Which has more atoms: 1 kg of iron or 1 kg of alumfcctoe; c2f. l,ux5+ ninum? See the periodic table or Appeocx,t 5u;cfne f2+lc.ndix B.

Name several properties of materi):oez.9y oi vyals that could be exploited to make a thermomet)e:yy9. o ivozer.

Which is larger, 1 C 08r9 *xxopasn$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with(ipx b(-g q -*c6 vbdi0by,kbe system B, but B is not in thermal equilibrium with system C, b kqvx06-igd c(-,ipy(bbb * ewhat can you say about the temperatures of A, B, and C?

A flat bimetallic strip consjg2j wh4 dl76wists of aluminum riveted to a strip of iron. When heated, the strip will bend. Which metal will be on the outside of the curve? [Hint: Seewljhw2d 7gj4 6 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 ofnlaoc1bfb.b7l - p5 -5w vria. 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 siup*pkzc 14- l8 *bcfehmple thermostat used to control a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid mercury that conducts electricity when it can flow to touch both contact wires. Explain how this dez-81fep*ulkpc h*4c bvice controls the furnace and how it can be set at different temperatures.

Long steam pipes that are fixed at the ends often have a section in the shape of*7qo66 ntw .ayyjqi -f a U. Why?6q j.yf6a-onqyt7 *wi

A flat, uniform cylinder of da7k+n0hrqjce-zy2 zq h)n1 :lead floats in mercury at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glaszsrq8:1q/ z aps thermometer is first placed in a hot tub of water, th/a8q 1r p:zqsze mercury initially descends a bit and then rises. Explain.

A glass container may a*6u f: roq3utbreak if one part of it is heated or cooled more rapidly than adjacent parts. Explai6*f: qaoutu3 rn.

The principal virtue of Pyrex glass ze+ yqig.hel3 x77vo8 is that its coefficient of linear expansion is much smaller than that for ordinary glass (Tablqizlxg8o7h v+ 73 ee.ye 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather c6 dn lq(a4/ykya4zv k4lock, accurate 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 sodpez89,,c jyvlzw83 l.xq(b t ya will cause its bottom and top to bulge so badly the can will not stand up. What haw( p, cy lxeql8 8bzyz.,9v3tjs happened?

When a gas is rapidly compressed (say-tpag.r i( 8ay, by pushing down a piston), its temperature increases. When a rt.g8a(i-a p ygas expands against a piston, it cools. Explain these changes 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 an aluminum sphere submergiwb+ kx ddh3t7tsz26;ed in water increase or decrease if+hitzd;6x3k72 btws d the temperature is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law fo9lwcc3*j l4iillows from kinetic theory and the relation between average kinetic energy and the absolute temperature9 wcjili3l4c*.

Explain in words how Gay-Lussac’s law follows fr)/ p2x/i7eb9 ol+ sieic2pavv om kinetic theory.

As you go higher in the .i k(ta 8zp)kmEarth’s atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minimum spefmoaok4b-q 4z6bpu5z* 2mks9 ed an object must have to leave the Earth and never return. T*kua29zmq64b5o-4fzms po b khe 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 Moon has practically no atmosphere.

Alcohol evaporates more quickly than water at ruf)w0lujt3*x1x g/dqoom temperature. What can you infer about the molecular properties of one relul* x/d1j0futq 3xw)gative to the other?

Explain why a hot humid day is far more uncomfortable than a hot dry dzx: kzgy k)1.bay at the same temperayb :.)zk gxk1zture.

Is it possible to boilsdl3,mg, ;hla4 1z pap- +izxm water at room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperature is0qdo:j 4m4du uwsa 1/x the same but the humidity is different. Which is more dense, the dry air or the humid air at the same To duxu1 :awm4/j0ds4q ? Explain.

Explain why it is dangerous to open the radiator cap of an overheated automob/d ou ybtp2.5mile enginuo mdt/.y25pbe.

Why does exhaled air appear as a little white cloud in the winter (Fi l,o pfh8ys,ok- s apk4j)ov76g. 13–28)?

