Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the peri.(b6r0r9yq q9 ywvqn 2f(ewyvodic table or Appen0(qe(92rn.y w ry yfwvq6qb9 vdix B.

Name several properties of materials that could be exploited to make a thermometof2)4ec f -6rzvao1na e)fvn 6oaf -2za4o 1ecrr.

Which is larger, 1 C;c7i zu d*0kcn $^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equili o1i/7:wkdqnybrium with system B, but B is not in thermal equilibrium w 17:oknydwq /iith system C, what can you say about the temperatures of A, B, and C?

A flat bimetallic strip cons19n,s *b u;o2xzj9wsyi dl4eoists of aluminum riveted to a strip of iron. When heated, the strip will bebw*2 4o9y; 9jed1snxz,luo i snd. Which metal will be on the outside of the curve? [Hint: See Table 13–1.] Why?

In the relation $\Delta$L = $\alpha$ $L_0$ $\Delta$T, should $L_0$ be the initial length, the final length, or does it matter? Explain.

The units for the coefficient ofm s9n7r m5:und linear expansion $\alpha$ are $(C?)^{-1}$ and there is no mention of a length unit such as meters. Would the expansion coefficient change if we used feet or millimeters instead of meters? Explain.

Figure 13–27 shows a diagram of a simple thermose3jajy4 .ev +98rc engtat used to control a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. Thje y3j n4 v8gre+ea.c9e electric switch is a glass vessel containing liquid mercury that conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and how it can be set at different temperatures.

Long steam pipes that are fixed at the ends often ha*5i7rnz yjteis).h )y ve a section in the shape of a esh.zjrii))7t y 5*ynU. Why?

A flat, uniform cylinder of lead floats in mercury at p 19)6kkwtkct dmy:a qu hn5:00 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glass thermometer is first placed in a hob8l0ir hl5l0,l tm *f b-1ihmgt tub of water, the mercury initially descends a bit and then rises. Explainmi,lb1l5rg0 i-8*hlhl f0t b m.

A glass container may break if one part of it is heate5:rou4a x+g*oiw9 7(l dnwwvpd or cooled more rapidly than adjacent parts. Explain.nvw o*wdwor4 l i(+7pg9:ax5u

The principal virtue of Pyrex glass is that its coefficient or-2n;tz 1rprs0zd kx tz69h)l f linear expansion is much smaller than that for ordinary glass (Table 13–1). Explain why this gives rise to the in16t- zs2n;d r xzlth 90rrpzk)creased heat resistance of Pyrex.

Will a grandfather clock, accurat +xld1 *t 9cbn:el:4af3vxwmpe at 20 $^{\circ} $ C, run fast or slow on a hot day (30 $^{\circ} $ C)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

Freezing a can of soda will causej38my8 llot4+aix n.t its bottom and top to bulge so badly the can will not stan l+ itjt8ml38a.xno4 yd up. What has happened?

When a gas is rapidly compressed (say, by pushing down a piston), i8lb8dy):p9 a p uwxxj8ts temperature increases. When a gas expands against a piston, it cools. Explain these changesdu pwx 8x:9ylbja )88p in temperature using the kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force on an4 vkvm 32x6lhox f6k(e aluminum sphere submerged in water increase or decrease if63 x62kholvx (k4mfev the temperature is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinfgfrhrcj( z-54 :sknlw39os .etic theory and the relation between average kinetic energy and thsf 5-3wc z:gls94o.njr (fk rhe absolute temperature.

Explain in words how Gay-Lussl8,q oa0z 8gee yu (ufu-j)9tv/xqa50ho g-raac’s law follows from kinetic theory.

As you go higher in t ,sw,kzu 9 3.;gltuoushe Earth’s atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minimum speed an l2z+ kodgyp4 0qf.oi+ object must have to leave the Earth and never return. The escape velocity for the Moon is about one-fifth what it is for the Earth due to the Moon’s smaller mass. Explain why the Moon4+ g+d yo 2pkoql.z0if has practically no atmosphere.

Alcohol evaporates more quickly than water at room temperature.jg-vt w924cuu What can you infer about the molecular properties of one relative to the otheru24gc9- jv wtu?

