Principles of Physics a Calculus Based Text

Raymond A. Serway, John W. Jewett, Jr.

Chapter 17

Energy in Thermal Processes: The First Law of Thermodynamics - all with Video Answers

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Chapter Questions

Problem 1

On his honeymoon, James Joule traveled from England to Switzerland. He attempted to verify his idea of the interconvertibility of mechanical energy and internal energy by measuring the increase in temperature of water that fell in a waterfall. For the waterfall near Chamonix in the French Alps, which has a 120 -m drop, what maximum temperature rise could Joule expect? He did not succeed in measuring it, partly because evaporation cooled the falling water and also because his thermometer was not sufficiently sensitive.

Rob Ball

Rob Ball

Numerade Educator

Problem 2

Consider Joule's apparatus described in Figure P17.2. The mass of each of the two blocks is $1.50 \mathrm{kg}$, and the insulated tank is filled with $200 \mathrm{g}$ of water. What is the increase in the water's temperature after the blocks fall through a distance of $3.00 \mathrm{m} ?$

Vipender Yadav

Numerade Educator

Problem 3

A 55.0 -kg woman cheats on her dietand eatsa 540 -Calorie $(540 \mathrm{kcal})$ jelly doughnut for breakfast. (a) How many joules of energy are the equivalent of one jelly doughnut? (b) How many steps must the woman climb on a very tall stairway to change the gravitational potential energy of the womanEarth system by a value equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is $15.0 \mathrm{cm}$
(c) If the human body is only $25.0 \%$ efficient in converting chemical potential energy to mechanical energy, how many steps must the woman climb to work off her breakfast?

Rob Ball

Numerade Educator

Problem 4

The temperature of a silver bar rises by $10.0^{\circ} \mathrm{C}$ when it absorbs $1.23 \mathrm{kJ}$ of energy by heat. The mass of the bar is 525 g. Determine the specific heat of silver from these data.

Salamat Ali

Numerade Educator

Problem 5

A 50.0 -g sample of copper is at $25.0^{\circ} \mathrm{C}$. If $1200 \mathrm{J}$ of energy is added to it by heat, what is the final temperature of the copper?

Rob Ball

Numerade Educator

Problem 6

An electric drill with a steel drill bit of mass $m=27.0 \mathrm{g}$ and diameter $0.635 \mathrm{cm}$ is used to drill into a cubical steel block of mass $M=240 \mathrm{g}$. Assume steel has the same properties as iron. The cutting process can be modeled as happening at one point on the circumference of the bit. This point moves in a helix at constant tangential speed $40.0 \mathrm{m} / \mathrm{s}$ and exerts a force of constant magnitude $3.20 \mathrm{N}$ on the block. As shown in Figure $\mathrm{P} 17.6,$ a groove in the bit carries the chips up to the top of the block, where they form a pile around the hole. The drill is turned on and drills into the block for a time interval of 15.0 s. Let's assume this time interval is long enough for conduction within the steel to bring it all to a uniform temperature. Furthermore, assume the steel objects lose a negligible amount of energy by conduction, convection, and radiation into their environment. (a) Suppose the drill bit cuts three-quarters of the way through the block during 15.0 s. Find the temperature change of the whole quantity of steel. (b) What If? Now suppose the drill bit is dull and cuts only one-eighth of the way through the block in 15.0 s. Identify the temperature change of the whole quantity of steel in this case. (c) What pieces of data, if any, are unnecessary for the solution? Explain.

Rob Ball

Numerade Educator

Problem 7

In cold climates, including the northern United States, a house can be built with very large windows facing south to take advantage of solar heating. Sunlight shining in during the daytime is absorbed by the floor, interior walls, and objects in the room, raising their temperature to $38.0^{\circ} \mathrm{C}$. If the house is well insulated, you may model it as losing energy by heat steadily at the rate $6000 \mathrm{W}$ on a day in April when the average exterior temperature is $4^{\circ} \mathrm{C}$ and when the conventional heating system is not used at all. During the period between 5: 00 p.m. and 7: 00 a.m., the temperature of the house drops and a sufficiently large "thermal mass" is required to keep it from dropping too far. The thermal mass can be a large quantity of stone (with specific heat $\left.850 \mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}\right)$ in the floor and the interior walls exposed to sunlight. What mass of stone is required if the temperature is not to drop below $18.0^{\circ} \mathrm{C}$ overnight?

Rob Ball

Numerade Educator

Problem 8

An aluminum calorimeter with a mass of $100 \mathrm{g}$ contains $250 \mathrm{g}$ of water. The calorimeter and water are in thermal equilibrium at $10.0^{\circ} \mathrm{C}$. Two metallic blocks are placed into the water. One is a 50.0 -g piece of copper at $80.0^{\circ} \mathrm{C}$. The other has a mass of $70.0 \mathrm{g}$ and is originally at a temperature of $100^{\circ} \mathrm{C}$. The entire system stabilizes at a final temperature of $20.0^{\circ} \mathrm{C}$. (a) Determine the specific heat of the unknown sample. (b) Using the data in Table 17.1 , can you make a positive identification of the unknown material? Can you identify a possible material? (c) Explain your answers for part (b).

Rob Ball

Numerade Educator

Problem 9

A combination of $0.250 \mathrm{kg}$ of water at $20.0^{\circ} \mathrm{C}, 0.400 \mathrm{kg}$ of aluminum at $26.0^{\circ} \mathrm{C},$ and 0.100 kg of copper at $100^{\circ} \mathrm{C}$ is mixed in an insulated container and allowed to come to thermal equilibrium. Ignore any energy transfer to or from the container. What is the final temperature of the mixture?

Vipender Yadav

Numerade Educator

Problem 10

If water with a mass $m_{h}$ at temperature $T_{h}$ is poured into an aluminum cup of mass $m_{\mathrm{M}}$ containing mass $m_{c}$ of water at $T_{c},$ where $T_{h}>T_{c},$ what is the equilibrium temperature of the system?

Rob Ball

Numerade Educator

Problem 11

A 1.50 -kg iron horseshoe initially at $600^{\circ} \mathrm{C}$ is dropped into a bucket containing $20.0 \mathrm{kg}$ of water at $25.0^{\circ} \mathrm{C}$. What is the final temperature of the water-horseshoe system? Ignore the heat capacity of the container and assume a negligible amount of water boils away.

