Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the periodic table c ( umhplh w7lj):-c5for Appendix B.:hluc-mcp5 )7lf jwh (

Name several properties of materials that c,wvd1cxqc r83zylc+a; h m j+;ould be exploited to make a thermometerccy,+ zr vclqxwm1aj+dh;8;3 .

Which is larger, 1 C7g/sm+ghaatl 43tu)-7 flnty $^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with system B, but B is not injlwhitc,) s, . thermal equilibrium with system C, what can .,c i),hswltj you say about the temperatures of A, B, and C?

A flat bimetallic strip consists of aluminum riveted tot-9up2xg p1vc a strip of iron. When heated, the strip will bend.c9 p12v-px utg Which metal will be on the outside of the curve? [Hint: See Table 13–1.] Why?

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

The units for the coe nz(m mv,oo4in 9,aj,efficient of linear expansion $\alpha$ are $(C?)^{-1}$ and there is no mention of a length unit such as meters. Would the expansion coefficient change if we used feet or millimeters instead of meters? Explain.

Figure 13–27 shows a diagram of a simple thermostat used to control a fp hf dfh,6 z2lr4vpg:*,py0j wurnace (or other heating or cooling system). The bimetallic strip consists of 4hp2d,y r,jfw :lppfhz6g0 *v 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 temperatures.

Long steam pipes that at5gl k kz rrv ;/0ouokm);7h/cre fixed at the ends often have a section in the shape of aohtzml) orcru5 ;; kkkv// g07 U. Why?

A flat, uniform cylinder of lead floats in mercury at +cv-e,n-j 8wdvtg9 x-wn p bauj-s,5 l0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glass thermometer is first placed i +ecvj30p( im.luf /gaoa5bo2 n a hot tub of water, the mercury initially descends l. g bp 5i2mu ca+f3jo/eo(0ava bit and then rises. Explain.

A glass container may break if on7fs l,bhuf;z53hpot )e part of it is heated or cooled more rapidly than adjacent parts. Efhoubtfl 7p)z5;3,hs xplain.

The principal virtue of Pyrex glass 0d(wg9-lrk .jlssq x- is that its coefficient of linear expansion is -r gl.0k(sj x9lqdw- smuch smaller than that for ordinary glass (Table 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accurate at 20 yzo/um1:6awi. so,e x$^{\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 and top tosc4z*) rmj1q ,tuq0zdq3e +qp bulge so badly the can will not stand up. Whmqqdu*zz+ 3ct0s rq, j qe1)4pat has happened?

When a gas is rapidly compressed7hasm ci7 w*b. (say, by pushing down a piston), its temperature increases. When a gas expands against a piston, it cool. w*hb7a cims7s. 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 aluw/pe(l4y8);b hsmn w xminum sphere submerged in water increase or decrease if the temperature is incre swmx ;b84lnp)why(/ eased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinetic theory and the relation+sz ud j/ym fh6s;.1yz between averam+;y1juh.ssdy/ f z6z ge kinetic energy and the absolute temperature.

Explain in words how Gay-Lussac’s law follows from kinetic gun8xdz/ vt 0 njk 3jbpn zx293+:hqv4theory.

As you go higher in the Earth’s atmg u7agoj5kvi8e, 07*t5z)oin5y0 cor rb wx0bosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth w58orrk+ n3fa/vr -a:aseo0 7 0pwpnfrefers to the minimum speed an object must have to leave the Earth and never return. The escape velocip0ovofa 0e87an-+awr p5 fr3nws:k r/ty 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 h ;9twpiws4z)at room temperature. What can you infer about the molecular properties of one relative to the9 hiw 4z;ts)wp other?

Explain why a hot humid day is far more uncre,7 e f3w)pp tkr,8rsomfortable than a hot dry day at the same tep , eep7s wkt83fr,rr)mperature.

Is it possible to boil water at room temper*5tdoav9ayw ocp9fn+y6 :(r mature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperabh1jyso yjzd: n ye)(7d 3daoio (+h.:ture is the same but the humidity is different. Which is more dense, the dry air or the humid air yd o.ys:7ija(ydnj oho(dz3:+he)b1at the same T? Explain.

Explain why it is dangerous to open the radiator c)r/ 1ans nz y1raqz8*bpmm0wg 9;8u rg+xy u(yap of an overheated automobile 08;aaun/ wz9)1(q8r gm*puryym 1z nsybx+rgengine.