Explain why a hot humid day is far more uncomfortable than a hot dtyolm 3gx eiw4b(vxd*mj/ 59wj43j n) ry day at the same temperature.g9ji*lyonwx jv3 4e(/j 3mm4wd b5tx)

Is it possible to boil water app+dp8pyiy04 m 9nk9h t room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperature is the same but the humidi d23( wrubvif9hmhf28ty is different. Which is more dense, t wfi8m2hr9(f3 vuhd2bhe dry air or the humid air at the same T? Explain.

Explain why it is dangerous to open the radiator cpodo2 pwl 0,n9ap of an overheated automobile enginew2po ln9od0,p.

Why does exhaled air appear as a little white cloud in the wintnozxp zd)h*(9er (Fig. 13–28)?

  How many atoms are there in a 3.4-gram cop/g;sp,taacuvxt ; oerq1v;9 4y2 p1gf per penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram go89kk v2ei ( ezeflw+8qm;6wqpld ring compare to the number in a silver ring of the q2k8z9k+eef wwp8m eq6l (i;vsame mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often tamh ijm8c.5qy0b j 85fdken to be 68°F. What is this on the Celsius scale?5fydmbmj qhc 0ij858.   $^{\circ} $ C
(b) The temperature of the filament in a lightbulb is about 1800 $^{\circ} $ C. What is this on the Fahrenheit scale?    $^{\circ} $ F

  Among the highest and lowesto b)iw t2mw9 :04gfc* h+r wenv20 oa9c/jwsmm temperatures recorded are 136 $^{\circ} $F in the Libyan desert and -129 $^{\circ} $F in Antarctica. What are these temperatures on the Celsius scale?high =    $^{\circ} $ C
low =    $^{\circ} $ C

  (a) 15 $^{\circ} $ below zero on the Celsius scale is what Fahrenheit temperature?    $^{\circ} $ F
(b) 15 $^{\circ} $ below zero on the Fahrenheit scale is what Celsius temperature?   $^{\circ} $ C

  In an alcohol-in-glass thermometer, the alcohol columnad+1q0euvut9*5rq qz has length 11.82 cm at 0.dz9t quu r5q*a+0e 1qv0 $^{\circ} $ C and length 22.85 cm at 100.0 $^{\circ} $ C. What is the temperature if the column has length
(a) 16.70 cm,    $^{\circ} $ C
(b) 20.50 cm?    $^{\circ} $ C

  A concrete highway is buipohm. 5ms7 2fdvnt/ u5lt of slabs 12 m long (20 $^{\circ} $ C). How wide should the expansion cracks between the slabs be (at 20 $^{\circ} $ C) to prevent buckling if the range of temperature is -30 $^{\circ} $ C to +50 $^{\circ} $ C?    m

  Super Inva$^{TM}$, an alloy of iron and nickel, is a strong material with a very low coefficient of linear expansion [0.2$ \times10^{ -6}$(C?)$^{-1}$]
A 2.0-m-long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this table expand along its length if the temperature increases 5.0 $^{\circ} $ C? Compare to tabletops made of steel.   $ \times10^{-6 }$ m    $ \times10^{-4 }$ m

  The Eiffel Tower (Fig. 13–29) is built of wrought iron approximately ;n h2oqe*2iep81 2oi8txpu du300 m tall. ethoinp*8ui;8px1oue2 2dq 2 Estimate how much its height changes between July (average temperature of 25°C) and January (average temperature of 2 $^{\circ} $ C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.    m

  To make a secure fit, rivets that are larger than3w7 gqpqa1 f (y*c+bns the rivet hole are often used and the rivet is cooled nygf7w 3b 1q*apscq(+(usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed in a hole 1.869 cm in diameter at 20 $^{\circ} $ C. To what temperature must the rivet be cooled if it is to fit in the hole?    $^{\circ} $ C

  The density of water e7 q1 n)mqgp q/8e9uiiat 4 $^{\circ} $ C is $ 1\times10^{3 }kg/m^3$ What is water’s density at 94 $^{\circ} $ C?    kg/$m^3$

  A quartz sphere is 8.75 uy,j u+w4 e/s1 0glrxxlv pi4;cm in diameter. What will be its change in volume if it u4r x+ ;1jw y vpli,/g4luse0xis heated from 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.dp-sx 7eoa phb6s ,.u(vb5/xd0 mL of water at 100.0$^{\circ} $ C. If the temperature decreased to 20.0 $^{\circ} $ C, how much water could be added to the glass?    mL

  It is observed that 55.50 mL7o3;iprm 4zyz1jlkiq,2e 0q0fqw*et of water at 20 $^{\circ} $ C completely fills a container to the brim. When the container and the water are heated to 60 $^{\circ} $ C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container?    $ \times10^{-5 }$ /$C^0$(b) What is the most likely material of the container? The density of water at 60°C is 0.98324g/ml.

