mm thick. What is the difference in temperature between the inner and outer surfaces of the glass?

(Ill) A house thermostat is normally set to 22C, but at night it is turned down to 12C for 9.0 h. Estimate how much more heat would be needed (state as a percentage of daily usage) if the thermostat were not turned down at night. Assume that the outside temperature averages 0C for the 9.0 h at night and 8C for the remainder of the day, and that the heat loss from the house is proportional to the difference in temperature inside and out. To obtain an estimate from the data, you will have to make other simplifying assumptions; state what these are.

(Ill) Approximately how long should it take 9.5 kg of ice at 0C to melt when it is placed in a carefully sealed Styrofoam ice chest of dimensions 25 cm X 35 cm X 55 cm whose walls are 1.5 cm thick? Assume that the conductivity n f Stvrnfnam is d n n h le that n f air and that th e n iitsid e

(Ill) A cylindrical pipe has inner radius R1 and outer radius R2. The interior of the pipe carries hot water at temperature 7 \. The temperature outside is T2 (< Tj). (a) Show that the rate of heat loss for a length L of pipe is dQ _ 2ir k fc - T2)L dt ~ \n(R2/Ri) where k is the thermal conductivity of the pipe, (b) Suppose the pipe is steel with R\ = 3.3 cm, R2 = 4.0 cm, and T2 = 18C. If the pipe holds still water at Tx = 71 C, what will be the initial rate of change of its temperature? (c) Suppose water at 71 C enters the pipe and moves at a speed of 8.0 cm/s. What will be its temperature drop per centimeter of travel?

(Ill) Suppose the insulating qualities of the wall of a come mainly from a 4.0-in. layer of brick and an R -19 layer of insulation, as shown in Fig. 19-35. What is the total rate of heat loss through such a wall, if its total area is 195 ft2 and the temperature difference across it is 12 F?

"A soft-drink can contains about 0.20 kg of liquid at 5C. Drinking this liquid can actually consume some of the fat in the body, since energy is needed to warm the liquid to body temperature (37C). How many food Calories should the drink have so that it is in perfect balance with the heat needed to warm the liquid (essentially water)?"

(a) Find the total power radiated into space by the Sun, assuming it to be a perfect emitter at T = 5500 K. The Suns radius is 7.0 X 108m. ( b ) From this, determine the power per unit area arriving at the Earth, 1.5 X 1011m away.

To get an idea of how much thermal energy is contained in the worlds oceans, estimate the heat liberated when a cube of ocean water, 1 km on each side, is cooled by 1K. (Approximate the ocean water as pure water for this estimate.)

A mountain climber wears a goose-down jacket 3.5 cm thick with total surface area 0.95 m2. The temperature at the surface of the clothing is 18C and at the skin is 34C. Determine the rate of heat flow by conduction through the jacket (a) assuming it is dry and the thermal conductivity k is that of goose down, and (b) assuming the jacket is wet, so k is that of water and the jacket has matted to 0.50 cm thickness.

During light activity, a 70-kg person may generate 200kcal/h. Assuming that 20% of this goes into useful work and the other 80% is converted to heat, estimate the temperature rise of the body after 30 min if none of this heat is transferred to the environment.

Estimate the rate at which heat can be conducted from the interior of the body to the surface. Assume that the thickness of tissue is 4.0 cm, that the skin is at 34C and the interior at 37C, and that the surface area is 1.5 m2. Compare this to the measured value of about 230 W that must be dissipated by a person working lightly. This clearly shows the necessity of convective cooling by the blood.

A marathon runner has an average metabolism rate of about 950 kcal/h during a race. If the runner has a mass of 55 k o e s tim a te h nw rrmr.h w a te r sh e w o u ld lo se to e v a n o ra tio n

A house has well-insulated walls 19.5 cm thick (assume conductivity of air) and area 410 m2, a roof of wood 5.5 cm thick and area 280 m2, and uncovered windows 0.65 cm thick and total area 33 m2. (a) Assuming that heat is lost only by conduction, calculate the rate at which heat must be supplied to this house to maintain its inside temperature at 23C if the outside temperature is -15C. (b) If the house is initially at 12C, estimate how much heat must be supplied to raise the temperature to 23C within 30 min. Assume that only the air needs to be heated and that its volume is 750 m3. (c) If natural gas costs $0,080 per kilogram and its heat of combustion is 5.4 X 107J/kg, how much is the monthly cost to maintain the house as in part (a) for 24 h each day, assuming 90% of the heat produced is used to heat the house? Take the specific heat of air to be 0.24 kcal/kg-C.

In a typical game of squash (Fig. 19-36), two people hit a soft rubber ball at a wall until they are about to drop due to dehydration and exhaustion. Assume that the ball hits the wall at a velocity of 22 m/s and bounces back with a velocity of 12 m/s, and that the kinetic energy lost in the process heats the ball. What will be the temperature increase of the ball after one bounce? (The specific heat of rubber is about 1200 J/kg-C.)