  How many atoms are there in a 3.4-gram copper pent/m. sjp, j9aq+ 6abgx*h- rcjny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring compare to3;c+,s8h:jhzjd /qmyfu6 sy m the number in a silveu6j s/8 cjhy;+zsmqhf:m, 3 ydr ring of the same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. What is zcx+ *m*g;z1pjx r;aac bmy:67so w1zthis on the Celsius scale?z*p o+s1b6c:cy;*w xmzm1 j; rzaaxg7    $^{\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 lowest tempe: b /u3my)d ank1lql+wda,j j;ratures 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 al56b87yime 5wj j-5d;j tfs1pwt2nchncohol column has length 11.82 cm at 0.5 hf5- enj68w m;5scb jp d1tiwnt7yj20 $^{\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 built of slabs 12 vofs (jdgm ;*u u9tl)0m 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 wra f*7jg6k-mb,):xij / ht:n v7q dajkcought iron approximately 300 m tall. Estimate how much its height cfjk7tha7v : aq6-xcj*k:m),jinb/ d g hanges 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 th r7+0csg4he;5 sitwkhk90hes at are larger than the rivet hole are often used and the rivet is cooled (usuallyk;sc4eeh5 h+00r9wht iks7gs 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 at qlmr8 t*rbny/ m2472l*b a kpqbmd7b5 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 cm in diameter. What will be 0c(a;yrqkxed 3rji.(((bipdn34 sq qits change in volume if it idqy4 0(qqsc3x j;d(i( pnb3. e(kraris heated from 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 mL ofuv y4)h jd/gt2 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 55.50qkai0gn8 .1vw mL 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 of iron. At 20 )l4m: xhxy qp:$^{\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 gfgkr;3 ;g - pqsi aa m-u/zhj( x29qly6r-z5vin a long, narrow vessel so it can expand in essentially one direction only, show that the effective coefficient of linear expansion is approximately equal to the coef- ay(j2- r5rv9;ux3/km z6zhgl;sf-a gqgpiq ficient of volume expansion $\beta$.

(a) Show that the change in thfl .)hjjwz/t2 b7(h;,ta ,utran 6 nole density $\rho$ 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 and width w has coefficient o,ks eh/v 1 kclw4 ,pwcip/h1v,f linear expansion,c,vw/h ,1i1 p/cw4l hpekvks $\alpha$ 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 so+g cd 2m.n edmf(ke8j8lid, $\beta$ = 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 cbiiey: )ws7 u:lock is made of brass and keeps perfect time at 1 i:es:w7bi)y u7 $^{\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 thermometer has an inside diameter of 0vjes0 n1j,db)yd *we1.140 mm. The bulb has a volume of 0.250nj)be,w*se vy 1dj d15 $cm^3$ 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 cylip2 d.ljys:y29i ie4 mzndrical wheel of radius 0.41 m is rotating about itpz y2ld4e.mi i92s: yjs axle 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 desired length when at 15°C. How much stress is requib;ex-46ydywf n, ll(fred to keep it at this length if the nflw6( y4fd ,-;ye lxbtemperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sectional arec.p ,;r gxe15xsw cq/pa 0.041$m^2$ 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 c 4( xjdf(.2dd-roeeem*b, khcm 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 tempergl/eni u 4t33 1+hz bobg88jcuatures 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 what temperature on the7 s1.e(*tghz tjwv u;q svi(z: Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth at4nht .lx0t/ dnd 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 atmospheric pressure ag4 v4zn udu)t wn4o20j,alx)q nd a temperature of ab2xqd,ou unz 4)t)vj4glw 0na 4out 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 at STP using the ideal ga:b 12*uvovewh5r r3 bes law.    kg/$m^3$

  A storage tank contains 21.6 kg of nitro( w7jeulrd;x8,xw2hs6o r*h rgen ($N_2$) 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 h h53i(tx b.acaztf*y) ;jur *of nitrogen ($N_2$)
(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 gas is at 14bmb+ s(xwwnr: u -en-0.0$^{\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 container holdi/ky i 4fqi9x l ,a5c/qb3tzqj;ng 105.0 kg of argon gas at ixl / ;ty43zq,akq 9b ijc5qf/385 K?   $ \times10^{ 8}$Pa