Vipender Yadav

Numerade Educator

Problem 12

An aluminum cup of mass 200 g contains 800 g of water in thermal equilibrium at $80.0^{\circ} \mathrm{C}$. The combination of cup and water is cooled uniformly so that the temperature decreases by $1.50^{\circ} \mathrm{C}$ per minute. At what rate is energy being removed by heat? Express your answer in watts.

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 13

How much energy is required to change a 40.0 -g ice cube from ice at $-10.0^{\circ} \mathrm{C}$ to steam at $110^{\circ} \mathrm{C}$ ?

Vipender Yadav

Numerade Educator

Problem 14

A 50.0 -g copper calorimeter contains 250 g of water at $20.0^{\circ} \mathrm{C} .$ How much steam must be condensed into the water if the final temperature of the system is to reach $50.0^{\circ} \mathrm{C}$ ?

Rob Ball

Numerade Educator

Problem 15

In an insulated vessel, $250 \mathrm{g}$ of ice at $0^{\circ} \mathrm{C}$ is added to $600 \mathrm{g}$ of water at $18.0^{\circ} \mathrm{C}$. (a) What is the final temperature of the system? (b) How much ice remains when the system reaches equilibrium?

Rob Ball

Numerade Educator

Problem 16

Two speeding lead bullets, one of mass $12.0 \mathrm{~g}$ moving to the right at $300 \mathrm{~m} / \mathrm{s}$ and one of mass $8.00 \mathrm{~g}$ moving to the left at $400 \mathrm{~m} / \mathrm{s}$, collide head-on, and all the material sticks together. Both bullets are originally at temperature $30.0^{\circ} \mathrm{C}$. Assume the change in kinetic energy of the system appears entirely as increased internal energy. We would like to determine the temperature and phase of the bullets after the collision. (a) What two analysis models are appropriate for the system of two bullets for the time interval from before to after the collision? (b) From one of these models, what is the speed of the combined bullets after the collision? (c) How much of the initial kinetic energy has transformed to internal energy in the system after the collision? (d) Does all the lead melt due to the collision? (e) What is the temperature of the combined bullets after the collision? (f) What is the phase of the combined bullets after the collision?

Rob Ball

Numerade Educator

Problem 17

A 3.00 -g lead bullet at $30.0^{\circ} \mathrm{C}$ is fired at a speed of $240 \mathrm{m} / \mathrm{s}$ into a large block of ice at $0^{\circ} \mathrm{C},$ in which it becomes embedded. What quantity of ice melts?

Vipender Yadav

Numerade Educator

Problem 18

An automobile has a mass of $1500 \mathrm{kg}$, and its aluminum brakes have an overall mass of 6.00 kg. (a) Assume all the mechanical energy that transforms into internal energy when the car stops is deposited in the brakes and no energy is transferred out of the brakes by heat. The brakes are originally at $20.0^{\circ} \mathrm{C}$. How many times can the car be stopped from $25.0 \mathrm{m} / \mathrm{s}$ before the brakes start to melt? (b) Identify some effects ignored in part (a) that are important in a more realistic assessment of the warming of the brakes.

Rob Ball

Numerade Educator

Problem 19

A 1.00 -kg block of copper at $20.0^{\circ} \mathrm{C}$ is dropped into a large vessel of liquid nitrogen at $77.3 \mathrm{K}$. How many kilograms of nitrogen boil away by the time the copper reaches $77.3 \mathrm{K}^{2}$ (The specific heat of copper is $0.0924 \mathrm{cal} / \mathrm{g} \cdot^{\circ} \mathrm{C}$, and the latent heat of vaporization of nitrogen is 48.0 cal/g.

Rob Ball

Numerade Educator

Problem 20

A resting adult of average size converts chemical energy in food into internal energy at the rate $120 \mathrm{W}$, called her basal metabolic rate. To stay at constant temperature, the body must put out energy at the same rate. Several processes exhaust energy from your body. Usually, the most important is thermal conduction into the air in contact with your exposed skin. If you are not wearing a hat, a convection current of warm air rises vertically from your head like a plume from a smokestack. Your body also loses energy by electromagnetic radiation, by your exhaling warm air, and by evaporation of perspiration. In this problem, consider still another pathway for energy loss: moisture in exhaled breath. Suppose you breathe out 22.0 breaths per minute, each with a volume of 0.600 L. Assume that you inhale dry air and exhale air at $37^{\circ} \mathrm{C}$ containing water vapor with a vapor pressure of 3.20 kPa. The vapor came from evaporation of liquid water in your body. Model the water vapor as an ideal gas. Assume that its latent heat of evaporation at $37^{\circ} \mathrm{C}$ is the same as its heat of vaporization at $100^{\circ} \mathrm{C}$. Calculate the rate at which you lose energy by exhaling humid air.

Rob Ball

Numerade Educator

Problem 21

An ideal gas is taken through a quasi-static process described by $P=\alpha V^{2},$ with $\alpha=5.00 \mathrm{atm} / \mathrm{m}^{6},$ as shown in Figure Pl7.21. The gas is expanded to twice its original volume of $1.00 \mathrm{m}^{3} .$ How much work is done on the expanding gas in this process?

Rob Ball

Numerade Educator

Problem 22

One mole of an ideal gas is warmed slowly so that it goes from the $P V$ state $\left(P_{p} V_{i}\right)$ to $\left(3 P_{p}, 3 V_{i}\right)$ in such a way that the pressure of the gas is directly proportional to the volume. (a) How much work is done on the gas in the process?
(b) How is the temperature of the gas related to its volume during this process?

Vipender Yadav

Numerade Educator

Problem 23

An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of $8000 \mathrm{g}$ and an area of $5.00 \mathrm{cm}^{2}$ and is free to slide up and down, keeping the pressure of the gas constant. How much work is done on the gas as the temperature of 0.200 mol of the gas is raised from $20.0^{\circ} \mathrm{C}$ to $300^{\circ} \mathrm{C} ?$

Vipender Yadav

Numerade Educator

Problem 24

An ideal gas is enclosed in a cylinder that has a movable piston on top. The piston has a mass $m$ and an area $A$ and is free to slide up and down, keeping the pressure of the gas constant. How much work is done on the gas as the temperature of $n$ mol of the gas is raised from $T_{1}$ to $T_{2}$ ?