A bicycle pump is a cylinder 22 cm long and 3.0 cm in diameter. The pump contains air at 20.0 C and 1.0 atm. If the outlet at the base of the pump is blocked and the handle is pushed in very quickly, compressing the air to half its original volume, how hot does the air in the pump become?

A microwave oven is used to heat 250 g of water. On its maximum setting, the oven can raise the temperature of the liquid water from 20C to 100C in 1 min 45 s (= 105 s). (a) At what rate does the oven input energy to the liquid water? (b) If the power input from the oven to the water remains constant, determine how many grams of water will boil away if the oven is operated for 2 min (rather than just 1 min 45 s).

The temperature within the Earths crust increases about 1.0 C for each 30 m of depth. The thermal conductivity of the crust is 0.80W/C-m. (a) Determine the heat transferred from the interior to the surface for the entire Earth in 1.0 h. (b) Compare this heat to the amount of energy incident on the Earth in 1.0 h due to radiation from the Sun.

An ice sheet forms on a lake. The air above the sheet is at 18C, whereas the water is at 0C. Assume that the heat of fusion of the water freezing on the lower surface is conducted through the sheet to the air above. How much time will it take to form a sheet of ice 15 cm thick?

An iron meteorite melts when it enters the Earths atmosphere. If its initial temperature was -105C outside of Earths atmosphere, calculate the minimum velocity the meteorite must have had before it entered Earths atmosphere.

A scuba diver releases a 3.60-cm-diameter (spherical) bubble of air from a depth of 14.0 m. Assume the temperature is constant at 298 K, and that the air behaves as an ideal gas. (a) How large is the bubble when it reaches the surface? (b) Sketch a PV diagram for the process, (c) Apply the first law of thermodynamics to the bubble, and find the work done by the air in rising to the surface, the change in its internal energy, and the heat added or removed from the air in the bubble as it rises. Take the density of water to be 1000 kg/m3.

A reciprocating compressor is a device that compresses air by a back-and-forth straight-line motion, like a piston in a cylinder. Consider a reciprocating compressor running at 150 rpm. During a compression stroke, 1.00 mol of air is compressed. The initial temperature of the air is 390 K, the engine of the compressor is supplying 7.5 kW of power to compress the air, and heat is being removed at the rate of 1.5 kW. Calculate the temperature change per compression stroke.

The temperature of the glass surface of a 75-W lightbulb is 75C when the room temperature is 18C. Estimate the temperature of a 150-W lightbulb with a glass bulb the same size. Consider only radiation, and assume that 90% of the energy is emitted as heat.

Suppose 3.0 mol of neon (an ideal monatomic gas) at STP are compressed slowly and isothermally to 0.22 the original volume. The gas is then allowed to expand quickly and adiabatically back to its original volume. Find the highest and lowest temperatures and pressures attained by the gas, and show on a PV diagram where these values occur.

At very low temperatures, the molar specific heat of many substances varies as the cube of the absolute temperature: which is sometimes called Debyes law. For rock salt, T0 = 281 K and k = 1940J/mol*K. Determine the heat needed to raise 2.75 mol of salt from 22.0 K to 48.0 K.

A diesel engine accomplishes ignition without a spark plug by an adiabatic compression of air to a temperature above the ignition temperature of the diesel fuel, which is injected into the cylinder at the peak of the compression. Suppose air is taken into the cylinder at 2 8 0 K and volume V\ and is compressed adiabatically to 5 6 0 C ( ~ 1 0 0 0 F ) and volume V2. Assuming that the air behaves as an ideal gas whose ratio of C p to C y is 1 .4 , calculate the compression ratio V\/V2 of the engine.

When 6.30 X 105 J of heat is added to a gas enclosed in a cylinder fitted with a light frictionless piston maintained at atmospheric pressure, the volume is observed to increase from 2.2 m3 to 4.1 m3. Calculate (a) the work done by the gas, and (b) the change in internal energy of the gas. (c) Graph this process on a PV diagram.

In a cold environment, a person can lose heat by conduction and radiation at a rate of about 200 W. Estimate how long it would take for the body temperature to drop from 36.6C to 35.6C if metabolism were nearly to stop. Assume a mass of 70 kg. (See Table 19-1.)

(II) Suppose 1.0 mol of steam at 100C of volume 0.50 m3 is expanded isothermally to volume 1.00 m3. Assume steam obeys the van der Waals equation (P + n2a /V 2)(V /n - b) = RT, Eq. 18-9, with a = 0.55 N m4/mol2 and b = 3.0 X 10_5m3/mol. Using the expression dW = P dV, determine numerically the total work done W. Your result should agree within 2% of the result obtained by integrating the expression for dW