Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the periodic table )ldqs)wvek-k70d .xin4l m( m or Appendix x.(ksi deqml k7))n-4w d l0vmB.

Name several properties ov(0t*(oitrl dl4 m ddo td17-nf materials that could be exploited to make a thermomete1 * 4vindt (rtmdtld7o(l- o0dr.

Which is larger, 1 C ls+z6/a fz b0 sdk+ii8$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with system B, but B is not in thermal equl 4vryh;at/ fu(/kkur2dr2.-rdnw a8 ilibrium with system C, what can you k./ uarrlft2-yr radnvw;hdk2(48/u say about the temperatures of A, B, and C?

A flat bimetallic strip consists of aluminum riveted to a strip of iron. Whar/aa. b*/lh+hcu(w ven heated, the strip will bend. Which metal will be on the out ( ara *h.+//clhubwavside 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 o1 a;mfuzc- pu *mtehg .s9ds)+ e+/rhxf 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 diagratp.*pxg/egho)m : 7bthf( dh2m of a simple 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 device controls the furnace and how it can be set at different temperatur(fg*hp hb7g/oted tx.)p: mh2 es.

Long steam pipes that are fixed at the ends often havqz wkwp( zj) .f4r+oq,e a section in the shape of a.z+qqjzw ,(wfk p4o)r U. Why?

A flat, uniform cylinder of lead flo, ;yk+2igsrk waw,lu 7ats in mercury at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-gld gig c;3bp2eh4b(a6aum ,(w zass thermometer is first placed in a hot tub of water, the mercury initially descends a bie(z h;cpmgw4bidb ,(aa3u62gt and then rises. Explain.

A glass container ma,o6 c. uu:54gkm nbk.;nrecqc y break if one part of it is heated or cooled more rapidly tha4cu5 , un.eoqgrnm kk:6.bcc;n adjacent parts. Explain.

The principal virtue of Pyrex gla0t wxtx-2o4zi ss is that its coefficient of linear expansion is much smaller tha4iw t- ot02zxxn that for ordinary glass (Table 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accura,bszi9o (t1n w2b wy/ate 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 cause its bottom andof/.axxqe: jxi(.9*isx 1mlj top to bulge so badly the can will not stand up..oq 9si.lxj1*j:faxxx/e m i( What has happened?

When a gas is rapidly 6mrm4 ;5tog 7jo-c ub8ttid 9ll)il(a 2/zsqacompressed (say, by pushing down a piston), its temperature increases. When a gas expands against a pqdtsjm2co bllzt94io a);( gu 6am /7 r8it-l5iston, 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 sphernna6htp n 8o+6vob /6q:/ a*+ bwzmefwe submerged in water increase or decrease if the temperature +n6 onvtah*w6 /: eb+mbzop fa 8/wnq6is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinetic theory and the relatio fyqu1dehmv7+g d)r hk-)a* f4n betaqk-*vrfg fmue+h 417ddhy )) ween average kinetic energy and the absolute temperature.

Explain in words how Gay-Ltoj*j.0 kb:vj .hh6x02bj2iu9 j nyywussac’s law follows from kinetic theory.

As you go higher in the Earth’s atmosphv co(l)plkud ashmi 9nxl1c56r+5t, )ere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minicxlr,0 w4yzd2 2dw1gymum speed an object must have to leave the Earth and never return. The escape velocity for the Moon is about one-fifth what it i02, d wyzwrc21xy4lgds 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 room temperaturdyn5jx s -a6qls,s1uudt6)g ;l z.i+i e. What can you infer about the molecular t) ag-liyqs , ;u. 6ujind5zsl61+ds xproperties of one relative to the other?

Explain why a hot humid day is far mok ie q-vdr9 zhr1;oh.n,y(;n dxp ;3jore uncomfortable than a hot dry day at the same temperan;ryj od ,pnv9i ;;-1(kh 3.qerd zxhoture.

Is it possible to boil wah+fsp,u2 2qo dter at room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when c uchh ;+r9hd7the air temperature is the same but the humidity is different. Which is more dense, the dry air or the humid air d+h7 h ur;hcc9at the same T? Explain.

Explain why it is dangerous to open the radiator cap of an overheated automobiz/5 bqwcfm,+ qle/zb ,+m c5qqfw engine.

Why does exhaled air appear as a little white cloud in thegahqwe vcw1m i ,*.8sv1kpfp/u*en )* winter (Fig. 13–28)?