  (a) A brass plug is to be placed in a ring made ofvvfs-/w; sjjc7yv/2mq dxc5t+eluo,. 7p:gr iron. At 20 $^{\circ} $ C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit?    $^{\circ} $ C
(b) What if the plug were iron and the ring brass?    $^{\circ} $ C

If a fluid is contained in a long, narrow vessel so it can expand in essentiap.2c nxqr q(jfjw:nue0- w*7v lly one direction vw.:qcjrjnuxq* (pn72 w0e-fonly, show that the effective coefficient of linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change in the deqi* hfe/,bfktx*v78 ensity $\rho$ of a substance, when the temperature changes by $\Delta$T is given by $\rho$ = -$\beta$$\rho$$\Delta$T
(b) What is the fractional change in density of a lead sphere whose temperature decreases from 25 $^{\circ} $ C to -40 $^{\circ} $ C？

A uniform rectangular plate of length l ajam5 o -8pwq-lnd width w has coefficient of linear expansioolq5m-wa8 j-pn $\alpha$ Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change $\Delta$T is $\Delta$A = 2$\alpha l w$$\Delta$T See Fig. 13–30.

Show that for an isotropic soljfld 2 p099ldd,c w.tmld,3leid, $\beta$ = 3$\alpha$ if the amount of expansion is small. $\beta$ and $\alpha$ are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13–30.]

  The pendulum in a grandfather clock is made of brass and keeps perfect tim,i92r) k+szjahu)j jys19isve at 17 a1+rs,uj2) vk9 i9js)zis hyj$^{\circ} $ C. How much time is gained or lost in a year if the clock is kept at 25 $^{\circ} $ C? (Assume the frequency dependence on length for a simple pendulum applies.)$\approx$    min(Round to the nearest integer)

  (a) The tube of a mercury thermo phi(;ha8 .m rolmk i,i;h5k;vmeter has an inside diameter of 0.140 mm. The bulb has a volume 8(hhh.; i mkmk;o,5ir ;a livpof 0.255 $cm^3$ How far will the thread of mercury move when the temperature changes from 11.5 $^{\circ} $ C to 33.0 $^{\circ} $ C? Take into account expansion of the Pyrex glass.    cm(b) Determine a formula for the length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

  A 23.4-kg solid aluminum cylindrical wheel of radius 0.41 m is rotating aboutrwwb fo/ 0 azbal9(pkez36 l:qxif*;7 its axle0a*9rbi;b( pz/z6xw3qewll: aof 7kf on frictionless bearings with angular velocity $\omega$ = 32.8 rad/s If its temperature is now raised from 20.0 $^{\circ} $ C to 75.0 $^{\circ} $ C, what is the fractional change in $\omega$?   

  An aluminum bar has the desir,qcaa)1 k 7puced length when at 15°C. How much stress is required to keep it at t ac1a upk,7)cqhis length if the temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sectional area 0.04a-sxz6wq )nade0 rx111$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diameter 134.122 q(o s0t( jw)f* yjx;oycm at 20$^{\circ} $ C is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 cm at 20$^{\circ} $ C. It is 7.4 cm wide and 0.65 cm thick.
(a) To what temperature must the band be heated so that it will fit over the barrel? $\approx$   $^{\circ} $ C(Round to the nearest integer)
(b) What will be the tension in the band when it cools to 20$^{\circ} $ C?    N

  What are the following te)hoc22g g,gpt hjg c3l.w.+y gmperatures on the Kelvin scale:
(a) 86$^{\circ} $ C,    K
(b) 78$^{\circ} $F,    K
(c) -100$^{\circ} $C    K
(d) 5500°C,    K
(e) -459$^{\circ} $F    K

  Absolute zero is whatr5x-lc ;(b8 te9jb. sxneqib9 temperature on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures inz28b:3yk)j m:7 +ns v4qep fyep qfz2l the interior of the Earth and Sun are about 4000$^{\circ} $ C and $ \times10^{6 }$ $^{\circ} $ C respectively.
(a) What are these temperatures in kelvins?    K    $ \times10^{ 6}$K
(b) What percent error is made in each case if a person forgets to change $^{\circ} $ C to K? $\approx$    %(Round to the nearest integer) $\approx$    %(Round to three decimal places)

