Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the per 3g .a4yh +fiz,d5zrwniodic table o.dyaf+ghw zn3r 45z,ir Appendix B.

Name several properties of materials that could q audds)lfl9nxszk0+3:q(:k be exploited to make a thermometerd03d:)nkqxasz9lf u sq: k l(+.

Which is larger, 1 C hy.) 7mbc -2tgq sse1g$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with system B, but B is no:yxcxg a b e89op0qi ob uwo2m6a)s7wp19vd5,t in thermal equilibrium with wsxo8 9o,e1 p59y7 c):xa2gb a6im quvw0dbopsystem C, what can you say about the temperatures of A, B, and C?

A flat bimetallic strip consists of aluminum riveted to a strip 9ptw3)2g( x 2rdso ance3ca0 cof iron. When heated, the strip will bend. Which metal will be owca 9d cc3st3r a)(p20go2xne n 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 of ;z,g t2sgvjedp+*+ty 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 diij 67tbdv +mr9agram 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 togj6rt 9d b+v7miether. 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 temperatures.

Long steam pipes that are fixed at txu k.zmey*o,; he ends often have a section in the shape of a m;.eu,z kx*yoU. Why?

A flat, uniform cylinder o ,6yxn,v l.ir2apn+ xrazvl4 rbl*e14 f 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-glass thermometer is first ji +(uqwlmsly;08 gsob-g 4fj8fjiqi); x)z ;placed in a hot tub of water, the mercury initially descefgq+ujj4m y0 8 q)lsi o xib(;8s)l;g jfiw;z-nds a bit and then rises. Explain.

A glass container may break if one part of it is heated or co4 zb oz*:dt lyy7hrku/1zz* 1 f*brqj+oled more rapidly than d 71* ty* fzhryz1 zbolkq*:ur/j+4bz adjacent parts. Explain.

The principal virtue of Pyrex glass is that its coefficient oybjf4y 5xnfs. ba5uws2:i,1vf linear expansion is much smaller than that for ordinary glass (Table 13–1). Explain why this 5w y.v4yu bfsi,as:b5nfx2 j1gives rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accfj;)i,af6 on turate 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 wil2gzeqy2: 2 i+quu t)qml cause its bottom and top to bulge so badly the can will not stand up zgtuuq2q2yei :+2 qm). What has happened?

When a gas is rapidly compressed (say, by pushing down a pisto1-rvqvgm +s( qn), its temperature increases. When a gas expands against a piston, it cools. Explain tqq+grv(m v1-shese 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 submerged in water incrcu fc zaf 1pgk-6+s,lwf- 9.p/mihd0sease or decrease if the temperature is increased from 6u,+scfc f-f9a1-gs phw /midz l.0pk20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kine(zx1z+ mnj3q ptic theory and the relation between average kinetic energy and the absz 1x +qzjpm(n3olute temperature.

Explain in words how Gay-Lussac’s law follows from kinetic theorn :*u i je;u13ypybmz:p rat*-y.

As you go higher in the Earth’s atmosphere, the rswni7 + .bjfi l8u1-xlosvk 17atio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to tfwgmf0/*zib( i4ud:loh:l*( yxuca7he minimum speed an 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 Moon has 4:l w(:oaf*hgfi7u /lzmxic(ybud0 *practically no atmosphere.

Alcohol evaporates more quickly than water at room temperature. Whe9puay)n /j+o. .ch6vouo tc3at can you infer about the molecular properties of one relativcnayo6o)hu/9.pcvj et+ou.3 e to the other?

Explain why a hot humid day is far more uncomfortable tha 2g+sp2- kj9qt bqxl(g)r-kf sn a hot dry day at the same te(lp2jftg+kq- br g2 9)skq-xsmperature.