Why does exhaled air appear as a littlsi(wrut 9u*ewdw2uy c(-7u n2e white cloud in the winter (Fig. 13–28)?

  How many atoms are there in a 3.4-gram copper pennyk,s*m *gm wr2lror9-w?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring compare to the;/n/eqb3 sg8qp.hpi h number in a silver ring of the sambhp 3hnep/q.;g iq/8se mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to bx/ ngoz2uym7 *e 68°F. What is this on the Celsius scale?gu n*mo/x72zy   $^{\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 recorded pvua e1p22bz6efn- d.rao//d 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 x23b+suc jisfbhww+.l p.f )lh-2 j b6has length 11.82 cm at 0.h h6 .scwfj2sil+bupfw bjl-) x3b.+ 20 $^{\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 builegz( 59tjw-h xt of slabs 12 m long (20 $^{\circ} $ C). How wide should the expansion cracks between the slabs be (at 20 $^{\circ} $ C) to prevent buckling if the range of temperature is -30 $^{\circ} $ C to +50 $^{\circ} $ C?    m

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

  The Eiffel Tower (Fig. 13–29) is built of wrought iron approxixmqv;2 4w4oyrtx s4a,mately 300 m tall. 4q;avwo 42tmx4 ,xrsyEstimate how much its height changes between July (average temperature of 25°C) and January (average temperature of 2 $^{\circ} $ C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.    m

  To make a secure fit, rivets that are larger than the rivet hole are often u1.bg g4m3/xj2f kefxcsed and the rivet is cooled (usually in dry ice) before .2cx1 k3jfx ge fb/4mgit 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 wateri/agc h/ek7165-n+us yqxzvj at 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 its chan f7w/d9ga*oi t7ob4-ol *howq )tef0uge in volume if it is heated f4do o -oo* ibh0w7l*t97utfwegf/ )aq rom 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 mLlz7*4k-bk nl a+x5 h .prm(kkm 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 at 20 ooa gc2a3sf f 8l).f/x$^{\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 6;b, j8b+g jjpl4 5v0xcuplem. 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 q5i flcoo a4 du ac,ba0rh74/r0qhm9 )in essentially one direction only, show that the effective coefficient ofruqh9h4doa b ) or50/fc, 4a m7il0qac linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change8z54mtx my u3rtok65c in the 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 widt /+pnme lo 8sf)y25zaoh w has coefficient of linear exp8/5ae zl)f yoopsm +2nansion $\alpha$ 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 isonp6ie8guo0q *x0 r :nxtropic solid, $\beta$ = 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 brap8,9c7whyue now yyl27 ieu) 3ss and keeps perfect time at 17yu78 w7yn w2coi,lue)he p9y 3 $^{\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+v;(.p w-h-d zp6osr2ou wlqd inside diameter of 0.140 mm. The bulb - (o2su+lr;wwv6hzdp.o qp -d 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 8g z*j ftkjkvm56*i*xcylindrical wheel of radius 0.41 m is rotating about its axle on frict** *vfkjzijk58x m6gtionless 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 requiredrjx89)gp5yx 2 ivl:d hrz9u( o to keep it at thisxihr9j d) z5p(uox9g8 l vyr2: length if the temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sectional area 0.js+a3lhs4p)h9)2 rv 6xs++sn ne-flgp- nkjk 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 cm at 20ij uux oh0cro (15u*u/$^{\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 temperat;h6zs5u 9 io x..;b5vuamadoc ures 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 the F0e 7n 6s ;s8fbou-ushfahrenheit scale?    $^{\circ} $ F

  Typical temperaturesdrld * kch6v/s un0p,4 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, air at atmosphee/ 3id5l8orln6y);c(pcurze ric pressure and a temperature of ab3cr nz ouy;l)el86peicd5 (/rout 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 aw.y (g2phlpfn93l0 g oeg7/zz: uvc2k t STP using the ideal gas law.    kg/$m^3$

  A storage tank contains 21.6 kg of nitrt*.ff zi pl:z6z2sap,+ gq7 irogen ($N_2$) 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 m3,,zjy 5a2 jz/ 2wvy3i w4us:qdrijzcontains 18.5 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 gas is at 10.rio t: +.gae0r0$^{\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 105zn fble9) u e4fmv+.y;.0 kg of argon gas at 385 K?e4+b y)fz v;n9me.u lf   $ \times10^{ 8}$Pa

