The Physics of Energy 1st edition Robert L. Jaffe, Washington Taylor - Solutions

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Samples of copper, aluminum, and water experience the same temperature rise when they absorb the same amount of heat. What is the ratio of their masses?
A 35-g glass thermometer reads 21.6oC before it is places in 135mL of water. When the water and thermometer come to equilibrium, the thermometer reads 39.2oC. What was the original temperature of the water?
What will be the equilibrium temperature when a 245-g block of copper at 285oC is placed in a 145-g aluminum calorimeter cup containing 825 g of water at 12.0oC?
A hot iron horseshoe (mass = 0.40kg), just forget (Fig. 14-16). Is dropped into 1.35L of water in a 0.30-kg iron port initially at 20.0oC if the final equilibrium temperature is 25.0o C, estimate the initial temperature of the hot horseshoe.
A 215-g sample of a substance is heated to 330oC and then plunged into a 105-g aluminum calorimeter cup containing 165g of water and 1 17-g glass thermometer at 12.5oC. The final temperature is 35.0oC. What is the specific heat of the substance? (Assume no water boils away).
How long does it take a 750-W coffeepot to bring to a boil 0.75L of water initially at 8.0oC? Assume that the part of the pot which is heated with the water is made of 360 g of aluminum, and that no water boils away.
Estimate the Calorie content of 75 g of candy from the following measurements. A 15-g sample of the candy is allowed to dry before putting it in a bomb calorimeter. The aluminum bomb has a mass of 0.725 kg and is placed in 2.00kg of water contained in an aluminum calorimeter cup of mass o.624 kg.
When a 290-g piece of iron at 180oC is placed in a 95-g aluminum calorimeter cup containing 250 g of glycerin at 10oC, the final temperature is observed to be 38oC. Estimate the specific heat of glycerin.
The 1.20-kg head of a hammer has a speed of 6.5 m/s just before it strikes a nail (Fig. 14-17) and is brought to rest. Estimate the temperature rise of a 14-g iron nail generated by 10 such hammer blows done in quick succession. Assume the nail absorbs all the energy.
A 0.095-kg aluminum sphere is dropped from the roof of a 45-m-high building. If 65% of the thermal energy produced when it hits the ground is absorbed by the sphere, what is its temperature increase?
The heat capacity, C, of an object is defined as the amount of heat needed to raise its temperature by 1 Co. Thus, to raise the temperature by ΔT requires heat Q give by Q = C ΔT. (a) Write the heat capacity C in terms of the specific heat, e, of the material. (b) What is the hat
How much heat is needed to melt 16.50 kg of silver that is initially at 20oC?
During exercise, a person may give off 180 kcal of heat in 30 min by evaporation of water from the skin. How much water has been lost?
If 2.80 X 105 J of energy is supplied to a flask of liquid oxygen at – 183oC, how much oxygen can evaporate?
A 30-g ice cube at its melting point is dropped into an insulated container of liquid nitrogen. How much nitrogen evaporates if it is at its boiling point of 77K and has a latent heat of vaporization of 200 kJ/kg? Assume for simplicity that the specific heat of ice is a constant and is equal to its
A cube of ice is taken from the freezer at – 8.5oC and placed in a 95-g aluminum calorimeter filled with 310 g of water at room temperature of 20.0oC. The final situation is observed to be all water at 17.0oC. What was the mass of the ice cube?
An iron boiler of mass 230 kg contains 830 kg of water at 18oC. A heater supplies energy at the rate of 52,000kJ/h. How long does it take for the water?(a) To reach the boiling point, and (b) To all have changed to steam?
In a hot day’s race a bicyclist consumes 8.0 L of water over the span of four hours. Making the approximation that all of the cyclist’s energy goes into evaporating this water as sweat, how much energy in kcal did the rider use during the ride? (Since the efficiency of the rider is only about
What mass of steam at 100oC must be added to 1.00 kg of ice at 0oC to yield liquid water at 20oC?
The specific heat of mercury is 138J/kg Co. Determine the latent heat of fusion of mercury using the following calorimeter data: 1.00 kg of solid Hg at its melting point of -39.0oC is placed in a 0.620-kg aluminum calorimeter with 0.400kg of water at 12.80oC; the resulting equilibrium temperature
A 70-g bullet travelling at 250 m/s penetrates a block of ice at 0oC and comes to rest within the ice. Assuming that the temperature of the bullet doesn’t change appreciably, how much ice is melted as a result of the collision?