Vipender Yadav

Numerade Educator

Problem 25

(a) Determine the work done on a gas that expands from $i$ to $f$ as indicated in Figure $\mathrm{P} 17.25 .$ (b) What If? How much work is done on the gas if it is compressed from $f$ to $i$ along the same path?

Vipender Yadav

Numerade Educator

Problem 26

A sample of an ideal gas goes through the process shown in Figure $\mathrm{P} 17.26 .$ From $A$ to $B$, the process is adiabatic; from $B$ to $C,$ it is isobaric with $100 \mathrm{kJ}$ of energy entering the system by heat; from $C$ to $D$, the process is isothermal; and from $D$ to $A$, it is isobaric with $150 \mathrm{kJ}$ of energy leaving the system by heat. Determine the difference in internal energy $E_{\mathrm{int}, B}-E_{\mathrm{int}, A}$.

Vipender Yadav

Numerade Educator

Problem 27

A thermodynamic system undergoes a process in which its internal energy decreases by $500 \mathrm{J} .$ Over the same time interval, $220 \mathrm{J}$ of work is done on the system. Find the energy transferred from it by heat.

Vipender Yadav

Numerade Educator

Problem 28

A gas is taken through the cyclic process described in Figure $P 17.28 .$ (a) Find the net energy transferred to the system by heat during one complete cycle. (b) What If? If the cycle is reversed-that is, the process follows the path $A C B A-$ what is the net energy input per cycle by heat?

Rob Ball

Numerade Educator

Problem 29

Consider the cyclic process depicted in Figure P17.28. If $Q$ is negative for the process $B C$ and $\Delta E_{\text {int }}$ is negative for the process $C A$, what are the signs of $Q, W$, and $\Delta F_{\text {int }}$ that are associated with each of the three processes?

Rob Ball

Numerade Educator

Problem 30

Why is the following situation impossible? An ideal gas undergoes a process with the following parameters: $Q=10.0 \mathrm{~J}$, $W=12.0 \mathrm{~J},$ and $\Delta T=-2.00^{\circ} \mathrm{C}.$

Rob Ball

Numerade Educator

Problem 31

An ideal gas initially at 300 K undergoes an isobaric expansion at $2.50 \mathrm{kPa}$. If the volume increases from $1.00 \mathrm{m}^{3}$ to $3.00 \mathrm{m}^{3}$ and $12.5 \mathrm{kJ}$ is transferred to the gas by heat, what are (a) the change in its internal energy and (b) its final temperature?

Vipender Yadav

Numerade Educator

Problem 32

In Figure $\mathrm{P} 17.32,$ the change in internal energy of a gas that is taken from $A$ to $C$ along the blue path is $+800 \mathrm{J}$. The work done on the gas along the red path $A B C$ is $-500 \mathrm{J}$. (a) How much energy must be added to the system by heat as it goes from $A$ through $B$ to $C ?$ (b) If the pressure at point $A$ is five times that of point
$C,$ what is the work done on the system in going from $C$ to $D P$ (c) What is the energy exchanged with the surroundings by heat as the gas goes from $C$ to $A$ along the green path?
(d) If the change in internal energy in going from point $D$ to point $A$ is $+500 \mathrm{J}$, how much energy must be added to the system by heat as it goes from point $C$ to point $D ?$

Rob Ball

Numerade Educator

Problem 33

A 1.00 -kg block of aluminum is warmed at atmospheric pressure so that its temperature increases from $22.0^{\circ} \mathrm{C}$ to $40.0^{\circ} \mathrm{C}$ Find (a) the work done on the aluminum, (b) the energy added to it by heat, and (c) the change in its internal energy.

Rob Ball

Numerade Educator

Problem 34

(a) How much work is done on the steam when $1.00 \mathrm{mol}$ of water at $100^{\circ} \mathrm{C}$ boils and becomes $1.00 \mathrm{mol}$ of steam at $100^{\circ} \mathrm{C}$ at 1.00 atm pressure? Assume the steam to behave as an ideal gas. (b) Determine the change in internal energy of the system of the water and steam as the water vaporizes.

Vipender Yadav

Numerade Educator

Problem 35

An ideal gas initially at $P_{i}, V_{i}$ and $T_{i}$ is taken through a cycle as shown in Figure P17.35. (a) Find the net work done on the gas per cycle for 1.00 mol of gas initially at $0^{\circ} \mathrm{C}$. (b) What is the net energy added by heat to the gas per cycle?

Vipender Yadav

Numerade Educator

Problem 36

An ideal gas initially at $P_{i}, V_{i}$, and $T_{i}$ is taken through a cycle as shown in Figure P17.35. (a) Find the net work done on the gas per cycle. (b) What is the net energy added by heat to the system per cycle?

Vipender Yadav

Numerade Educator

Problem 37

A 2.00 -mol sample of helium gas initially at $300 \mathrm{K}$ and 0.400 atm is compressed isothermally to 1.20 atm. Noting that the helium behaves as an ideal gas, find (a) the final volume of the gas, (b) the work done on the gas, and (c) the energy transferred by heat.

Vipender Yadav

Numerade Educator

Problem 38

One mole of an ideal gas does $3000 \mathrm{J}$ of work on its surroundings as it expands isothermally to a final pressure of 1.00 atm and volume of 25.0 L. Determine (a) the initial volume and (b) the temperature of the gas.

Vipender Yadav

Numerade Educator

Problem 39

A 1.00 -mol sample of hydrogen gas is heated at constant pressure from $300 \mathrm{K}$ to $420 \mathrm{K}$. Calculate (a) the energy transferred to the gas by heat, (b) the increase in its internal energy, and (c) the work done on the gas.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 40

A sample of a diatomic ideal gas has pressure $P$ and volume $V .$ When the gas is warmed, its pressure triples and its volume doubles. This warming process includes two steps, the first at constant pressure and the second at constant volume. Determine the amount of energy transferred to the gas by heat.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 41

Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by $2.00 \mathrm{K}$.