  A tank contains 26.0 kin mhy..hk,c0g 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 buoyant lift by heating theg1td06 1igftx.qw3lu air inside the balloon, which makes it less dense than the air outt0dgu 3.t 1gixwq lf61side. 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 f+gjj-(i 7y jdkar: mv+b,d7 lair 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 at 1hlekvx01 my+68.0 $^{\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 sbk57,uyqti 8-7 gwz; suuk 6qzea 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 t+9u2 nud pb iihc-j4*eoxz8n,r-;zmof molecules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water ariqb:()0,gqw qto 7rb 3r2 vwere there in 1.000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) dl mwj)f.3b y*li;r d3moles,    $ \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.a w; nfg90cpq.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 75o(udiamsu:qg*j5t each 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 of conu:tji5* (7 5qgumsoadstant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational rosv gj+* (+z.-z 0ldm8dth ntkinetic energy of an oxygen molecule at ST(sotzh*.80r+ dn m gzdj+ t-vlP?    $ \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 the Sun augo qomzi, f fd/6me59m zd/91t a temperature of aboute zif 9m9md615zo udfoq,m/g / 6000 K.    m/s

  By what factor will the rms jfyq u*9r0au *+l(qur:)bdcy speed of gas molecules increase if the temperature is i)yc:dl 0 +yuqufrj(*uqba* r 9ncreased 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, g3imtyreq- 69 ,bm3pe82kv jrfiven in units of km/s: 6, 2, 4, 6, 0, 4, 1, 8, 5, 3, i,8fpre6jke-23ytq mm b r93v 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in a gas at 20.0cvlo2cb- jc0 q a:f6(x $^{\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, by wg 0:8mfiooj1cuu 8e sm3 jim;(hat fact3e08m:m(usomji;gjc8iu f o 1or does $v_{rms}$ change?   

Show that the rms speed of molecules in a girgox w5cb) lc+d ;,w0as 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 th6z-- 6zyadfq* ,jofqw -3ag nyeir rms speeds agzo6a- z q*fj f-yd-w ,3ynq6is equal to the inverse ratio of the square roots of their molecular masses.

  What is the rms speed of nitrogen moy;kzjmtdxefb+ fq:; +96*k yflecules contained in an 8.5$-m^3$ volume at 2.1 atm if the total amount of nitrogen is 1300 mol?    m/s

  Calculate (a) the rms speed of an oh.j1vr,iwj nj7/tj 3k xygen 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 distna/ /2gkl 4v,;t vpgqgance between nitrogen molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose molecular mass ixln2f24g: gkfs 89 u in a livi2glxn gkf:24f ng 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 af4uobh e)gx;4 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 uravtfpt41 jhr8 0nium, $^{235}$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 xk6xq o+-d8an 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 phas.yihdp c44hsw+m)4ua e when the pressure is 0.01 atm and the temperature is (a) 90 44h.samcdwuh4+ pi y)$^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50% on a da ch)g6fm1 9kbzy when the temperaturmgc)z9f6hk 1 be is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure aqpi.hqv+ +kcc*laj7z *a5m4 zt a place where water boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mountains is 0.72 atm, est ffenw3 jfbniash(oi+14/3dm 4 .ta:dimate the temperab/m 3+i 4afhdw(fs.j a4fo 3dtn1:neiture at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a dn f;k:*uw l x9c/rub:+w3n ztvay when the partial pressure of water is 530 Pa and the rw b:9funl x: /u;r3*wzvcnk+telative humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a day w6lw0*susew5g n4 xfx4 hen the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside a pressure cooker ;sy g0irm:i +uqkyc(q.w 8 ;gmk c-s)kif the water is boiling at a 8(ysgqwcs iq0)-cim;y k+:k ; .kurgmtemperature 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 4tng,hwq mq0/n)l xs; volume 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 point o;s,d-0w(sw/96hkm.aaibtx/ lv z xj: du d g7zf 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 needg 332ki2rp tn+jm8 swned for a glycine molecule (see Table 13–4) to diffuse a dist2 ipr+83m3tsn2kn w jgance of 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 suryza2c.nz8h.ny3wr.m 2t p l b4face of insects to the interior through tiny tubes called tracheae. An avehrp n 2mzz2t.l3ab8y4.y n wc.rage 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 calih:a px20cpt +zbrated 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 h4paa7zj +57x;cqw-oln v c 4snas 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 temperature. How muk)). 8qrjybr m 4e8uhfb4vxua8 ey0b8ij m) t+ch error will be made in a recipe calling for 300 mL of cool water, if the water and the cup are hot, at 80ixmabq.jrfeurb)k4v8 08uj8+t ))mbe y48yh $^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a helium gas cylinder is initially 28 atm. Afis wg q-p8q1v(+ t2frtter many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of t gsi+8qvp- (rwqtf 12the original gas remains in the cylinder?   

