Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the pe4uux a9thn7g, riodic table or Appen,xu 7nauht9g 4dix B.

Name several properties 3 gll)6oc tdp;j/dq2xof materials that could be exploited to make a thermomet;gp/xc3 ldqj )ld 26toer.

Which is larger, 1 C 3b7hu ea 4 ej-m+tt:yt$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with system B, but B is not in thef+;sdfrh3)dp 1cm*r trmal equilibrium with system C, what cfdd3f1 )c+pmt ;hrr*san you say about the temperatures of A, B, and C?

A flat bimetallic str w:k y38o*tvcvip consists of aluminum riveted to a strip of iron. When heated, the strip will8yw*k:o tvcv 3 bend. 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 coefficiy i74jlv 8lep9ent 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 ab i34vqg z)m. e()rizmwha;3eb7h7hp furnace (or other heating or cooling system). The bimetallic strip consists of two strips of diffevhq;h. er3 iema4 w)pg(3 )mi bh7b7zzrent 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 are fixed at the ends often h,x)mu,g hafaa:9u ks, ave a section in the shape of a )kxsg u:a ,,,9umaahfU. Why?

A flat, uniform cylinder of lead float d4s)w zeb1rv0s in mercury at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-g8kbg,c 9*p, xj g vdsi4j p4xexl;(n+hlass thermometer is first placed in a hot tub of water, the mercury initv egsxpb8l4 cjj dg;*9xh(pnikx4+,,ially descends a bit and then rises. Explain.

A glass container may break if one parcfjlz8gw 72)rt of it is heated or cooled more rapidly than adj28f7jwc)r g zlacent parts. Explain.

The principal virtue of Pyrex glass is that its coef0i bw-e4e(wt uficient of linear expansion is much smaller than that for ordinary glass (Table 13–1). Explain why this i0 ewwtue4 b(-gives rise to the increased heat resistance of Pyrex.

Will a grandfather clocq)2476n fkqduhv 7bf3pa b a9zk, accurate at 20 $^{\circ} $ C, run fast or slow on a hot day (30 $^{\circ} $ C)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

Freezing a can of soda will cause its bottom and top to bulge so badly tht6 shdkd 0k+fnj-g9k7e can wiltnh7kk g+d60sk9f jd-l not stand up. What has happened?

When a gas is rapidly compressed (say, by pushing dh u:ycw+:ah94 rmt+tcown a piston), its temperature increases. When a gas expands against a piston, ++::trch umw4cah 9ytit cools. Explain these changes in temperature using the kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force on an aluminum sphere submerged in wate 0ga;g:bm7d ne4,e dlkr increase or decrease if the temperature is increa;ld 4mg ee7 g:nbd,ak0sed from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinetic theory and the relationa*jg34b zwkxzu,2a* l between average kinetic energy and the absolute temperata2xzg ,a4 jk3wz*u* blure.

Explain in words how Gay-Lussac’s law follows fr2,x z ;)9 tzlcabwnp ed78*rlbom kinetic theory.

As you go higher in the Earth’s+pp2 hpyr:gq,0 p/pjx sy73v i atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minimujzpd 44/d*) su95s9aumohu sum speed an object must have to leave the Earth and never return. T5*4uo9d)u/zup ssa4 h 9 dujsmhe escape velocity for the Moon is about one-fifth what it is for the Earth due to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere.

Alcohol evaporates more quickly than water at room temperature. What can you9j zk+ *devt+p infer about the molecular properties of one relative to t jpek+9vd+zt* he other?

Explain why a hot humid day is far more u jh)zbb0-u bupa75 tf8ncomfortable than a hot dry day at the same temperapu)7b bj-80ub fzhta5 ture.

Is it possible to boil water at room temperature (2095-eu,5kom k yrr6 fbh $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperature/p8.6okt uvi4td2sac is the same but the humidity is different. Which is more dense, the dry air or the humid air at the same T?p24us ov6/k.ca t8 dti Explain.

Explain why it is dangerous to open the rad7g i-hk ;dmqg,j8 tzr1iator cap of an overheated automobile engineg -jrhi m 8,q7kzdgt;1.

Why does exhaled air appear au11lup: 305 s3v iwu/j.kqgo,ibn c uws a little white cloud in the winter (Fig. 13–28)?