Rob Ball

Numerade Educator

Problem 42

A 1.00 -L insulated bottle is full of tea at $90.0^{\circ} \mathrm{C}$. You pour out one cup of tea and immediately screw the stopper back on the bottle. Make an order-of-magnitude estimate of the change in temperature of the tea remaining in the bottle that results from the admission of air at room temperature. State the quantities you take as data and the values you measure or estimate for them.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 43

A vertical cylinder with a heavy piston contains air at $300 \mathrm{K}$ The initial pressure is $2.00 \times 10^{5} \mathrm{Pa}$, and the initial volume is $0.350 \mathrm{m}^{3} .$ Take the molar mass of air as $28.9 \mathrm{g} / \mathrm{mol}$ and assume $C_{V}=\frac{5}{2} R$ (a) Find the specific heat of air at constant volume in units of $\mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$. (b) Calculate the mass of the air in the cylinder. (c) Suppose the piston is held fixed. Find the energy input required to raise the temperature of the air to $700 \mathrm{K} .$ (d) What If? Assume again the conditions of the initial state and assume the heavy piston is free to move. Find the energy input required to raise the temperature to $700 \mathrm{K}$.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 44

This problem is a continuation of Problem 16.29 in Chapter $16 .$ A hot-air balloon consists of an envelope of constant volume $400 \mathrm{m}^{3}$. Not including the air inside, the balloon and cargo have mass 200 kg. The air outside and originally inside is a diatomic ideal gas at $10.0^{\circ} \mathrm{C}$ and $101 \mathrm{kPa}$, with density $1.25 \mathrm{kg} / \mathrm{m}^{3}$. A propane burner at the center of the spherical envelope injects energy into the air inside. The air inside stays at constant pressure. Hot air, at just the temperature required to make the balloon lift off, starts to fill the envelope at its closed top, rapidly enough so that negligible energy flows by heat to the cool air below it or out through the wall of the balloon. Air at $10^{\circ} \mathrm{C}$ leaves through an opening at the bottom of the envelope until the whole balloon is filled with hot air at uniform temperature. Then the burner is shut off and the balloon rises from the ground.
(a) Evaluate the quantity of energy the burner must transfer to the air in the balloon. (b) The "heat value" of propane the internal energy released by burning each kilogram- is $50.3 \mathrm{MJ} / \mathrm{kg} .$ What mass of propane must be burned?

Rob Ball

Numerade Educator

Problem 45

In a constant-volume process, $209 \mathrm{J}$ of energy is transferred by heat to 1.00 mol of an ideal monatomic gas initially at $300 \mathrm{K}$. Find (a) the work done on the gas, (b) the increase in internal energy of the gas, and (c) its final temperature.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 46

A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of $12.0 \mathrm{L}$ to a final volume of $30.0 \mathrm{L}$. (a) What is the final pressure of the gas? (b) What are the initial and final temperatures? Find (c) $Q,(\mathrm{d}) \Delta E_{\mathrm{int}},$ and (e) $W$ for the gas during this process.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 47

A 4.00 -L sample of a diatomic ideal gas with specific heat ratio $1.40,$ confined to a cylinder, is carried through a closed cycle. The gas is initially at 1.00 atm and 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. (a) Draw a $P V$ diagram of this cycle. (b) Determine the volume of the gas at the end of the adiabatic expansion. (c) Find the temperature of the gas at the start of the adiabatic expansion.
(d) Find the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle?

Rob Ball

Numerade Educator

Problem 48

An ideal gas with specific heat ratio $\gamma$ confined to a cylinder is put through a closed cycle. Initially, the gas is at $P_{i}, V_{i}$ and $T_{i}$. First, its pressure is tripled under constant volume. It then expands adiabatically to its original pressure and finally is compressed isobarically to its original volume. (a) Draw a $P V$ diagram of this cycle. (b) Determine the volume at the end of the adiabatic expansion. Find (c) the temperature of the gas at the start of the adiabatic expansion and (d) the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle?

Dominador Tan

Numerade Educator

Problem 49

During the compression stroke of a certain gasoline engine, the pressure increases from 1.00 atm to 20.0 atm. If the process is adiabatic and the air-fuel mixture behaves as a diatomic ideal gas, (a) by what factor does the volume change and (b) by what factor does the temperature change? Assuming the compression starts with $0.0160 \mathrm{mol}$ of gas at $27.0^{\circ} \mathrm{C},$ find the values of $(\mathrm{c}) Q,(\mathrm{d}) \Delta E_{\text {int }},$ and $(\mathrm{e}) W$ that characterize the process.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 50

Why is the following situation impossible? A new diesel engine that increases fuel economy over previous models is designed. Automobiles fitted with this design become incredible best sellers. Two design features are responsible for the increased fuel economy: (1) the engine is made entirely of aluminum to reduce the weight of the automobile, and (2) the exhaust of the engine is used to prewarm the air to $50^{\circ} \mathrm{C}$ before it enters the cylinder to increase the final temperature of the compressed gas. The engine has a compression ratio- that is, the ratio of the initial volume of the air to its final volume after compression-of $14.5 .$ The compression process is adiabatic, and the air behaves as a diatomic ideal gas with $\gamma=1.40$.

Rob Ball

Numerade Educator

Problem 51

Air in a thundercloud expands as it rises. If its initial temperature is $300 \mathrm{K}$ and no energy is lost by thermal conduction on expansion, what is its temperature when the initial volume has doubled?

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 52

How much work is required to compress 5.00 mol of air at $20.0^{\circ} \mathrm{C}$ and 1.00 atm to one-tenth of the original volume (a) by an isothermal process? (b) What If? How much work is required to produce the same compression in an adiabatic process? (c) What is the final pressure in part (a)? (d) What is the final pressure in part (b)?