Is it possible to boil water at room temperapii71l- ntj n6 ytfx*ne 82ipn4 sm0a9ture (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperature is thep6cdx/:uuunn;* mcjfic3k80y,x j t/ same but the humidity is different. Which is more dense, the dry air or the humid air at the same Tn: xnfkdu yjt6cxm/* j0u 3cip8cu,/;? Explain.

Explain why it is dangerou;u-y k7haj )ogu 3d1dis to open the radiator cap of an overheated automobile engj;k1-g 3y) od d7auuhiine.

Why does exhaled air ayzbd5l7i- ovesaj jgn94+7:hp 19oscppear as a little white cloud in the winter (Fig. 13–28)?

  How many atoms are therd ra5+6 jsw,+fr vyim+e in a 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 nb6yo5 fgr9w x5umber in a silver ring of the same m5oyf9 gwrbx56 ass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. What is this on the Celew*l6u-l .*i j vefc0dsius scale? *0 iufwve lc*de-6jl.   $^{\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 recs+j+z5p 2yyc ruae 2(gorded 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 alcohoc x+ccuw; nq2m,) (hyul column has length 11.82 cm at 0.0 (w q, umu+ccn;2hx c)y$^{\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 slab;*4 sz df-xmt ko9t*ods 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 wrough 4.yyf/u yz3kz5/i ermt iron approximately 300 m tall. Estimate how much its height changes betuyyze r/4i.y z5mkf /3ween 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, rivtmtxg45e p; ,30g krye0jh2pblo ( uv1ets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placeg3,21r(jueybhl5 ;ov0xe p04mg tpktd 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 at7-w 3w wqu94 tutxd-nn 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 i: c:h 52*ixdpmaw1pwwts change in volume if it is heapmc w :ai1w*2w:5dhpx ted from 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled t*lq )6vackd i1oy47l so the brim with 350.0 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.ahdus zt6b7s ,d73u 0s50 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 b j7*dj e-lrcw9x8 odq8e placed 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 vessel so it can expand in eg/a chtt alya u3+y39vqz9l 78ssentially one direction only, show h3g9 tyat+79ava3/l z lcu 8qythat the effective coefficient of linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change in the den.xccp6o.txrp :w8 1uo sity $\rho$ 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 of linew ttr0v, )6r6:tj znvoar expo6),jv n6tz0:rtw rvtansion $\alpha$ 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 solidcbxlrd5uwhva 336 h5/, $\beta$ = 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 7 7dhh*ht9ns ykeeps perfect time at 17 h79t*7n sdhyh$^{\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 0.140 mm. The bjwiunk99.)p8v6zs ho ulb has6n9h9 .v8o )pujzsiw k 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 cylindrical wheel of rkw4a1limx+*teg xb; +adius 0.41 m is rotating about its axle on frictionlessi+ ;txmew gl*4bk a+x1 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 strj .gm i mlb(yk0y1:f2x )n3wgless is required to keep it at this length if the temperature nwj lg)lb1 0.i3kym:gf2y(mxincreases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-secrdtw+)(fcjy+ e /9jpt tional 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 134.123zqq rv 7qj tuiu8y.l:wijw7 9+j-h2y2 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 temperatures on the Kels)6(lzgbn r1w vin 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 tepb0 ;k 1rqcuqifps(5,mperature on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures lx lat b.;by.)t7phb0 in 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, azo j+5d9mdb rjwm;2e 7ir at atmospheric pressure and a temperature of about j7;9wmde 5j zo2dbm+r20$^{\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 idew hwsbb;x .p,.*lr :cbal gas law.    kg/$m^3$

  A storage tank contains 21.6 kg o. ha;2zxrhe3bcdgrw -48) sqbf 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 18.5 kg oflxh xk4id(:0 ff x++bo 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 isp0kp 2 qccgf+0yb* vm. 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 container holding 105.0 kg of argon mrmt*xpz+ n8 xo*/w2(olc-j ggas at 385o wm* *c-r/xp2xot8(+gmzlnj K?   $ \times10^{ 8}$Pa