  Estimate the number of air molecules inlqvaj7k.zwt2z pb;davg i.et h/2:0c0 3yfs 3 a room of length 6.5 m, width 3.1 m, and height 2.5 m. Assume tht/.2cwfzspvk l3bhq d.0a vi:ytz0 2gj7a3;ee temperature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of matlg c*t9b,wz a0ter 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 +3t7ultyzhe-l*is* q is about 3- lquht iys*+t7*zl e$10^{-12} N/m^2$ At such a pressure, how many molecules are there per $cm^3$ at 0$^{\circ} $C?    $\frac{molecules}{cm^3}$

  If a scuba diver fills his lungs to full capacity of 5.5 L when 10 qn*wv :u r6a3*pox.plm below the sur:p3uva.6o lr* qnw*pxface, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?    L

  A space vehicle returning from the Moon enters Earth’s atmosphere at a speed 9mpb ) o9gp weqw5x/q,of about 40,000 km/h Molecules (assume nitrogen) striking the nose of the vehicle with this sp)w5/qp egx9 q9 owbm,peed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)    K

  The temperature of an idea. lne8alsx8u: 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 770sgff1f oid/y:x gv0o,i)n*x- m$^2$ (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 tcciji0 j /ab31za(z :mhe surface of the Earth, estimate the total number of airjabzc0/ i1ja:3ic ( zm molecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen molecules j4djp(m a2 ma7contained 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 o tey.sf.x9 m9df oxygen used in a hospital has gauge pressure = 2000 psi (13,800 kPa) and at T = 259K How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.d9f 9y.tes xm.4 L/min. $\approx$    hour

  An iron cube floats in a bowl o fz *kc5x .5qnb+*ec quae1:jsf 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 gasoline at 0fdqfvc.wn * 0 i/df101cxrww)$^{\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 around2pc et ee dps4.)(wusnj4x0s4 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(6/j iuh.rak0d7nvef 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 stan2sx f8wnb9o o3i:z6ah dard, 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 charged, has il*iexhcxp2l )kzu.4n 5 / /gua 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 Ea bt i(ped)w9 sh+i mzk1o(7.sjrth 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 sus a39n(fcr0j (x,ga/vz o4bmgbpended 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 aabno4 (f9bzc 0( ,xg j3mr/vgare thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diameter (spherical) bubble of air from a depthml8t pon1: ,ea of 14.0 m in a lake. Assume the temperature is constant atepn o: ,at1lm8 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 following two days: 5p(ie*e ;o ulz y*wl 49np:fal n5*pya:*ul f;eo9(lw 4ie lz p
(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 dens)l+lht*mjj f2 m;w 0auity of iron at STP, and when it is a solid deep in the Earth where the temperaturem*2lt m)la fujw0; hj+ 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 idealb2w2m8dhd vd8hv( ry* gas at constant pressure, the*y(28b dd v8mrd2hvhw coefficient of volume expansion is equal to $\beta$ = 1/T where T is the temperature in kelvins. Compare to Table 13–1 for gases at T = 293K (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P where P is the pressure.

  In humid climates, people constantly dehumidify theih)4v8*n p7xkdrkbk-v r cellars to prevent rot and mildew. If the cpr)7k v8dknk-v4 hb*x ellar in a house (kept at 20$^{\circ} $C) has 95 $m^2$ of floor space and a ceiling height of 2.8 m, what is the mass of water that must be removed from it to drop the humidity from 95% to a more reasonable 30%?    kg