  If 3 $m^2$ of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0$^{\circ} $ C. What is the volume?    $m^3$

  In an internal combustion engine, air at atmos. a61o 7wt)qmr 3+guqv l7iexbic4 eb:pheric pressure and a temperature of abouul77vw+t4exiriq.c)1g6m qe: a3 bo bt 20$^{\circ} $C is compressed in the cylinder by a piston to $\frac{1}{9}$ of its original volume (compression ratio = 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.    $^{\circ} $ C

  Calculate the density of oxygen o-8yu+9yiedh 1 iw*qiat STP using the ideal gas law.    kg/$m^3$

  A storage tank contains 21.6 kg of nitrogetrar0f69m/ len ($N_2$) at an absolute pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by an equal mass of $CO_2$    atm

  A storage tank at STP contains 18.5 kg of j lg1r .6 4lqtvw c4nvu27hy:cnitrogen ($N_2$)
(a) What is the volume of the tank? $\approx$   $m^3$(“Round to one decimal places)
(b) What is the pressure if an additional 15.0 kg of nitrogen is added without changing the temperature?    $ \times10^{5 }$Pa    atm

  If 18.75 mol of helium ge h .: f1t+6n)b(nhy9txbgl azas is at 10.0$^{\circ} $C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions.    $m^3$
(b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.    $^{\circ} $ C

  What is the pressure inside a 35.0-L containiws suy,c nb1o/t;j42 er holding 105.0 kg of argon gas at 385 wb oti;jy 1ss, c2un4/K?   $ \times10^{ 8}$Pa

  A tank contains 26.0 kg of /sx3q .rwxd+r $O_2$ gas at a gauge pressure of 8.70 atm. If the oxygen is replaced by helium, how many kilograms of the latter will be needed to produce a gauge pressure of 7.00 atm?    kg He

  A hot-air balloon achiev yx6nqlpp47 c0 aq):qfes its buoyant lift by heating the air inside the balloon, which makes it les7ppnlq:x0qf4 )ac q6ys dense than the air outside. Suppose the volume of a balloon is 1800 $m^3$ and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0 $^{\circ} $ C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.) $\approx$    $^{\circ} $ C(Round to the nearest integer)

  A tire is filled withrg 3cf:see t(d )n23eb air at 15 $^{\circ} $ C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 38 $^{\circ} $ C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained?    %

  If 61.5 L of oxygen akcxaqi6;lh ;x es1.4at 18.0 $^{\circ} $ C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 50.0°C, what will the new pressure be?    atm

  A helium-filled balloon escapes a child’s hand at sea level and 20.0 g4rnw(j*hj;f $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number53pjtl0 9jkuufn 29m p of molecules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there j,3 epi1jq7zv in 1.000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) molesi ,t:zs:tt1lb ,    $ \times10^{22 }$ 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. $\approx$    $ \times10^{46 }$ molecules

  A cubic box of volumek9eu d( pv:jh4fx/x dgm(jwl4hu g:73 5.1$ \times10^{ -2}m^3$ is filled with air at atmospheric pressure at 20 $^{\circ} $ C. The box is closed and heated to 180 $^{\circ} $ C. What is the net force on each side of the box?    N

  Estimate how many molecules of air are in each 2.0-L breath you inhale tnu *z9vvm9vi 0tk,k e, k5d2uahat were also in the lakaeiv uk5 dk 0,9*2tv9vzun,mst breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the aver k* :kevs/+tkxage translational kinetic energy of an oxygen molecule at STPx:vskt *+k ke/?    $ \times10^{-21 }$ J
(b) What is the total translational kinetic energy of 2.0 mol of $O_2$ molecules at 20 $^{\circ} $ C?   $ \times10^{3 }$ J

  Calculate the rms speed of helium atomz1)go j 1de +fy((ulors near the surface of the Sun at a temperature of about 6000 K. fz(reyod)uj1l (+g1o   m/s

  By what factor will the rms speed of gas mol2fmh rx: -zs4xecules increase if the temperature is incr shm-x2:4rfz xeased from 0 $^{\circ} $ C to 100 $^{\circ} $ C?   