  A tank contains 26.0 . xsr4w eow59bkg 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 achie*fyq7v rqtl(v 3f 1*goves its buoyant lift by heating the air inside the balloon, wh 1* f3(tlfg*7oyvqqrvich 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 witpyh iu6fy m *+rkj392eh 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 aac6s )jsx,i2 bz7 -ta*s bkx32u1vvpg t 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 le/l 0v(jif d0zzvel 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 oflg7l2dru1u .d,s 1uts molecules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of wateqw5et wv2q0,eu ( )pefr are there in 1.000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number ofmfkx 0q)(*k bl-kazd79w yb2e eh3 s1i (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 volumet im. 0ynn a2*tn .mku..oajp.nqsv-np- +jc) 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- :5x q z;xlt/2,wk:ogeqp.mhx y7tza 2.0-L breath you inhale that were also in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and o5t ;gzx y2qak:wmx-,tqz e7lxo/p :h. f constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic energy of an oxygen m)fh4aw(my wm dgl g)l94z g:y-olecule at STP?ym)zwl9h4 -gf wga : )lg(ymd4    $ \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 atom;y 8 ztsrm12pls near the surface of the Sun at a temperature oz 8psmryl1t2 ;f about 6000 K.    m/s

  By what factor will thexg)l w9v(b s.f rms speed of gas molecules increase if the temperature is increasefb w)9x (vslg.d 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 t) r) d h7h0wevey(6mrkq i7zw0he following speeds, given in units of km/s: 6, 2, 4, 6, 0, 4, 1, 8, 5, 3, 7, and 8. Calculate the rms sp)v(izw 7m7dqr re0h60y hke) weed. $v_{rms}$ =    km/s

  The rms speed of molecules aj (i;w2sv 7j:z )i/ykwlnb gt1* bs/sin a 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 vol xhz5o1zyyp (42id6/i c7dbf hume is held constant, by what faci4(i z hdpdxzf/bh2cy5oy 1 76tor does $v_{rms}$ change?   

Show that the rms speedjs9n q(bo2yt zy4si4s8q, w +6a0+ix wd8zgnf of molecules 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, the ratio of thjqav; ho:.w + kfhx5y1eir rms speeds is equal to the inverse ratio of the square roots of5awh1v kjo.:+ xhqy; f their molecular masses.

  What is the rms speed of nitrogen mol (oi6um29rnj wegu13s ecules 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 sicc74xfj*- yv4 p :yetpeed of an 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 betweene bx1omvf5nc9m pqv5w ,f:auxx4d:/ 4 nitrogen molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose molecugo67q0ii)v;fm4v z1h xdqkm cs )5;zqpr7li.lar mass is 89 u in a living lmqiv4f67zz r.kmgdpsiv 0ohic7; )q)x15;q cell at 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 P of a gas can be wrie4 9fxrh r tl 4yx72o3/lvjc7sh1ui6atten 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 uranium0ff ,5fbq qr7h, $^{235}$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 phases (ozdzqtsl+ --1ubq+sr 6z+lf c38oj dcan $CO_2$ 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 the mtq5bt 6-u3yyerq v 6(uvps08 temperature is (a) 96myt8y05 s v3-u(bqquev6r pt0 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity g 2yzq)jd2 ez8y 5l+xmis 50% on a day when the temperature mlq+d5xz2ge8jzy )2yis 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place wherex5tvrs2 qe, forl1//ioq 0gz 9gxv7. z water boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mou61 yiztkfy+f :ntains is 0.72 atm, estimate the ty6ti 1yfkf +z:emperature at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partia5be-+h64 p ultfx4z xkl pressure of water is 530 Pa and the rel b6-f5 pu+lhztexx 44kative humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of waterzv7tpy(l*sjgd5 xzde, d -,;z on a day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressuj2 1r c(5iu5iv2 wyfa1yg xb3d/tgi9qre inside a pressure cooker if the water is boiling at a temperu gcf1y5(5x9qywit1 2idja/2i3vrgb ature 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 g65n(ffxo9a* hvix1 v i,ro-x0$m^3$ at 25 $^{\circ} $ C is 80%, what mass of water can still evaporate from an open pan?    kg