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 53

Air (a diatomic ideal gas at $27.0^{\circ} \mathrm{C}$ and atmospheric pressure is drawn into a bicycle pump (Figure $P 17.53$ ) that has a cylinder with an inner diameter of $2.50 \mathrm{cm}$ and
length $50.0 \mathrm{cm} .$ The downstroke adiabatically compresses the air, which reaches a gauge pressure of $8.00 \times 10^{5}$ Pa before
entering the tire. We wish to investigate the temperature increase of the pump. (a) What is the initial volume of the air in the pump? (b) What is the number of moles of air in the pump? (c) What is the absolute pressure of the compressed $\operatorname{air} ?(\mathrm{d})$ What is the volume of the compressed air? (e) What is the temperature of the compressed air? (f) What is the increase in internal energy of the gas during the compression? What If? The pump is made of steel that is $2.00 \mathrm{mm}$ thick. Assume $4.00 \mathrm{cm}$ of the cylinder's length is allowed to come to thermal equilibrium with the air. (g) What is the volume of steel in this 4.00 -cm length? (h) What is the mass of steel in this 4.00 -cm length? (i) Assume the pump is compressed once. After the adiabatic expansion, conduction results in the energy increase in part (f) being shared between the gas and the 4.00 -cm length of steel. What will be the increase in temperature of the steel after one compression?

Dominador Tan

Numerade Educator

Problem 54

During the power stroke in a four-stroke automobile engine, the piston is forced down as the mixture of combustion products and air undergoes an adiabatic expansion. Assume (1) the engine is running at 2500 cycles/min; (2) the gauge pressure immediately before the expansion is $20.0 \mathrm{atm} ;$ (3) the volumes of the mixture immediately before and after the expansion are $50.0 \mathrm{cm}^{3}$ and $400 \mathrm{cm}^{3}$, respectively (Fig. P17.54)
(4) the time interval for the expansion is one-fourth that of the total cycle; and (5) the mixture behaves like an ideal gas with specific heat ratio $1.40 .$ Find the average power generated during the power stroke.

Rob Ball

Numerade Educator

Problem 55

Inacrude model (Fig. P17.55) of rotating diatomic chlorine molecule (Cl_), the two Cl atoms are $2.00 \times 10^{-10} \mathrm{m}$ apart and rotate about their center of mass with angular speed $\omega=$ $2.00 \times 10^{12} \mathrm{rad} / \mathrm{s} .$ What is the rota-
tional kinetic energy of one molecule of $\mathrm{Cl}_{2},$ which has a molar mass of $70.0 \mathrm{g} / \mathrm{mol} ?$

Rob Ball

Numerade Educator

Problem 56

A certain molecule has $f$ degrees of freedom. Show that an ideal gas consisting of such molecules has the following properties: (a) its total internal energy is $f n R T / 2,$ (b) its molar specific heat at constant volume is $f R / 2,(c)$ its molar specific heat at constant pressure is $(f+2) R / 2,$ and (d) its specific heat ratio is $\gamma=C_{P} / C_{V}=(f+2) / f$.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 57

The relationship between the heat capacity of a sample and the specific heat of the sample material is discussed in Section $17.2 .$ Consider a sample containing 2.00 mol of an ideal diatomic gas. Assuming the molecules rotate but do not vibrate, find (a) the total heat capacity of the sample at constant volume and (b) the total heat capacity at constant pressure. (c) What If? Repeat parts (a) and (b), assuming the molecules both rotate and vibrate.

Dominador Tan

Numerade Educator

Problem 58

A team of researchers discovers a new gas, which has a value of $\gamma=C_{P} / C_{V}$ of 1.75.

Dominador Tan

Numerade Educator

Problem 59

A bar of gold (Au) is in thermal contact with a bar of silver (Ag) of the same length and area (Fig. P17.59). One end of the compound bar is maintained at $80.0^{\circ} \mathrm{C}$ and the opposite end is at $30.0^{\circ} \mathrm{C}$ When the energy transfer reaches steady state, what is the temperature at the junction?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 60

The human body must maintain its core temperature inside a rather narrow range around $37^{\circ} \mathrm{C}$ Metabolic processes, notably muscular exertion, convert chemical energy into internal energy deep in the interior. From the interior, energy must flow out to the skin or lungs to be expelled to the environment. During moderate exercise, an $80-\mathrm{kg}$ man can metabolize food energy at the rate $300 \mathrm{kcal} / \mathrm{h},$ do $60 \mathrm{kcal} / \mathrm{h}$ of mechanical work, and put out the remaining $240 \mathrm{kcal} / \mathrm{h}$ of energy by heat. Most of the energy is carried from the body interior out to the skin by forced convection (as a plumber would say), whereby blood is warmed in the interior and then cooled at the skin, which is a few degrees cooler than the body core. Without blood flow, living tissue is a good thermal insulator, with thermal conductivity about $0.210 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$. Show that blood flow is essential to cool the man's body by calculating the rate of energy conduction in kcal/h through the tissue layer under his skin. Assume that its area is $1.40 \mathrm{m}^{2},$ its thickness is $2.50 \mathrm{cm},$ and it is maintained at $37.0^{\circ} \mathrm{C}$ on one side and at $34.0^{\circ} \mathrm{C}$ on the other side.

Ajay Singhal

Numerade Educator

Problem 61

A student is trying to decide what to wear. His bedroom is at $20.0^{\circ} \mathrm{C}$. His skin temperature is $35.0^{\circ} \mathrm{C}$. The area of his exposed skin is $1.50 \mathrm{m}^{2}$. People all over the world have skin that is dark in the infrared, with emissivity about 0.900 . Find the net energy transfer from his body by radiation in $10.0 \mathrm{min}$.

Vipender Yadav

Numerade Educator

Problem 62

A box with a total surface area of $1.20 \mathrm{m}^{2}$ and a wall thickness of $4.00 \mathrm{cm}$ is made of an insulating material. A $10.0-\mathrm{W}$ electric heater inside the box maintains the inside temperature at $15.0^{\circ} \mathrm{C}$ above the outside temperature. Find the thermal conductivity $k$ of the insulating material.

Shahab Ullah

Numerade Educator

Problem 63

The surface of the Sun has a temperature of about $5800 \mathrm{K}$ The radius of the Sun is $6.96 \times 10^{8} \mathrm{m}$. Calculate the total energy radiated by the Sun each second. Assume the emissivity of the Sun is 0.986.

Vipender Yadav

Numerade Educator

Problem 64

At our distance from the Sun, the intensity of solar radiation is $1370 \mathrm{W} / \mathrm{m}^{2}$. The temperature of the Earth is affected by the greenhouse effect of the atmosphere. This phenomenon describes the effect of absorption of infrared light emitted by the surface so as to make the surface temperature of the Earth higher than if it were airless. For comparison, consider a spherical object of radius $r$ with no atmosphere at the same distance from the Sun as the Earth. Assume its emissivity is the same for all kinds of electromagnetic waves and its temperature is uniform over its surface. (a) Explain why the projected area over which it absorbs sunlight is $\pi r^{2}$ and the surface area over which it radiates is $4 \pi r^{2}$. (b) Compute its steady-state temperature. Is it chilly?