  A gas is at 20 $^{\circ} $ C. To what temperature must it be raised to double the rms speed of its molecules?    $^{\circ} $ C

  Twelve molecules have the following speeds, given in unitsvdpo igrf0-t )4 ;dets4b r:doyaf+13 of km/s: 6, 2, 4, 6, 0, 4, 1, 8, 5, 3, 7, and 8. Calculate td4t)-s g04o ;+ed 3bprrtodfafiy 1: vhe rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in anv;c1xe xc /+1tjov(n gas at 20.0 $^{\circ} $ C is to be increased by 1.0%. To what temperature must it be raised?    $^{\circ} $ C

  If the pressure of a gas is doubled while its volume is held constant,l g k.g9nx6wu d205onx 4eu8sc by what fa6k. n09ul2xdxwco 5 e8ggus4nctor does $v_{rms}$ change?   

Show that the rms speed of molecules inf g-lu,njwcm;( x0 2fj a gas is given by $v_{rms}$ = $\sqrt{3P\\rho}$ where P is the pressure in the gas, and $\rho$ is the gas density.

Show that for a mixture of two gases at the same temperature, the rakys,p7 (vjbjx tsn 6.2tio of their rms speeds is equal bp26,vjj t7s(snkx. yto the inverse ratio of the square roots of their molecular masses.

  What is the rms speed of nitrogum49p.*eo h/ts/ t jxqen molecules contained in an 8.5$-m^3$ volume at 2.1 atm if the total amount of nitrogen is 1300 mol?    m/s

  Calculate (a) the rms speed of an os wug408: rz5iz0iwe oxygen molecule at 0 $^{\circ} $ C    m/s
(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 collisions with other molecules.    round trips per sec

  What is the average distance between nitrogen molecules at STP? i-1-m j/7e z v kvr1:3 0qhkaycym,ul.tb+b xt   $ \times10^{-9 }$m

  (a) Estimate the rms speed ofl 3 ,e6szicaqz+.u7fb an amino acid whose molecular mass is 89 u in a living cell at 3z3ul . 7bisq+c6zaf e,7 $^{\circ} $ C.    m/s
(b) What would be the rms speed of a protein of molecular mass 50,000 u at 37 $^{\circ} $ C?    m/s

Show that the pressure P of a gas z5m rj -r8ij+kgcu* s:can be written P = $\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of ura6ea9wj se1 w)knium, $^{235}$U and $^{238}$U (the superscripts refer to their atomic mass), can be separated by a gas-diffusion process by combining them with fluorine to make the gaseous compound UF$_6$ Calculate the ratio of the rms speeds of these molecules for the two isotopes, at constant T.   

(a) At atmospheric pressure, in what pzl64b p;ueitpw (b0j0hases can $CO_2$ exist? (b) For what range of pressures and temperatures can $CO_2$ be a liquid? Refer to Fig. 13–21.

Water is in which phase when the pressure is 0.01 atd+ux j, xo7l ;mt)z*cbm and the temperature is (a) 90j+ zlxu, dc*)mx ot;7b $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximhixl5l yl)a2,ately) if the humidity is 50% on a day when the temperature is)i2l,ayx hl5l 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where water boils at 9:zjp;wkuz5th. f a 5o.0 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particuhhfc56q 7:eu /n yqe:ylar place in the mountains is 0.72 atm, estimate fh/57:ecu yn 6:heyqqthe temperature at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressu1ksbyp0 oe )j7re of water is 530 Pa and the relative humidity is 40sk)yj70e 1bop%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a9hobsiww q7iv. v/9 k,8+f, fx(hs gtd day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside a pressure cooker if the water xo; vu23y+4w ruu3eb jis boilin4 u3+ur b2; exvow3jyug at a temperature of 120 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a room of vp;n37rqssow ve8yi:/ m6 o/mholume 680$m^3$ at 25 $^{\circ} $ C is 80%, what mass of water can still evaporate from an open pan?    kg

  Air that is at its dew poinqwz4j1m7aw1 yah kn.)t of 5 $^{\circ} $ C is drawn into a building where it is heated to 25. 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 glyci2n-fbf*l7nelg kf c3 ifoz963 ne molecule (see Table 13–4) to diffuse a distance of 15 f fo2 n*c- f36zn7l f9iegb3kl$\mu m$ in water at 20$^{\circ} $ C if its concentration varies over that distance from 1 mol/$m^3$ to 0.4 mol/$m^3$ Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u. t $\approx$    s ([color=rgba(0, 0, 0, 0.85)]Round to one decimal places) $v_{diffuse}$    $ \times10^{ -5}$ m/s
$v_{rms}$    m/s