  Air that is at its dew pointe0.pnz.cs3+ze 4tggw 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 Tauxcfb: e h838wble 13–4) to diffuse a distance of 18 hfw:e8xb3u c5 $\mu m$ 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 - s;lrehkx;y:im17 mep ru5h4surface of insects to the interior through tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-y7 uimphe4;:; k mrlh- 1x5rsesectional 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 b tp72);oslo l; gto(,9 yozdereen 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 measure has been calibrata-gyo0d5 ig2r ed 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 tempe2)e s.e jnorq6mldt-9 rature. How much error will be made in a recipe calling 9smed2e6on )rqlt -.j for 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 initialrf0gz:dg:xg) 0u2bl8v.d u gh ly 28 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 avlf:.0g0)8:dhgzdux b2ur ggtm. What fraction of the original gas remains in the cylinder?   

  Estimate the number of air molecules in a room of length 6.5 m, widt9wv;:phj7v16r mvp a:y +gom3z ;su kph 3.1 m, and height 2.5 m. Assume ;9 : rzppjv7apu swhok 1gvvm:6+m;y3 the temperature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density ofyfao1a p8eby0 ;, kjd2 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 attainable using the best available vacuum techniques ii zbi*oo9- v;ts about z -itooi; *vb9$10^{-12} N/m^2$ 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 ( 18ri;o afeovof 5.5 L when 10 m below the surface, to what volume would his lungs expand if he quickly rose to the surface? Is this ad(ar o8f;oe 1vivisable?    L

  A space vehicle returning from the Moon enters Ea,t2puyen-ch o ogn)j8 -6x8efrth’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 temperan-8uycgejx8-)62,p f etnho o ture, 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 ideaj2jzpt5)a;k,tl7g+0 l7 g ca lstufb+l gas 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 770myjssh:jxo8o205 x-vf$^2$ (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 ofili/no ial3d;87)n8. svn cjp atmospheric pressure at the surface of the Earth, estimate the total number of air molecl vj7i.88dnici lnp3;/an )o sules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speedt cedyy x3+:n1i2t9ncy35n yi of nitrogen 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 of oxygen 1jdp4c; u5mf iused 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, measured at atmosphm; dfij4 5cp1ueric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mercuxupn2 w7.ggd*zmtq 6 .ry 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 av0f( (4wn yadw c7(zrft 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 snf ,6k9 tvhj41z puye)yugly 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 tightly onto a glass l 0jc3.jy 6o-cet6lt jjar 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 the x;-ryzvott/ :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 charg +u:;btzrgs/ g/1fh /vmcy et(ed, 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 Earth18 9yc6kooh e(x9eww p 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 suspend m)h3 g:w:w0ukurar :qed against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid ela u:uaw0rghrq) kwm 3::stically, assuming they have a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releas;9ecq*bk v v3h ys0lnfm8co4;es a 3.00-cm-diameter (spherical) bubble of air from a depth of 14.0 m in a lake. Assume the temperature is constacsn3ok4 m ev yvcqh;;*lb08f 9nt 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 the follv7y4j2b( qc biowing two days: b 27bcqiv(4yj
(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 STt-i je5kdg69, y0xt:rh2wogu P, and when it is a solid deep in the Earth where hg, w -52ki6txte ud 0:jry9ogthe 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, peu o (uk271ac6n)ms gfor an ideal gas at constant pressure, the como61aecun2u ) p g7(skefficient 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 const2lysaz;-lguqxbo u s5 b2. :7eantly dehumidify their cellars to prevent rot and mildew. If the cellar in a house (kept at 2 b.e xu;2a7llzqyu5 2sgob:s-0$^{\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