Vipender Yadav

Numerade Educator

Problem 65

At high noon, the Sun delivers $1000 \mathrm{W}$ to each square meter of a blacktop road. If the hot asphalt transfers energy only by radiation, what is its steady-state temperature?

Pawan Yadav

Numerade Educator

Problem 66

Section 16.7 described experimental data on the decrease in temperature with altitude in the Earth's atmosphere. Model the troposphere as an ideal gas, everywhere with equivalent molar mass $M$ and ratio of specific heats $\gamma$. Absorption of sunlight at the Earth's surface warms the troposphere from below, so vertical convection currents are continually mixing the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surroundings, so its internal energy decreases and it drops in temperature. Assume that the vertical mixing is so rapid as to be adiabatic. (a) Show that the quantity $T P^{(1-\gamma) / \gamma}$ has a uniform value through the layers of the troposphere. (b) By differentiating with respect to altitude $y,$ show that the lapse rate is given by $$\frac{d T}{d y}=\frac{T}{P}\left(1-\frac{1}{\gamma}\right) \frac{d P}{d y}$$ (c) A lower layer of air must support the weight of the layers above. From Equation $15.4,$ observe that mechanical equilibrium of the atmosphere requires that the pressure decrease with altitude according to $d P / d y=-\rho g$. The depth of the troposphere is small compared with the radius of the Earth, so you may assume that the free-fall acceleration is uniform. Proceed to prove that the lapse rate is $$\frac{d T}{d y}=-\left(1-\frac{1}{\gamma}\right) \frac{M g}{R}$$ Problem 16.50 in Chapter 16 calls for evaluation of this theoretical lapse rate on the Earth and on Mars and for comparison with experimental results.

Dominador Tan

Numerade Educator

Problem 67

On a cold winter day, you buy roasted chestnuts from a street vendor. Into the pocket of your down parka you put the change he gives you: coins constituting $9.00 \mathrm{g}$ of copper at $-12.0^{\circ} \mathrm{C} .$ Your pocket already contains $14.0 \mathrm{g}$ of silver coins at $30.0^{\circ} \mathrm{C}$. A short time later the temperature of the copper coins is $4.00^{\circ} \mathrm{C}$ and is increasing at a rate of $0.500^{\circ} \mathrm{C} / \mathrm{s}$. At this time, (a) what is the temperature of the silver coins and (b) at what rate is it changing?

Dominador Tan

Numerade Educator

Problem 68

A sample of a monatomic ideal gas occupies $5.00 \mathrm{L}$ at atmospheric pressure and $300 \mathrm{K}$ (point $A$ in Fig. $P 17.68$ ). It is warmed at constant volume to 3.00 atm (point $B$ ). Then it is allowed to expand isothermally to 1.00 $\operatorname{atm}(\text { point } C)$ and at last compressed isobarically to its original state. (a) Find the number of moles in the sample. Find
(b) the temperature at point $B$, (c) the temperature at point $C$, and (d) the volume at point $C$ (e) Now consider the processes $A \rightarrow B, B \rightarrow C,$ and $C \rightarrow A .$ Describe how to carry out each process experimentally. (f) Find $Q, W$, and $\Delta E_{\text {int }}$ for each of the processes. (g) For the whole cycle $A \rightarrow B \rightarrow C \rightarrow A$, find $Q, W$ and $\Delta E_{\text {int }}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 69

An aluminum rod $0.500 \mathrm{m}$ in length and with a crosssectional area of $2.50 \mathrm{cm}^{2}$ is inserted into a thermally insulated vessel containing liquid helium at $4.20 \mathrm{K}$. The rod is initially at $300 \mathrm{K}$. (a) If one-half of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to $4.20 \mathrm{K}$ ? Assume the upper half does not yet cool. (b) If the circular surface of the upper end of the rod is maintained at $300 \mathrm{K},$ what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached $4.20 \mathrm{K}$ ? (Aluminum has thermal conductivity of $3100 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$ at $4.20 \mathrm{K} ;$ ignore its temperature variation. The density of liquid helium is $\left.125 \mathrm{kg} / \mathrm{m}^{3} .\right)$

Dominador Tan

Numerade Educator

Problem 70

For bacteriological testing of water supplies and in medical clinics, samples must routinely be incubated for $24 \mathrm{h}$ at $37^{\circ} \mathrm{C}$. Peace Corps volunteer and MIT engineer Amy Smith invented a low-cost, low-maintenance incubator. The incubator consists of a foam-insulated box containing a waxy material that melts at $37.0^{\circ} \mathrm{C}$ interspersed among tubes, dishes, or bottles containing the test samples and growth medium (bacteria food). Outside the box, the waxy material is first melted by a stove or solar energy collector. Then the waxy material is put into the box to keep the test samples warm as the material solidifies. The heat of fusion of the phase-change material is $205 \mathrm{kJ} / \mathrm{kg} .$ Model the insulation as a panel with surface area $0.490 \mathrm{m}^{2}$, thickness $4.50 \mathrm{cm}$ and conductivity $0.0120 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C}$. Assume the exterior temperature is $23.0^{\circ} \mathrm{C}$ for $12.0 \mathrm{h}$ and $16.0^{\circ} \mathrm{C}$ for $12.0 \mathrm{h}$
(a) What mass of the waxy material is required to conduct the bacteriological test? (b) Explain why your calculation can be done without knowing the mass of the test samples or of the insulation.

Dominador Tan

Numerade Educator

Problem 71

A flow calorimeter is an apparatus used to measure the specific heat of a liquid. The technique of flow calorimetry involves measuring the temperature difference between the input and output points of a flowing stream of the liquid while energy is added by heat at a known rate. A liquid of density $900 \mathrm{kg} / \mathrm{m}^{3}$ flows through the calorimeter with volume flow rate of $2.00 \mathrm{L} /$ min. At steady state, a temperature difference $3.50^{\circ} \mathrm{C}$ is established between the input and output points when energy is supplied at the rate of $200 \mathrm{W}$. What is the specific heat of the liquid?