A 54.0-kg ice-skater moving at 6.4m/s glides to a stop. Assuming the ice is at 0oC and that 50% of the heat generated by friction is absorbed by the ice, how much ice melts?
At a crime scene, the forensic investigator notes that the 8.2-g lead bullet that was stopped in a doorframe apparently melted completely on impact. Assuming the bullet was fired at room temperature (20oC), what does the investigator calculate as the minimum muzzle velocity of the gun?
One end of a 33-cm-long aluminum rod with a diameter of 2.0 cm is kept at 460oC, and the other is immersed in water at 22oC. Calculate the heat conduction rate along the rod.
Calculate the rate of heat flow by conduction in Example 14-10. assuming that there are strong gusty winds and the external temperature is –5oC.
(a) How much power is radiated by a tungsten sphere (emissivity e = 0.35) of radius 22cm at a temperature of 25oC?(b) If the sphere is enclosed in a room whose walls are kept at – 5oC, what is the net flow rate of energy out of the sphere?
Heat conduction to skin, suppose 200 W of heat flows by conduction from the blood capillaries beneath the skin to the body’s surface area of 1.5m2. If the temperature difference is 0.50Co, estimate the average distance of capillaries below the skin surface.
Two rooms, each a cube 4.0m per side, share a 12-cm-thick brick wall. Because of a number of 100-W lightbulbs in one room, the air is at 30oC, while in the other room it is at 10oC. How many of the 100-W bulbs are needed to maintain the temperature difference across the wall?
How long does it take the Sun to melt a block of ice at 0oC with a flat horizontal area 1.0m2 and thickness 1.0cm? Assume that the Sun’s rays make an angle of 30o with the vertical and that the emissivity of ice is 0.050.
A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 14-18). The copper end is placed in a furnace maintained at a constant temperature of 250oC. The aluminum end is placed in an ice bath held at constant temperature of 0.0oC. Calculate the
(a) Using the solar constant, estimate the rate at which the whole Earth receives energy from the Sun.(b) Assume the Earth radiates and 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
A 100-W lightbulb generates 95 W of heat, which is dissipated through a glass bulb that has a radius of 3.0cm and is 1.0 mm thick. What is the difference in temperature between the inner and outer surfaces of the glass?
Suppose the insulating qualities of the wall of a house come mainly from a 4.0-in, layer of brick and an R-19 layer of insulation, as shown in Fig. 14-19. What is the total rate of heat loss through such a wall, if its total area is 240 ft2 and the temperature difference across it is 12Fo?
A double-glazed window has two panes of glass separated by an air space, Fig. 14-20.(a) Show that the rate of heat flow through such a window by conduction is given by where k1, k2, and k3 are the thermal conductivities for glass, air, and glass, respectively.(b) Generalize this expression for any
Approximately how long should it take 11.0 kg of ice at 0oC 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 1.5cm think? Assume that the conductivity of Styrofoam is double that of air and that the outside temperature is 32oC.
A soft-drink can contains about 0.20 kg of liquid at 5oC. Drinking this liquid can actually consume some of the fat in the body, since energy is needed to warm the water to body temperature (37oC). How many food Calories should the drink have so that it is in perfect balance with the heat needed to
Of coal gives off 30 MJ/kg when it is burned, how much coal would be needed to heat a house that requires 2.0 X 105 MJ for the whole winter? Assume that 30% of the heat is lost up the chimney?
To get an idea of how much thermal energy is contained in the world’s oceans, estimate the heat liberated when a cube of ocean water, 1 km on each side, is cooled by 1 K. (Approximate the ocean water as pure water for this estimate.)
A 15-g lead bullet is tested by firing it into a fixed block of wood with a mass of 1.05 kg. The block and imbedded bullet together absorb all the heat generated. After thermal equilibrium has been reached, the system has a temperature rise measured as 0.020Co. Estimate the entering speed of the
(a) Find the total power radiated into space by the Sun, assuming it to be a perfect emitter at T = 5500 K. The Sun€™s radius is 7.0 X 108 m.(b) From this, determine the power per unit area arriving at the Earth, 1.5 X 1011 m away (Fig .14-21)
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, calculate the temperature rise of the body after 1.00h if none of this heat were transferred to the environment.
A 340-kg marble boulder rolls off the top of a cliff and falls a vertical height of 140m before striking the ground. Estimate the temperature rise of the rock if 50% of the heat generated remains in the rock.
