Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the periodic f8daz +p txc/h2p1h2rtable or8drptfz2hc x/+1ph2a Appendix B.

Name several properties of mate;x5lyd( l:8jx 0abvzo rials that could be exploited to make a thermometer.xv5 b(x:;8zlo ldyaj 0

Which is larger, 1 C :po+k f7.2 6sqysqqlt $^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal e,pzqxw:3s-z ;mgtzu) quilibrium with system B, but B is not in thermal equilibrium with system C, what can you say aboz:p)s;3,xzmuq w- zg tut the temperatures of A, B, and C?

A flat bimetallic strndpz(vit1(c8rq m-3 p bzsmb 90-19rikwp wd,ip consists of aluminum riveted to a strip of iron. When heated, the strip will bend. Which metal will be on the outside of the curve? [Hint: See Ta mpwszb0 ni19k3dpqr m-crvbp(d9( iwzt8,-1ble 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 linear expansionng d+.d 5wn* zqsgyq4f ddh ++1,rd9av $\alpha$ 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 co 4119socptww7zons i-ntrol a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid mercury that conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and how it can be set at different9pwsots -zn1i1oc4w 7 temperatures.

Long steam pipes that are fixed at the ends 4gxsl c/ay c3vz,l, a2often have a section in the shape of a U. /cl sxzg432,, vlca ayWhy?

A flat, uniform cylinder of lead floats in mercury at 8xh*g bv6obq)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 placed in a 8(..mfp3iylgyb zy,aga 95 ih c9cpz 7hot tub of water, the mercury lgc 9a pfp(yymh8i7zazb.3y,9.gci 5 initially descends a bit and then rises. Explain.

A glass container may breakdgl m5v,xzt9 fp8xyk.1 c(2ve if one part of it is heated or cooled more rapidly tha8xm521kcp l(e 9vg.d zvxty,f n adjacent parts. Explain.

The principal virtue of Pyrex glass is tkz-)w42bo 38ei6 lj jsg4tk.o+ j arvmhat its coefficient of linear expansion is much smaller than that for ordik6g+z4elsa3 m ik)t2jjw-ro.8 bv j4onary glass (Table 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accyoiu ih1 ke 0 l*+.3feah5bad;urate 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 bul*fbyus5 r b 8)w,jwnx.ge so badly the can will not stand up. What has happenedy sw 8.f)ubwr nj,b*5x?

When a gas is rapidly compressed (say, 0g(hro6c(du ydd3 )ty by pushing down a piston), its temperature increases. When a gas expands against a piston, it cools. Explain these changes in temperature g uc6 yhy0 tdd((odr3)using the kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force onivy13x/eh rm;: oxee/dl 5f.g an aluminum sphere submerged in water increase or decrease if the temperature is increased fromex. vm1r;eio3hgfe5 d y:/lx/ 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinetic theory ang:m9nl qbj1 nmow9n4x ,ut a+.sj8n.g d the relation between average kinetic enen a48+,n sn9bjo9um1. :nqtxwmj lg.grgy and the absolute temperature.

Explain in words how Gay-Lussac’s law follows fr. ( 3la8v5fml ciqr1ulom kinetic theory.

As you go higher in the :h8x2vrcsa95 ; a+n2zfyf id dEarth’s atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minimum speed an object must 0ztqkr ru80q wwcq9-b-i)6ry have to leave the Earth and never return. The escape velocity for the Moon is about one-fifth what it is for the Earth c 0k-ti0wrbq) -98yqqr u6rwzdue to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere.

Alcohol evaporates more quickly than water at room tempel9zl)lh ow:k)wbo:m g* ;/zi, ima/x drature. What can you infer about the molecularl,z o/ib:ok )9x mgi)wh *dl;mzw: /la properties of one relative to the other?

Explain why a hot humid day is far more uncomfor)9z hr9d -rihttable than a hot dry day at the same 9h-rz9 r)tihdtemperature.

Is it possible to boil wate**/z0a2 ddetd h dnfq en(8:sur at room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the yf .tsix6qd1. jju (p-air temperature is the same but the humidity is different. Which is mordj.tu6x 1f (psq-.jyie dense, the dry air or the humid air at the same T? Explain.

Explain why it is dangerous to open the radiogddz h/s/5/ )khh:utc1c;m lator cap of an overheated automobile ocu/ddl/zh15)st;kh m: c hg/engine.

Why does exhaled air appear as a lwqn+f+ mse.8qc8uv1h ittle white cloud in the winter (Fig. 13–28)?