  Oxygen diffuses from the surface of insects to the interior through l*fkus aw*(v v in/g:f),n 8katiny tubes called tracheae. An average trachea is about 2 mm long and (nav*k8n: ,)ali kvw/fsg fu*has cross-sectional area of $ 2\times10^{-9 } m^2$ Assuming the concentration of oxygen inside is half what it is outside in the atmosphere,
(a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20$^{\circ} $ C is about 8.7 mol/$m^3$ then $\approx$    mol/$m^3$(Round to one decimal places)
(b) calculate the diffusion rate J,    $ \times10^{-11 }$ mol/s
(c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $ 1\times10^{-5 } m^2/s$    s

  A precise steel tape measure has been calib2l vavq/g3 .yzi-1 s 4o3cw,g yd2xvpbrated at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A precise steel tape measure has been calma. o t uyngn7k/abr32arx823ibrated at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A Pyrex measuring cup was calibraci d/u)tbmo(nrxpe*n1/ 1 1 r.ml +uqfted at normal room temperature. How much error will be made in a recipe calling f1xn)l q1mu/erubdom. ni+r (ft/1pc * or 300 mL of cool water, if the water and the cup are hot, at 80$^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a helium gas cylinder is initially 28 atm. Afcagqe;l)yxq x2 56 k1tsg8mx e6-bvz;ter many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of thev6 eqb1l;t xymzxx-85s2ka )gcq g;6 e original gas remains in the cylinder?   

  Estimate the number of air molecu52 4lrym ,ezzo1o,tt jles in a room of length 6.5 m, width 3.1 m, and height 2.5 m. Assume the temperat,zo1t t45 lj2 ozr,emyure is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density ozehv199o7 vsof matter is about one atom per $cm^3$ mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).$v_{rms}$ =    m/s    $ \times10^{-22 }$ atm

  The lowest pressure attajc9)jwz +bl(m ct0s((iohb-pinable using the best available vacuum techniques is about hl(ibwbs( p jtzjo)m0(+c-9 c$10^{-12} N/m^2$ At such a pressure, how many molecules are there per $cm^3$ at 0$^{\circ} $C?    $\frac{molecules}{cm^3}$

  If a scuba diver fills his lungs to full capacity of 5.5 L when 10 m epd rj;70sq1/w3 a zqjbelow the surface, to what volume would his lungs expand if he quickly rose to the surface? Is this advisa rwaqz3se0;/dq17 jpj ble?    L

  A space vehicle returning from tgmislk a2mu9t2 ;g( 1i:x oed lm66jl5he 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 materials; indeed, part of it does vaporize,g2 6s 5 to:i2xj;e (d6ulmkamimgl9l1 and this is seen as a bright blaze upon reentry.)    K

  The temperature of an ideal gasd i6-/i wd6 i8bclqki) is increased from 110$^{\circ} $C to 360$^{\circ} $C while the volume and the number of moles stay constant. By what factor does the pressure change? By what factor does $v_{rms}$ change?$\frac{P_2}{P_1}$ =    $\frac{(v_{rms})_2}{(v_{rms})_1}$ =   

  A house has a volume of 77ug iba:d r7(ekh,f;6w-hv*ix 0m$^2$ (a) What is the total mass of air inside the house at 20$^{\circ} $C?    kg
(b) If the temperature drops to -10$^{\circ} $C what mass of air enters or leaves the house?    kg

  From the known value of atmospheric pressure at the s:7a os,fq u(olurface of the Earth, estimate to,lf:qa s(ou7 he total number of air molecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogvu5c-k ;b+loren molecules contained in a 7.6$-m^3$ volume at 4.2 atm if the total amount of nitrogen is 1800 mol?    m/s

  A standard cylinder ofi f( 3q0;uncdx oxygen used in a hospital has gauge pressure = 2000 psi (13,800 kPa) and at T = 259K How long will the cylinder last if the flow(quixdf3 nc;0 rate, measured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mec2+rd n 0okq/yx0+d y f,q8skgsk;u0urcury at 0$^{\circ} $C. (a) If the temperature is raised to 25$^{\circ} $C, will the cube float higher or lower in the mercury? ----待选择----lowerheigher 
(b) By what percent will the fraction of volume submerged change?    %