  A tank contains 26.0 kne (7k2 ripy8b.cr6:bdzqk t)pdy5f4g of $O_2$ 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 achieves its buoyandi1to r q6i87ut lift by heating the air inside the balloon, which mio86 qd 7r1uitakes it less 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 with air 187ij 5sgtn 7 jrhroq(u/9h piat 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 at 1*( zwkyf:.gvn 8.0 $^{\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 cha4fakn0)bv- r ef xc5)ild’s hand at sea level and 20.0 $^{\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 number of moleculz,. zxr2fzb4 ees / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water-u q.d0ovcrno0v0c 69vosm7n are there in 1.000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) axt 0 hirvgrl. 5qp)po ;*z;e9moles,    $ \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 volume 5.1u5n c6//c5ei3xu 0ojpbdq/ il$ \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 +hiwemwz1 w .xyud +76 v+9fawthat were also in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and of constant density.e1+6 mw w.+fizwuhwxy dv+7 a9]   $\frac{molecules}{breath}$

  (a) What is the average translationalvcv s12hh9)hubnae f(1o i,d4 kinetic energy of an oxygen molecule at STP? dhhu f912 ,bvhi4)se1oa c(nv   $ \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 atoms near the surface of thef opu f9z,+bh3s po.5epa3a3 g Sun at a temperaturefa+.3 puof hb9sa3pop 5, ez3g of about 6000 K.    m/s

  By what factor will the rms spe; gqhk2uh6zbl)k 6v7 c64qhsred of gas molecules increase if the temperature is increabsq vk rc 667uhg4;zq)kh62h lsed 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 uni3x egw1b br61uts of km/s: 6, 2, 4, 6, re1x3b1buw g 60, 4, 1, 8, 5, 3, 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in a ye gs1y7v+y k:c )xzf9gas 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, 61to.0wcbq( -j mb h+zj1fxpxby what fcpmf.o6x1b0zj xh (j-qbwt +1actor does $v_{rms}$ change?   

Show that the rms speed of moleg ubt +blk53pfvkn*5 jzz+5-b7xd :mfcules in 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, s lyqrpg0 apqh t9q ,*(1+.ylhthe ratio of their rms speeds is equal to the inverse rarh,lgy*9q 0ah1+y(pqqp s .tltio of the square roots of their molecular masses.

  What is the rms speed of nitrogen molecules contained in an 866hanv iq+hq0fm(it gvh)(6 t5a g3 d0zwdd9o.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 br,-0allz2cp9 j wwf8n 9uz tw3qha4+ 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 1,t q3cs/ph nnyzny99 molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose molecxabv + q7qvy7w-1ki8 3fs. zlrular mass is 89 u in a living cell at 37 sxv yr+.a iwbk lf37 81q-zq7v$^{\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 can be fr3v dtq /3md1written 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 6h pe483tvdxlnrj3w3pk auiap 0 y2s*:;lp n:uranium, $^{235}$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 pht1(veq2 v)iy+om5.mc5qc bn qases 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);olf(n; r6v gh7 z7za)lrjhz is 0.01 atm and the temperature is (a) 90z (7r7a; ) gh)zjhln lozvf6;r $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (apquapy :fw)6* gn-b)7x1rm vsiproximately) if the humidity is 50% on a day when the tem7f) qm r6-uavipg n )ybx*1w:sperature is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressurw50 :qhcodr4l3xx 3eue at a place where water boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in tht,+ 1n tkcpwl*z 23hlee mountains is 0.72 atm, estimate the temperature at which waterztk1*e,2+ tw 3hlcl pn boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure of water is 530 Pa*jf9r qdnxm.9 zsk (*2)g9witxod 0 cz and the relative humidity is 40djq x*rgm 0oc.k 2*zd9xz9f n9 wst)(i%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a ih 9jm( u-0u;xwe3njm day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside6k2 gxxwz *ax7zb5f4a a pressure cooker if the water is boiling at a tempeb7 gz6x kax*xafw2z54rature 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 volume 68 88 8); ,pgdtqituuzoubqf7)m0$m^3$ at 25 $^{\circ} $ C is 80%, what mass of water can still evaporate from an open pan?    kg