Vipender Yadav

Numerade Educator

Problem 72

A flow calorimeter is an apparatus used to measure the specific heat of a liquid. The technique of flow calorimetry involves measuring the temperature difference between the input and output points of a flowing stream of the liquid while energy is added by heat at a known rate. A liquid of density $\rho$ flows through the calorimeter with volume flow rate $R$. At steady state, a temperature difference $\Delta T$ is established between the input and output points when energy is supplied at the rate $P .$ What is the specific heat of the liquid?

Shahab Ullah

Numerade Educator

Problem 73

Following a collision between a large spacecraft and an asteroid, a copper disk of radius $28.0 \mathrm{m}$ and thickness
$1.20 \mathrm{m}$ at a temperature of $850^{\circ} \mathrm{C}$ is floating in space, rotating about its symmetry axis with an angular speed of $25.0 \mathrm{rad} / \mathrm{s}$. As the disk radiates infrared light, its temperature falls to $20.0^{\circ} \mathrm{C} .$ No external torque acts on the disk. (a) Find the change in kinetic energy of the disk. (b) Find the change in internal energy of the disk. (c) Find the amount of energy it radiates.

Dominador Tan

Numerade Educator

Problem 74

$\mathrm{A}$ group of campers arises at 8: 30 a.m. and uses a solar cooker, which consists of a curved, reflecting surface that concentrates sunlight onto the object to be warmed (Fig. P17.74). During the day, the maximum solar intensity reaching the Earth's surface at the cooker's location is $I=600 \mathrm{W} / \mathrm{m}^{2}$. The cooker faces the Sun and has a face diameter of $d=0.600 \mathrm{m}$ Assume $40.0 \%$ of the incident energy is transferred to $1.50 \mathrm{L}$ of water in an open container, initially at $20.0^{\circ} \mathrm{C}$ The water comes to a boil, and the campers enjoy hot coffee for breakfast before hiking ten miles and returning by noon for lunch.

Dominador Tan

Numerade Educator

Problem 75

A $75.0-\mathrm{kg}$ cross-country skier moves across the snow (Fig. P17.75). The coefficient of friction between the skis and the snow is $0.200 .$ Assume that all the snow beneath his skis is at $0^{\circ} \mathrm{C}$ and that all the internal energy generated by friction is added to the snow, which sticks to his skis until it melts. How far would he have to ski to melt 1.00 kg of snow?

Shahab Ullah

Numerade Educator

Problem 76

One mole of an ideal gas is contained in a cylinder with a movable piston. The initial pressure, volume, and temperature are $P_{i}, V_{i},$ and $T_{i},$ respectively. Find the work done on the gas in the following processes. In operational terms, describe how to carry out each process and show each process on a $P V$ diagram. (a) an isobaric compression in which the final volume is one-half the initial volume
(b) an isothermal compression in which the final pressure is four times the initial pressure (c) an isovolumetric process in which the final pressure is three times the initial pressure.

Vipender Yadav

Numerade Educator

Problem 77

A 670 -kg meteoroid happens to be composed of aluminum. When it is far from the Earth, its temperature is $-15.0^{\circ} \mathrm{C}$ and it moves at $14.0 \mathrm{km} / \mathrm{s}$ relative to the planet. As it crashes into the Earth, assume the internal energy transformed from the mechanical energy of the meteoroidEarth system is shared equally between the meteoroid and the Earth and all the material of the meteoroid rises momentarily to the same final temperature. Find this temperature. Assume the specific heat of liquid and of gaseous aluminum is $1170 \mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$.

Dominador Tan

Numerade Educator

Problem 78

A student measures the following data in a calorimetry experiment designed to determine the specific heat of aluminum:
(a) Use these data to determine the specific heat of aluminum. (b) Explain whether your result is within $15 \%$ of the value listed in Table 17.1

Dominador Tan

Numerade Educator

Problem 79

An iron plate is held against an iron wheel so that a kinetic friction force of $50.0 \mathrm{N}$ acts between the two pieces of metal. The relative speed at which the two surfaces slide over each other is $40.0 \mathrm{m} / \mathrm{s}$. (a) Calculate the rate at which mechanical energy is converted to internal energy. (b) The plate and the wheel each have a mass of $5.00 \mathrm{kg}$, and each receives $50.0 \%$ of the internal energy. If the system is run as described for $10.0 \mathrm{s}$ and each object is then allowed to reach a uniform internal temperature, what is the resultant temperature increase?

Dominador Tan

Numerade Educator

Problem 80

(a) In air at $0^{\circ} \mathrm{C}$, a 1.60 -kg copper block at $0^{\circ} \mathrm{C}$ is set sliding at $2.50 \mathrm{m} / \mathrm{s}$ over a sheet of ice at $0^{\circ} \mathrm{C}$. Friction brings the block to rest. Find the mass of the ice that melts. (b) As the block slows down, identify its energy input $Q,$ its change in internal energy $\Delta F_{\text {int }}$, and the change in mechanical energy for the block-ice system. (c) For the ice as a system, identify its energy input $Q$ and its change in internal energy $\Delta F_{\text {int }}$. (d) A 1.60 -kg block of ice at $0^{\circ} \mathrm{C}$ is set sliding at $2.50 \mathrm{m} / \mathrm{s}$ over a sheet of copper at $0^{\circ} \mathrm{C}$. Friction brings the block to rest. Find the mass of the ice that melts. (e) Evaluate Qand $\Delta F_{\text {int }}$ for the block of ice as a system and $\Delta E_{\text {thech }}$ for the block-ice system. (f) Evaluate $Q$ and $\Delta E_{\text {int }}$ for the metal sheet as a system. (g) A thin, 1.60 -kg slab of copper at $20^{\circ} \mathrm{C}$ is set sliding at $2.50 \mathrm{m} / \mathrm{s}$ over an identical stationary slab at the same temperature. Friction quickly stops the motion. Assuming no energy is transferred to the environment by heat, find the change in temperature of both objects. (h) Evaluate $Q$ and $\Delta F_{\text {int }}$ for the sliding slab and $\Delta E_{\text {mech }}$ for the two-slab system.
(i) Evaluate $Q$ and $\Delta F_{\text {fint }}$ for the stationary slab.