  How many atoms are there in a 3.4-gram copperh ;*u0wsffb syj 1wc ug)jp*26 penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring compare to the numberut;uf39jr ) ka in a silver ring of the same mass?uf;k9)3 r ujat$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is ofe, oo *sdn dr- lc-t/l ilg+j-x8m87knten taken to be 68°F. What is this on the Celsius scale?+n- *8xd -j doll tr- mn,c7i8geksl/o   $^{\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 rp,g9vt v jr.;u,; q8( rx4- rjwejpkcrecorded 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 thermomeb*dj4gy)p vfe 3 z+n8eter, the alcohol column has length 11.82 cm at 0.0 3 pn4vdeef8*j) z+byg$^{\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 b,p :;i*qmieju4lakdg6 - c :ufuilt 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 (Fi+gf.)trr7p2 y* fog. q5thlovql4w0tg. 13–29) is built of wrought iron approximately 300 m tall. Estimate how much its height changes between July (average temperature of 25°C) and January (average temphtgq+g0vrqlt*f4w).5oof lryt. 2 7perature 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 guu:* e (-5 wxywo1rqhthat are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hoow yu:x(qeh -*1ur5wg le. 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 a,ij5 dyxwnbhco8td501s g.y1w 2nxu 9 t 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 diabu *kfsi94v,-b ky e1bmeter. What will be its change in volume if it is heated fromv 1bies-b4 ufkyk,9 b* 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 /9brusf4 ;b x))qsbmvmL 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 was1*wr v*vi v /tenhilc2na2 (.avgm tn(+),ckter at 20 $^{\circ} $ C completely fills a container to the brim. When the container and the water are heated to 60 $^{\circ} $ C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container?    $ \times10^{-5 }$ /$C^0$(b) What is the most likely material of the container? The density of water at 60°C is 0.98324g/ml.

  (a) A brass plug is to be placewm0s.x0 c,o d-gvwti7d 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 essecm361sg ct fa:g37cmontially one direction only, show that the effect:tacm 13gc csofg m673ive coefficient of linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change in the densipbt d05wi 527z,(ddefa. :rn ,mvhgp, ya/ahxty $\rho$ 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 coeffic, hudjk(p ,0mzient of linear exk zhu (pm,dj,0pansion $\alpha$ 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 sov 2w.j.fwvqq3 lid, $\beta$ = 3$\alpha$ if the amount of expansion is small. $\beta$ and $\alpha$ are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13–30.]

  The pendulum in a grandfather clock is made of brass and keeps p,l54xo5vg;ahs*zof b erfect time at 17h5g5vo z osfb ,l;*x4a $^{\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 mmk hm0b3zdu43s. The bulb haz3kbsum3 d0h4s 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 radius 0.41 m is rotating:;cw0m: 8t yyu+nsfzl about its axle on frictionlessf ylt z ;swu08m+y:cn: 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/ px3, y hxx je8l/nc+.a+afjl°C. How much stress is required to keep ilp3 xe j+8c,jf xx+y./hl/naat at this length if the temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of crossp7se ) q/h d3sk wq ksm*62z)b.f/qpvy-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 134.12x32ub;k: hcsk 2 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 o5 wtjhovy11tv:m79a 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 Fahrenheit scaiik l z0u3s*3ple?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth and Sun are;m/lfqztx) by fe3,v+ lzd;5b about 4000$^{\circ} $ C and $ \times10^{6 }$ $^{\circ} $ C respectively.
(a) What are these temperatures in kelvins?    K    $ \times10^{ 6}$K
(b) What percent error is made in each case if a person forgets to change $^{\circ} $ C to K? $\approx$    %(Round to the nearest integer) $\approx$    %(Round to three decimal places)

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

  In an internal combustion engine, air at atmospheric pressure and a tempera8e)zo9ad xwe 5ture edo)5aw xe z98of about 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 ppr :z1vc ii f;6mku(0ideal gas law.    kg/$m^3$

  A storage tank contains 21.6 o/-xf l x9a ;zdvbo3:jkg 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 18.5 kg og:s 4+ qnb1ijlf 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 gyszun +2.5w cat 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 holdin.t6co-ig/ ih cg 105.0 kg of argon gas at 38 -i/otccgi h6.5 K?   $ \times10^{ 8}$Pa

  A tank contains 26.0ro)i)2slx3 ws kg 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 the air 3p8ifzkk v 8e6inside the balloon, which makes it less dense than t8zk6 38efkvpi he 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 at 153q5 5axds5ecr $^{\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 18.0ublc0i 3m.sta/ mosot07bwki*7*8mx $^{\circ} $ C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 50.0°C, what will the new pressure be?    atm