  Air that is at its dew poi3ocu6e( bfrky o2. hq3nt 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 glycine molecule (see Table 13–4) to diffuse a di6 iohci- ;.h/1r6h /ldaeun dostance onhd/h 6heii .d1ao; co-lru/6 f 15 $\mu m$ 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 interiorx-w hzb ejq* .u+i4py, through tiny tubes calle+x*4qihuew -. z,pjb yd tracheae. An average trachea is about 2 mm long and 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 beenz:ssc (yoe o;9/wmu: utk9,r h calibrated 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 measure9imdy ;(.g7 .pcwa;mmxkl fg 5 has been calibrated 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 calibrated at normal room temperat ihikuy qmrdl2qv+ 0v6(7n1(jure. How much error will be made in a recipe calling for 300 mL of c((l hyuvq2r0v+ikj 7 n6dmqi1ool 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 ikhdz1 2qjr -(g2d5gtw s initially 28 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the original g g (jdwrdkg-q 252hz1tas remains in the cylinder?   

  Estimate the number of air molecules inb fy4up ;j*h6 qz2rg(s(6cdie a room of length 6.5 m, width 3.1 m, and height 2.5 m. 2 su6j hdq(fi4eryb g;(p*6cz Assume the temperature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of matter is nr2:kl3c zgvd0i;ln7 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 attainable using the best available vacuum techniquehq-lvag9 xv. 5ua 5d, 0xyb+ges is aboux5 dg9u.axa,h+ vyl 0q -eb5vgt $10^{-12} N/m^2$ 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 fulttsdo pky4 /ai0s5z0l p)1 a2ng:1kqgl capacity of 5.5 L when 10 m below the surface, to what volume would his lungs expand if l25tpkts p/) oyg1q0 a :4na0s1zg dikhe quickly rose to the surface? Is this advisable?    L

  A space vehicle returningjg7 v d;cga(3ezs 1rh*f1owm* 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;gc7 he*3wv(1 afrdsgj *zm 1o temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)    K

  The temperature of an ideal gas is 6 kg::;cx(ll ihfwd4dincreased 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 7700hwk oo e2f(59, ufrtsm$^2$ (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; m 37)ol5b9nb9 c/sdq2atc1dir nh kv atmospheric pressure at the surface of the Earth, estimate the total number of air molecules in the Earth’299/1rn l da cbdbtvck qsion)5h;m73s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen molecules contained ic257p3 ery1)3(:araspsfc ktab gg 0vn a 7.6$-m^3$ volume at 4.2 atm if the total amount of nitrogen is 1800 mol?    m/s

  A standard cylinder of oxyzl:. f:. xfaytntsgu/dn;- h0gen 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 rate, m- ga0t/ult:f xzdsn:n .;. hyfeasured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of-l ft2t1g 6, ovagbxa6 liquid mercury 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 gasoli pswfu*9cm 5w63 hjmd:a uc0b1ne at 0$^{\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 fit snugly ar *r h.x7a.vuigz0s/q q:7;sy tu znqy(ound 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 tightlios(fo+vh4 2(ze oc8n (jzku1y 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 stan93kzezex i*f 8dard, adopted in 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 charge6s e*1)bvz-xd g:. x+c8zn+ fij jskbed, has 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 Eart-c jb2 haxz237orl)9 pybrlw( r:o6 qfh is $ 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 lirw daos:b 67v.d is suspended against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown aws ad76ob r:.vt 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diameter (spherical) bubble hczf7k ju6d.2 of air from a depth of 14.0 m in a lake. Assume the temperature is constant at27z6chkdj uf. 298 K, and the air behaves as a perfect gas. How large is the bubble when it reaches the surface?    cm

  Calculate the total water vapor pressure in the air on the followingl,oyy* h8uy -n two days: *h8 on- l,yyuy
(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 difference in the density of iron at STP, and whxf kq),t .ky9xen it is a solid deep in the Earth where tkq) yk.9xtf x,he 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 that, for an idea0ve+w no:i-f el gas at constant pressure, the coefficient of volume exp 0+wi-vfeone: ansion 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 dehumidify their cellars to prevent h( to -egpzt(*za41 xqrot and mildew. If the cellar in a house (kept ( 1p(qga4 zeh-x*zottat 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