Dominador Tan

Numerade Educator

Problem 81

The average thermal conductivity of the walls (including the windows) and roof of the house depicted in Figure $\mathrm{P} 17.81$ is $0.480 \mathrm{W} / \mathrm{m} \cdot^{\circ} \mathrm{C},$ and
their average thickness is $21.0 \mathrm{cm} .$ The house
is kept warm with natural gas having a heat of combustion (that is, the energy provided per cubic meter of gas burned) of $9300 \mathrm{kcal} / \mathrm{m}^{3}$. How many cubic meters of gas must be burned each day to maintain an inside temperature of $25.0^{\circ} \mathrm{C}$ if the outside temperature is $0.0^{\circ} \mathrm{C}$, Disregard radiation and the energy transferred by heat through the ground.

Dominador Tan

Numerade Educator

Problem 82

A pond of water at $0^{\circ} \mathrm{C}$ is covered with a layer of ice $4.00 \mathrm{cm}$ thick. If the air temperature stays constant at $-10.0^{\circ} \mathrm{C}$, what time interval is required for the ice thickness to increase to $8.00 \mathrm{cm} ?$ Suggestion: Use Equation 17.34 in the form $$\frac{d Q}{d t}=k A \frac{\Delta T}{x}$$ and note that the incremental energy $d Q$ extracted from the water through the thickness $x$ of ice is the amount required to freeze a thickness $d x$ of ice. That is, $d Q=L_{l} \rho A d x$, where
$\rho$ is the density of the ice, $A$ is the area, and $L_{f}$ is the latent heat of fusion.

Dominador Tan

Numerade Educator

Problem 83

A certain ideal gas has a molar specific heat of $C_{V}=\frac{7}{2} R$
A 2.00 -mol sample of the gas always starts at pressure $1.00 \times 10^{5} \mathrm{Pa}$ and temperature $300 \mathrm{K}$. For each of the following processes, determine (a) the final pressure, (b) the final volume, (c) the final temperature, (d) the change in internal energy of the gas, (e) the energy added to the gas by heat, and (f) the work done on the gas. (i) The gas is heated at constant pressure to $400 \mathrm{K}$. (ii) The gas is heated at constant volume to $400 \mathrm{K}$. (iii) The gas is compressed at constant temperature to $1.20 \times 10^{5}$ Pa. (iv) The gas is compressed adiabatically to $1.20 \times 10^{5} \mathrm{Pa}$.

Dominador Tan

Numerade Educator

Problem 84

In a cylinder, a sample of an ideal gas with number of moles $n$ undergoes an adiabatic process. (a) Starting with the expression $W=-\int P d V$ and using the condition $P V^{\gamma}=$ constant, show that the work done on the gas is $$W=\left(\frac{1}{\gamma-1}\right)\left(P_{f} V_{f}-P_{i} V_{i}\right)$$ (b) Starting with the first law of thermodynamics, show that the work done on the gas is equal to $n C_{\nu}\left(T_{f}-T_{i}\right) .$ (c) Are these two results consistent with each other? Explain.

Dominador Tan

Numerade Educator

Problem 85

As a 1.00 -mol sample of a monatomic ideal gas expands adiabatically, the work done on it is $-2.50 \times 10^{3} \mathrm{J}$. The initial temperature and pressure of the gas are $500 \mathrm{K}$ and 3.60 atm. Calculate (a) the final temperature and (b) the final pressure.

Jordan Vanevery

Jordan Vanevery

Numerade Educator

Problem 86

A sample consists of an amount $n$ in moles of a monatomic ideal gas. The gas expands adiabatically, with work $W$ done on it. (Work $W$ is a negative number.) The initial temperature and pressure of the gas are $T_{i}$ and $P_{r}$ Calculate (a) the final temperature and (b) the final pressure.

Dominador Tan

Numerade Educator

Problem 87

A pitcher throws a 0.142 -kg baseball at $47.2 \mathrm{m} / \mathrm{s}$. As it travels $16.8 \mathrm{m}$ to home plate, the ball slows down to $42.5 \mathrm{m} / \mathrm{s}$ because of air resistance. Find the change in temperature of the air through which it passes. To find the greatest possible temperature change, you may make the following assumptions. Air has a molar specific heat of $C_{P}=\frac{7}{2} R$ and an equivalent molar mass of $28.9 \mathrm{g} /$ mol. The process is so rapid that the cover of the baseball acts as thermal insulation and the temperature of the ball itself does not change. A change in temperature happens initially only for the air in a cylinder $16.8 \mathrm{m}$ in length and $3.70 \mathrm{cm}$ in radius. This air is initially at $20.0^{\circ} \mathrm{C}$.

Dominador Tan

Numerade Educator

Problem 88

The rate at which a resting person converts food energy is called one's basal metabolic rate (BMR). Assume that the resulting internal energy leaves a person's body by radiation and convection of dry air. When you jog, most of the food energy you burn above your BMR becomes internal energy that would raise your body temperature if it were not eliminated. Assume that evaporation of perspiration is the mechanism for eliminating this energy. Suppose a person is jogging for "maximum fat burning," converting food energy at the rate $400 \mathrm{kcal} / \mathrm{h}$ above his BMR, and putting out energy by work at the rate 60.0 W. Assume that the heat of evaporation of water at body temperature is equal to its heat of vaporization at $100^{\circ} \mathrm{C}$. (a) Determine the hourly rate at which water must evaporate from his skin. (b) When you metabolize fat, the hydrogen atoms in the fat molecule are transferred to oxygen to form water. Assume that metabolism of 1 g of fat generates 9.00 kcal of energy and produces $1 \mathrm{g}$ of water. What fraction of the water the jogger needs is provided by fat metabolism?

Arun Bana

Numerade Educator

Problem 89

Water in an electric teakettle is boiling. The power absorbed by the water is $1.00 \mathrm{kW}$. Assuming the pressure of vapor in the kettle equals atmospheric pressure, determine the speed of effusion of vapor from the kettle's spout if the spout has a cross-sectional area of $2.00 \mathrm{cm}^{2}$. Model the steam as an ideal gas.

Dominador Tan

Numerade Educator