A 2.3-kg lead ball is dropped into a 2.5-L insulated pail of water initially at 20.0oC, if the final temperature of the water-lead combination is 28.0oC, what was the initial temperature of the lead ball?
A mountain climber wears a goose down jacket 3.5cm thick with total surface area 1.2m2. The temperature at the surface of the clothing is –20oC and at the skin is 34oC. Determine the rate of heat flow by conduction through the jacket?(a) Assuming it is dry and the thermal conductivity k is that
A marathon runner has an average metabolism rate of about 950 kcal/h during a race. If the runner has a mass of 55 kg, estimate how much water the would lose to evaporation from the skin for a race that lasts 2.5h.
Estimate the rate at which heat can be conducted from the interior of the body to the surface. Assume that the thickness off tissue is 4.0 cm, that the skin is at 34oC and the interior at 37oC, and that the surface area is 1.5m2. Compare this is to the measured value of about 230 W that must be
A house has well-insulated walls 17.5 cm thick (assume conductivity of air) and area 410 m2, a roof of wood 6.5 cm thick and area 280m2, and uncovered windows 0.65cm thick and total area 33m2. (a) Assuming that heat is lost only by conduction, calculate the rate at which heat must be supplied to
A 15-g lead bullet traveling at 220m/s passes through a thin wall and emerges at a speed of 160 m/s. If the bulled absorbs 50% of the heat generated.(a) What will be the temperature rise of the bullet?(b) If the bullet’s initial temperature was 20oC, will any of the bullet melt, and if so, how
A leaf of area 40cm2 and mass 4.5 X 10-4 kg directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of 0.80 kcal/kg K.(a) Estimate the rate of rise of the leaf’s temperature.(b) Calculate the temperature the leaf would reach if it lost all its heat by
Using the result of part (a) In Problem 58, take into account radiation from the leaf to calculate how much water must be transpired (evaporated) by the leaf per hour to maintain a temperature of 35oC.
An iron meteorite melts when it enters the Earth’s atmosphere. If its initial temperature was –125oC outside of Earth’s atmosphere, calculate the minimum velocity the meteorite must have had before it entered Earth’s atmosphere.
The temperature within the Earth’s crust increases about 1.0Co for 3each 30 m of depth. The thermal conductivity of the crust is 0.80 W/Co m.(a) Determine the heat transferred from the interior to the surface for the amount of energy incident on the Earth in 1 day due to radiation from the Sun.
In a typical game of squash (Fig. 14-22), 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 12m/s, and that the kinetic energy lost is the process
What will be the final result when equal masses of ice at 0oC and steam at 100oC are mixed together?
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 36.6oC to 35.6oC if metabolism were nearly to stop. Assume a mass of 70 kg. (See Table 14-1)
After a hot shower and dishwashing, there is “not hot water” left in the 50-gal (185-L) water heater. This suggests that the tank has emptied and refilled with water at roughly 10oC. (a) How much energy does it take to reheat the water to 50oC?(b) How long would it take if the heater output is
The temperature of the glass surface of a 60-W lightbulb is d65oC when the room temperature is 18oCm 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.
Calculate the number of molecules/m3 in an ideal gas at STP.
How many moles of water are there in 1.000 L? How many molecules?
Estimate the number of (a) Moles, and (b) Molecules of water in all the Earth’s oceans. Assume water covers 75% of the Earth to an average depth of 3 km?
A cubic box of volume 5.1 X 10-2 m3 is filled with air at atmospheric pressure at 20oC. The box is closed and heated to 180oC. What is the net force on each side of the box?
Estimate how many molecules of air are in each 2.0-L breath you inhale that was also in the last breath Galileo took.
(a) What is the average translational kinetic energy of an oxygen molecule at STP?(b) What is the total translation kinetic energy of 2.0 mol of O2 molecules at 20oC?
Calculate the rms speed of helium atoms near the surface of the Sun at a temperature of about 6000K.
By what factor will the rms speed of gas molecules increase if the temperature is increased from 0oC to 100oC?
A gas is at 20oC. To what temperature must it be raised to double the rms speed of its molecules?
Twelve molecules have the following speeds, given in units of km/s : 6,2,4,6,0,4,1,8,5,3,7, and 8. Calculate tem rms speed.
The rms speed of molecules in a gas at 20.0oC is to be increased by 1.0%. To what temperature must it be raised?
If the pressure of a gas is doubled while its volume is held constant, by what factor does vrms change?
Show that the rms speed of molecules in a gas is given by vrms = √3P/p, where P is the pressure in the gas, and p is the gas density.