  A helium-filled balloon escapes a child’s hand at sea level and 6:zlwp)6ixnd 20.0 $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number of mmom0)wmmag4 ( olecules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are thereku /s,dfjum8b1nx,6ya) ;lmm in 1.000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) m:ueq3 c z1b .smv)o9axxe9 lt4:6fchioles,    $ \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.q:f0 n gq12jmkj t e7ky:42,xim8hgla1$ \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 inhalfiv:rw 9nry *0e that were also in the last breath Galileo took. [Hint: Assume the atmosphery09rvrf*w:ni e is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic energy of an oxygen molecule at Stsp7oay9y.vqoqrnbn0o;; 62 Tp;y2oqao borvs7t 60n.9;ynqP?    $ \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 hjcxpp6+e7mhj+ zh-7atoms near the surface of the Sun at a temperature of about 6000 K. mp7ce+p-hjh6+j hz7 x    m/s

  By what factor will the rms spebz36kzvt1 +lt20b4zhtyoc: oed of gas molecules increase if the temperature is43bbzh v +tt1tyo2: c0zo6lk z increased from 0 $^{\circ} $ C to 100 $^{\circ} $ C?   

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

  Twelve molecules have the following speeds, given in units of km/s: 6, 2, 43dt0 kk)m/vgl2n y a9e, 6, 0, 4, 1, 8, 5, 3, 7, and 8m)l9t/kvdgy e k32an0. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules+z;)z +9b0bk x;r *rvv -qrhy.ksdhfi in 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 doubledna)s9 i4 dbh kry7(;fj while its volume is held constant, by what facto rn(;)a khjdi74sy9bfr does $v_{rms}$ change?   

Show that the rms speed of 1oyhcz iwlack ggx-28 cmtb2:* 5(k6h 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, t-pe6yba4+,tbzn +gfwhe ratio of their rms speeds is equal to the inverse rabpny+ bf,tgw46e az+- tio of the square roots of their molecular masses.

  What is the rms speed of nitro)6wv vm;.3il9 bgqtf xgen molecules contained in an 8.5$-m^3$ volume at 2.1 atm if the total amount of nitrogen is 1300 mol?    m/s

  Calculate (a) the rms speed of an oxygen bcuh,0pcw r9vx;0 (ktmolecule 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 betu +uo)m /,u-jfz2guetween nitrogen molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whosezlqezif b7e+xp d: c*:a8 97m.s am+ib molecular mass is 89 u in a livi lc+f7 7e qsd:9 x:+mzza8mi.ae*pibbng 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 pressurpjxbz3e;:8 ctpgwg 74e P 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 uraniu(su eyb szvj,ew(h qv9gb+,- ;m, $^{235}$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 phas ak d,fzz u5/vak6o vlgb-+50 vu(cf4ees 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.,8vq uw1lz n;j uqet+301 atm and the temperature is (a) 9q1q ewvtjl+3z8n,;uu0 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50% on a h+7jdueit)- uday when the tempera 7dt+iueu)j-hture is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where water boils at 90 4tzb-q:du.osvt(a f * $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mountains is 0.72 atm, eh; ogx a62xy ;n i6gifc,bph52stimate the temperature at whixxh gi2,2bp 6hc5ag fy;6 ;noich water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure of water is 53hqv : e3ez*l h -whxn4o;2dq0e0 Pa and th:zweh e0qv4o 3h*;q nle2h -dxe relative humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial presvx7v3v* w o1pq4i4pbu sure of water on a day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside a pressure cooker if the water isb:5u 0+gjzc*(cyia t2v4 g zbh boiling at a temperature b*4(0ig bhg:a +z2vucz5 cyjtof 120 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a r2oiq gp(ypfg-, g af5(oom of 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 g2/(f ch1n -it vluoe-point 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 xa h ,ocfg05u+e )7uajTable 13–4) to diffuse a distancee5agu 07j)o ,+x cfuha 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 surface of insects t5tk /vxyd:wwxu,, 4 ne;e4 zkio the interior through tiny tubes called trache;t ydn4kxi/ :5ex,vuew 4 kz,wae. 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 has6j hk.q 1cq,i kx +z o3rm.k/td3zwj(h 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 precise steel tape measure has been calibraf48z kdh mtk:)ted 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 mu9v:sq3z 6z asyeq;1(gg5 zujmch error will be made in a recipe calling for 300 mL of cool water, if the water 6saqy3 z(e z5g:s; m zvuqj9g1and the cup are hot, at 80$^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a helium gas cylinder is initially 28 atm. After many br b45 426h mo)ocotmgualloons have been blown up, the gaum2 4o4ob6m tcgr5uh) oge pressure has decreased to 5 atm. What fraction of the original gas remains in the cylinder?   