  The density of gasoline at u xil ck8cxjp9a,hn6 6,z3,yg0$^{\circ} $C is 0.68$ \times10^{3 }kg/m^3$ What is the density on a hot day, when the temperature is 38$^{\circ} $C?    kg/$m^3$
What is the percentage change?    %

  If a steel band were to f;ysr e1 tc3;hooleb.eyo iw)7 tc5g/)t* dx y3it snugly around the Earth’s equator at 25$^{\circ} $C, but then was heated to 45$^{\circ} $C, how high above the Earth would the band be (assume equal everywhere)?    m

  A brass lid screws ti-7srzwdn rx771 18u hrjqce.tghtly onto a glass jar at 20$^{\circ} $C. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 60$^{\circ} $C. The inside diameter of the lid is 8.0 cm at 20$^{\circ} $C. Find the size of the gap (difference in radius) that develops by this procedure.    cm

  The first length standard, adopted in:qmv0-s0k(yc3 cce hc the 18$^{th}$ century, was a platinum bar with two very fine marks separated by what was defined to be exactly 1 m. If this standard bar was to be accurate to within $\pm1.0 \mu m$ how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion for platinum is $ 9\times10^{ -6}C/^{-1}$. $\pm$ =    C$^{\circ} $

  A scuba tank, when fully charged, huost21huft b 6p4g9w*2 vtxer ;+g 3ekas a pressure of 195 atm at 20$^{\circ} $C. The volume of the tank is 11.3 L.
(a) What would the volume of the air be at 1.00 atm and at the same temperature?    L
(b) Before entering the water, a person consumes 2.0 L of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last?    min
(c) At a depth of 20.0 m of sea water and temperature of 10$^{\circ} $C, how long would the same tank last assuming the breathing rate does not change?    min

  The escape speed from the Earth is88ohkt4 3,j,ij-acfij-yq m y $ 1.12\times10^{4 } m/s$ so a gas molecule travelling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field. At what temperature is the average speed of
(a) oxygen molecules,    $ \times10^{5 }$K
(b) helium atoms equal to $ 1.12\times10^{4 } m/s$    $ \times10^{4}$K
(c) Can you see why our atmosphere contains oxygen but not helium?

  A 1.0-kg trash-can lid is suspendedmy mhv2 uur43g61yk*q against gravity by tennis balls thrown vertically upward at it. How many tennis balls yg16*rmmh qv k 42uu3yper second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diamo d61pxcue6u2k6 6cmug 3z e-jeter (spherical) bubble of air from a depth of 14.0 m in a lake. Assume the temperature is constant at 298 K, and the air behaves as a perfect gas. How large i6cm6ueu2z6jk3gou 1 d -6pcex s the bubble when it reaches the surface?    cm

  Calculate the total water vapor pressure in the air on the following two days: qwzpvwcfw;+p0)) q)t qtvc)+0)qw fpwp)z;w
(a) a hot summer day, with the temperature 30$^{\circ} $C and the relative humidity at 40%;    Pa
(b) a cold winter day, with the temperature 5$^{\circ} $C and the relative humidity at 80%.    Pa

  A sauna has 7$m^3$ of air volume, and the temperature is 90$^{\circ} $C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 13–3.)    kg

  Estimate the percent diff: 5-wa ithd9iierence in the density of iron at STP, and when it is a soitd:ih -5i9walid deep in the Earth where the temperature is 2000$^{\circ} $C and under 5000 atm of pressure. Assume the bulk modulus (90$\times 10^9N/m^2$) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.    %  ----待选择----decreaseincrease 

(a) Use the ideal gas law to show th31jmzx896qx k fvio : tx4sxk;at, for an ideal gas at constant pressure, thx6 9k43 m:oz8vs xxtx jiq1;fke coefficient of volume expansion is equal to $\beta$ = 1/T where T is the temperature in kelvins. Compare to Table 13–1 for gases at T = 293K (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P where P is the pressure.

  In humid climates, people constantly dehu;p;w) y9iss wm:.51pclcq lgumidify their cellars to prevent rot and mildew. If the cella;s;s.ql):i upc9lc ymp g5w1wr in a house (kept at 20$^{\circ} $C) has 95 $m^2$ of floor space and a ceiling height of 2.8 m, what is the mass of water that must be removed from it to drop the humidity from 95% to a more reasonable 30%?    kg