  How many atoms are there in 8bqjor4 ;gcq(7 pysfn2/ol h0 owl/htq,,qz8a 3.4-gram copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring compare to the numbynpui)8lbm:j8ha 5 * ber in a silver ring of tu p:85n )b lj8yi*bamhhe same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” iso,6g00 gph.hi:jo ray often taken to be 68°F. What is this on the Celsius scale? yih,ho gg6.0: ojr0ap   $^{\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 temperatures r vh9js3nkeh; hkypgg.nhf s)7t(9n(0ecorded 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 column has length 11.82 cm ;/6-gjtba0kfiu :0 4hrh zv fkat 0.0 fifhkb;t a u0r:-j6/vg04khz $^{\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 1(np diwa*bm ,v i8xe.02 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 wroughi*ap ;vo:hi k4wwlf79t iron approximately 300 m tall. Estimate how much its height cha:9 pki ;w4ifl woa*7vhnges 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 than the rivet hole are ofp*be )u9u is1ften used and the rivet is cooled (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 d)sf*ub puei 19iameter 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 4 j9).k-7yr mop- yrdsq$^{\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. gt(wb5 ;5cyhoWhat will be its change in volume if it is heated fg(h; boty 55cwrom 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 3i bv;u7kxsp l..nms- 650.0 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 mL of water as* *7ps:ttpz5q xn j4desz d0/4 k6a ,9cxcpgst 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 plt rmjgex 16j/ugqk /-7aced in a ring made of 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 vessn,g*otsvz , oz.i 8,flec,8ssel so it can expand in essentially one direction onn8l vgzofs,,8e*s,,c.so tz ily, 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 vke(stf( (v*7gxq7bz i +o o8qdensity $\rho$ 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 lennr. p/z)j q ddw:1;mjmgth l and width w has coefficient of linear exrpd);z w:1n jqj/mdm. pansion $\alpha$ 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 soli:xqn:jw8 k5m wd, $\beta$ = 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 grandfagag/5 m:+w miather clock is made of brass and keeps perfect time at 1wm5 /g+m aig:a7 $^{\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 mercuryy/-y fi +s+nsu thermometer has an inside diameter of 0.140 mm. The buy+sn-uyi sf+/lb has a volume of 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 cylind+j *1iad 4dru :j)zxznrical wheel of radius 0.41 m is rotating about its axle on frictionless bearings with angular veludxj)a zdjizn* +4r1:ocity $\omega$ = 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 tw (dlgjoe:m1.xvh 5w3he desired length when at 15°C. How much stress is required to keep it at 1h( w evm:x3dgow.5ljthis length if the temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel 0e l0ifwm+ x6mI-beam of cross-sectional area 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 134.1b ;3lo+9q.w/pjpudc ;.vxodm22 cm 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 ts( lbq 7;uhmc(emperatures 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 tempera+;eys2ws 28;fvo n8wahgv/o lture on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth and Sun axc 78icg p;.23,z vhfq9b cyvlre 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 combustchd(: *r66t3eit(.iuywejk i ion engine, air at atmospheric pressure and a temperature of abew * 6ck(te(hit6iidur:y.3jout 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 gas eoeal0ubonh y/rk/ 9c(*j3s.vraiv+jg*19b law.    kg/$m^3$

  A storage tank contains 2 tp0wx85tqfl9;yg/de1.6 kg of nitrogen ($N_2$) 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.u io1;s5et)nf6u o,ph(ui2 fh5 kg 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 gasbto oz(mvjl335dj ;0i 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 insidewz;2dc(7 .ojc eskap/ a 35.0-L container holding 105.0 kg of argon gas at 385 pocz/s( c7 2;aedjw .kK?   $ \times10^{ 8}$Pa

  A tank contains 26.0 kjq)6; srkuapsf() ak 5g 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 acxy1u49a0* +b6 /zcglc kjscduhieves its buoyant lift by heating the air inside the balloojs+g/*aydlu 4uc6 9bkzcx 10cn, which makes 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 (ykdv n23 96oh jab,dhat 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 18h *b,6ezu(ea,ze kf6d0og(ss.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 levrkk9 x55af -ruel 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 og6-owh h,orh/z478tyckcskjia;0 v /f molecules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of wavx w2 ;.5we(ds niyv r):mpj(wter are there in 1.000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number o,jt tt4o4i- f7kpke7o y f 9+ikw5x)qgf (a) moles,    $ \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. 5gu: ola9::e)hz8cc m f nv/ln)5gimu1$ \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 inhaleg s-ee7lvs 9x7nyb8t+ that were also v7e+tgs7s b8yn9e lx-in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic energy off w++c-t9rf hy an oxygen molecule at STP? + ct9+ hfyf-wr   $ \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 soav/ 82c n;c0q mb:gonurface of the Sun at a temperamo8 a;n: 0q2cn/bvg coture of about 6000 K.    m/s

  By what factor will the p 9sgv mr59x t:yh j6v4/xzm0orms speed of gas molecules increase if the temperature is increased fr6yxr94szmtx omvg:/v j59hp0 om 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 57ajvk valz14 units of km/s: 6, 2, 4, 6, 0, 4, akjv14lz a 7v51, 8, 5, 3, 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in a gas at 20.08wl y*((jlyoyxc /k8n $^{\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 wwvhp,wxi 5)3ypq mta *j)6n* held constant, by what factor does mwp5qvyphaw)*tn w, 3 i*)6jx$v_{rms}$ change?   

Show that the rms speed of molecules in a gas isy2744.y w r23rss pt. r we+afxngduq0,feh;l 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 temperatur:t zmnq-f d-sg616p bce, the ratio of their rms speeds is equal to the inverse ratio c-:zdmt1 6qb ns6gf p-of the square roots of their molecular masses.