Show that for a mixture of two gases at the same temperature, the ratio of their rms speeds is equal to the inverse ratio of the square roots of their molecular masses.
What is the rms speed of nitrogen molecules contained in an 8.5-m3 volume at 2.1 atm if the total amount of nitrogen is 1300 mol?
Calculate (a) the rms speed of an oxygen molecule at 0oC and (b) Determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collision with other molecules.
What is the average distance between nitrogen molecules at STP?
(a) Estimate the rms speed of an amino acid whose molecular mass is 89 u in a living cell at 37oC.(b) What would be the rms speed of a protein of molecular mass 50,000 u at 37oC?
Show that the pressure P of a gas can be written P = 1/3pv2, where p is the density of the gas and v is the rms speed of the molecules.
The two isotopes of uranium, 235U and 238 U (the superscripts refer to their atomic mass), can be separated by a gas-diffusion process by combining them with flouring to make the gaseous compound UF6. Calculate the ratio of the rms speeds of these molecules for the two isotopes, at constant T.
(a) At atmospheric pressure, in what phases can CO2 exist?(b) For what range of pressures and temperatures can CO2 be a liquid? Refer to Fig. 13-21.
Water is in which phase when the pressure is 0.01 atm and the temperature is? (a) 90oC,(b) –20oC?
What is the dew point (approximately) if the humidity is 50% on a day when the temperature is 25oC?
What is the air pressure at a place where water boils at 90oC?
If the air pressure at a particular place in the mountains is 0.72atm, estimate the temperature at which water boils.
What is the temperature on a day when the partial pressure of water is 530Pa and the relative humidity is 40%?
What is the partial pressure of water on a day when the temperature is 25oC and the relative humidity is 35%?
What is the approximate pressure inside a pressure cooker if the water is boiling at a temperature of 120oC? Assume no air escaped during the heating process, which started at 20oC?
If the humidity in a room of volume 680 m3 at 25oC is 80%, what mass of water can still evaporate from an open pan?
Air that is at its dew point of 5oC is drawn into a building where it is heated to 25oC. What will be the relative humidity at this temperature? Assume constant pressure of 1.0 atm. Take into account the expansion of the air.
Estimate the time needed for a glycine molecule (see Table 13.14) to diffuse a distance of 15 μm in water at 20oC if its concentration varies over that distance from 1.00 mol/m3 to 0.40 mol/m3. Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75u.
(a) Show that the concentration of oxygen in the air (assume 21% is oxygen) at 20oC is about 8.7 mol/m3, than (b) Calculate the diffusion rate J, and (c) Estimate the average time for a molecule to diffuse in. Assume the diffusion constant is 1 x 10-5 m2/s.
A precise steel tape measure has been calibrated at 20oC. At 34oC, (a) Will it read high or low, and(b) What will be the percentage error?
A Pyrex measuring cup was calibrated at normal room temperature. How much error will be made in a recipe calling for 300mL of cool water, if the water and the cup are hot, at 80oC, instead of at 20oC? Neglect the glass expansion.
The gauge pressure in a helium gas cylinder is initially 28atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the original gas remains in the cylinder?
Estimate the number of air molecules in a room of length 6.5m, width 3.1m, and height 2.5m. Assume the temperature is 22oC. How many moles does that correspond to?
In outer space the density of matter is about one atom per cm3, mainly hydrogen atoms, and the temperature is about 2.7K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).
The lowest pressure attainable using the best available vacuum techniques is about 10-12Nm/2. AT such a pressure, how many molecules are there per cm3 at 0oC?
If a scuba diver fills his lungs to full capacity of 5.5 L when 10 m below the surface, to what volume would his lungs expand if the quickly rose to the4 surface? Is this advisable?
A space vehicle returning from the Moon enters Earth’s atmosphere at a speed of about 40,000 km/h. Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature?” (Because of this high temperature, the nose of a space vehicle must be made of special
The temperature of an ideal gas is increased from 110oC to 360oC while the volume and the number of moles stay constant. By what factor does the pressure change? By what factor does vrms change?
A house has volume of 770m3. (a) What is the total mass of air inside the house at 20oC?(b) IF the temperature drops to – 10oC, what mass of air enters or leaves the house?
From the know value of atmospheric pressure at the surface of the Earth, estimate the total number of air molecules in the Earth’s atmosphere.

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The Physics of Energy 1st edition Robert L. Jaffe, Washington Taylor - Solutions

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