  Estimate the number of , papftpt(e/4k8cyt6 air molecules in a room of length 6.5 m, width 3.1 m, and height 2.5 m. Assume/t 4at,te kcpf (pp68y the temperature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of mattes5xp g4qwi6n) h67hqzrl4,ybr 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 tech3lyk e908m k my2,rygzniques is about 92,ymrgy3kl ym k80ez$10^{-12} N/m^2$ 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 capa;ruvzwb: 9 h 6dvz8o:ycity of 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 advisabley 89duw :rbz:o zv;h6v?    L

  A space vehicle returning from the Moon enters Earth’s atmosphere at a sj(r ev)1 +.8gotpk;fhz w3wy cpeed of about 40,000 km/h Molecules (assume nitrogen) striking the nose .8(1rvg +f; ehywpjcwot)k3 zof the vehicle with this speed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)    K

  The temperature of al du2f8evyhz .r7 1sm8n ideal 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 b ybc-t-ul zp+ c8z/:dk2chz/770m$^2$ (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, esti5sc0yjvgfndu i9h7 y;.p2 l v cg-y7i)mate the total number of air molip;gsy95y 7nuvcyd0g ij)-fhl7v c. 2 ecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogeaq8gu7gkm;,y f spl(4 n 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 used in ( )mgrsr:q 9u*fyaexd4(9aqq a hospital has gauge pressure = 2000 psi (13,800 kPa) and at T = 259K How long will the cylinder last if the flow rate, measured4d*m(sqaqq) ur:r 9g( f ey9ax at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mercury at 0hz 9taslhz/ j2yr37w /$^{\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 at0gnl7s6n u -lr 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 sn k,3wwdj ,aiw1ugly 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 glasshwq08 j 3rsx+k jar at 20$^{\circ} $C. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 60$^{\circ} $C. The inside diameter of the lid is 8.0 cm at 20$^{\circ} $C. Find the size of the gap (difference in radius) that develops by this procedure.    cm

  The first length standard, adopted in thg+n tm3v--tjke 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 pressubhp lboscu1n8b: ej. 6bf8 c8cm1j) 5ire of 195 atm at 20$^{\circ} $C. The volume of the tank is 11.3 L.
(a) What would the volume of the air be at 1.00 atm and at the same temperature?    L
(b) Before entering the water, a person consumes 2.0 L of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last?    min
(c) At a depth of 20.0 m of sea water and temperature of 10$^{\circ} $C, how long would the same tank last assuming the breathing rate does not change?    min

  The escape speed from the Eart v)o04vwoez 5g-;: zucfhk om;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 s0l6 5/yj. vxhanodzx4uspended against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, asn /xyaz hljvd.o50 46xsuming 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 (sphehrdwvz- wei4 7;.8g6nm,el /bka ofq1rical) bubble of air from a depth of 14.0 m in a lake. Assume the temperature is constant at 298 K, and the air behaves as a perfect gas. How large is the bubble when it reachvo6lid.rw1b;7,z/ - 4m qkf whgn 8eeaes the surface?    cm

  Calculate the total water vapor pressure idun a)fm,lb j9 j+cv,2n the air on the following two days: jal, ud9b)+ cjm2 ,vfn
(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 dl)yimj4ew. o 8i ,:pwhioj *j)ifference in the density of iron at STP, and when it is a solid deep in the Earth wher,jh)) i8o:ljw 4*j ipmwoiye .e the temperature is 2000$^{\circ} $C and under 5000 atm of pressure. Assume the bulk modulus (90$\times 10^9N/m^2$) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.    %  ----待选择----decreaseincrease 

(a) Use the ideal gas law to show that, for an ideal gas at constau,e73vzsounx64 -x7bcgq0f gnt pressure, the coefficient of volume expang-fz 34q us gn,7xocv70bu x6esion 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 constantlx rj5i q:e9m+uae- u-gy dehumidify their cellars to prevent rot and mildew. If the cer+u9 -:5q-jmeia xgeullar 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