  What is the rms speed of nitrogen molecules contained i1wt1q3m6kice ,6t ,j oskc2w zn 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 oxygen molecujtte3pr,m*) fle 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 mo ykt)fbzqg 4us040 db,rkn1 li6g;d3 rlecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose molecular mass*fl vt7v t,glhsce6(p1g .ym( is 89 u in a living cell aglyevt s htv6(7g(l1c ,pm *f.t 37 $^{\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 (gg9 o.xc4ui6g:g 5henz va6nP of a gas 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 uranium, wo4tt6x.izl *$^{235}$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 prhrf;hygg 8r4z7.,cc sessure, in what phases 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 atm and thev +1by7g3f baq7 b,ub olzig22 temperature is (a) 2 bi771 2ylqugo+g avb,3fz bb90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50% on a day when fq3xueqabn12 jvej2c68 p+m4 the temperature is mejqujvnfa8pb+e2c3 2164 x q25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where water boj*23djnmz yg )ils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mountains is 0.72 atm, estimzi3 pi51lsn 5elol-r 0iec g6/ate the temperaneliil i5/recl1g-5 o6 03z psture at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure of water is 530 Pa aol8nf 9qb00xhnd the relati lx09bfh 8no0qve humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on aaoaq1 mj d33l fdp.(a2:rv ks/ day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pres9 h0ewh 5ys4mxu i0.xnsure inside a pressure cooker if the water is boiling at a xe0 u5h94 iny.whmx 0stemperature 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 caeawup0r 2ab6m j 67g0)g h)yvolume 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 pz6lry (sko61d pq1vph p(7fu.oint 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 (s fd2vye3ucz85 ee Table 13–4) to diffuse a distance of 1u8d c2y 53zfev5 $\mu m$ 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 intepy,a( v)8ev:o tpytd; rior through tiny tubes called trachd;:yevo ,8 (pvt) aytpeae. 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 been calibrated at2xdi+2 bsd p: ujh/v4w 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 calibrated at 20 6y)bd tke);*gjc8f2 a7e7mfy ef1 uis$^{\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 co w(nz.:hm*d room temperature. How much error will be made in a recipe calling for 300 mL of cool water, if the water and the cup arzc* (h. od:mnwe 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 inia(yohq )k4, ggtially 28 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the ork 4ao() gg,hyqiginal gas remains in the cylinder?   

  Estimate the number of air molecules in a room of lengtuv2,x qh).naeh 6.5 m, width 3.1 m, and height 2.5q ,hu) .xnaev2 m. 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 rqr)2olxl pz jmr/6/- 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 attainablez-0rwlcc( 5(9pm qlta using the best available vacuum techniques is aboulza0qt-ccr (9p (m5lw t $10^{-12} N/m^2$ 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 w+u* /t wcmaf2lhen 10 m below the surface, to what volume would his lungs expand if he quickly rose to the sur*tm+w acluf /2face? Is this advisable?    L

  A space vehicle returning from the Moon enters ) 6kbbof351gbq ko tbfd8:w9f 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 temb9obkw5bd :ko 8g)tqffb 6 31fperature? (Because of this high 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 i 7 fe8h2xrqo,io edz,*ncreased 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 779 h7y53 yyb x7sgg3dqzsdz:ax5 xh+k+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 surface of the Earth, esleo3 *8a.vo ;nng+ yfetimate the total number of air molecules in the* elov3yn8ge +an;f.o Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen molecules contained4rjij5 gd;8bi 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 of oxygen used in a hospital has gwkx 1p0vv/;u, dp 6fkuauge pressure = 2000 psi (13,800 kPa) and at T = 259K How lp,fp1uukx6 vk w/ ;d0vong will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of li4.z(5odcqf njquid 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 gasolineqhvz( u04 f;em 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 aroun1 7i,daa yi4upd 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.s i1 )hbtmimn1 0ej-h+7n fy7cel/svghtly 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, ado 0 k0-7mimpdbbpted 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 charged, has a pressure of 19.mor0cyeqe-r ze .:,wpjt. y y; rn01n5 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 Eartrz fs-3f vejx(:4btosb1 u(7f h 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 lid is suspended against ;xpod. 7umqa3gravity by tennis balls thrown vertically upward at 3. udxapm; oq7it. How many tennis balls per 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-diameter (spherical)1zgj27)ct9hi pct m4v*hqmbw -k /,yp bubble of air from a depth of 14.0 m in a lake. Assume tky 1tczb )mj,p4w/2g 7-qvit*h 9hp mche temperature is constant at 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 jf8wy71ptrgi q4vh9*q 4e8euthe following two days: 941ufqv wh8ep 8qei t*4gjyr7
(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 a+ 2j0r)fbdxaa(0:m2 i zotcmut STP, and when it is a solid deep in the Earth where the temperature dr0m uc b x0o a:)2+jtmfi(z2ais 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 laa1t7 9lw8p mbow to show that, for an ideal gas at constant pressure, the co lb8pw9 tma71oefficient 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 dehumidify their cellars to prevent rot -u4h9 mq )icisand mildew. If the cellar in a house (kept at s)4hi9m u-icq 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