  How many atoms are there in 0 ue,i7pwldqd d;ksc/ut w90( a 3.4-gram copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring com2u5)nu5+hmu 8v0zkvkh:6ip/ u cce zmpare to the number in a silver ring of the sa 2ce 6p8iumh5zhzn):+cvm5k uu/ k uv0me mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. What is this on tf gq:5nsu0)v8c+ka8a7ug j6dpc v 6fahe Celsius scale?g q)d+a a0uja8gcp8f 6k7f 6v c:nvus5   $^{\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 are 136 e17: fqw 7r:msjmr+ by$^{\circ} $F in the Libyan desert and -129 $^{\circ} $F in Antarctica. What are these temperatures on the Celsius scale?high =    $^{\circ} $ C
low =    $^{\circ} $ C

  (a) 15 $^{\circ} $ below zero on the Celsius scale is what Fahrenheit temperature?    $^{\circ} $ F
(b) 15 $^{\circ} $ below zero on the Fahrenheit scale is what Celsius temperature?   $^{\circ} $ C

  In an alcohol-in-glass thermometer, the alcohol column has lendz+tks2.z p8 7mvu2rrgth 11.82 cm at 0.0mtsu2vd2 .k 87+prz rz $^{\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 slabnl /7*fxbp a5ys 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 (Figl w24srjh80fw. 13–29) is built of wrought iron approximately 300 m tall. Estimate how much its height changes between July (average temperature of 25°C) anwhwlr8 2f40j sd 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 usedr4qxfp;q:puzv(m m4* and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.prx um;4:m z*p4fv(q q871 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 atth):uzts jv evg)9h9 : 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 coi84/p:cqc5o c4by whm in diameter. What will be its change in volume if it is heated f h4boyco i /w:c5c8p4qrom 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 mL of waterp rw,o gf4n1:c 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 wa x:g655ytevanyk,uczv 64h.a ter at 20 $^{\circ} $ C completely fills a container to the brim. When the container and the water are heated to 60 $^{\circ} $ C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container?    $ \times10^{-5 }$ /$C^0$(b) What is the most likely material of the container? The density of water at 60°C is 0.98324g/ml.

  (a) A brass plug is to be placed in a ring made of ic2 mepd,0 w.o yohte33ron. 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 bkw5c mrhy)0l.4tt-8qoyp 2 q it can expand in essentially one direction only, show that the effective coefficient of linear expansion is approxycyb wkr4l h8t0q2 t.p)-qom 5imately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change in th(jn8g tlfm (dy2aj4r-e 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 le 3yi 6x2s2yxl)w5s tkhngth l and width w has coefficient of linear expansh6s kyl23x5)ysx i tw2ion $\alpha$ 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 isotropo1kde8-r 9xjve4ac2 g ic 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 brass and k sgy,opv25env:ie,;peeps perfect time at 1 opp;n5y, 2v:eg ,evis7 $^{\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.ffhc4m:ptjivznb ha 0gxx81 w)415 u+140 mm. The bulb has a volume xw4gtnv1 i+ b:z1f5h0x)mpc48j uh fa 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 i oa-)ichm 6s mt/*ti2as rotating about its axle on frictionle26omst mac)/tii*-h ass 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 desire:8dec:l 7t qezk-lgr2 d length when at 15°C. How much stress is required to keep it at this length if the temperatelg7dlcerq: :zkt2-8ure increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-s:u (( eez)cm*vsg)7kqtnf vk .ectional 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 134.1.*rhr32(gd0c2t hdwv.vl c w e22 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 temperatures2bt*p0j mb6 0zfx6 pya 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 temsr1 9 p;2vj26momg7sd c ,bfslperature on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth and Sun a ;a,o pyl21ts sdhg2/2zrml;m re 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 atmosphja3yn-tdkm2zy)3w3 6rvt qw6 zr1;t eeric pressure and a temperature o2z;ej 1q aktw)6n 6ywvryt d33zt3-mrf 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 ideal gas l.fl ;j1 /uxd) / shrub 4u,tluha3jw;qaw.    kg/$m^3$

  A storage tank contains 21.6 kfy;wgc+qx qf b *u:.e/g 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 ygzue, s5:df1 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.(cp0z vyl7x 4f0$^{\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 contaovkpb 09r23mnd8 )sf hlc6sue i;e d/.iner holding 105.0 kg of argon gas at 385 K?9h;s )uibs d./3v0fecped mr8k26l on    $ \times10^{ 8}$Pa

  A tank contains 26.0 kg of . -; lojb5cujd$O_2$ 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 inside the bal/pxh y;5sl /uuloon, which makes it less dense than the air outside. Suppose the volume of a balloon is /; 5 /spxlhuuy1800 $m^3$ 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 withfb.f,wrixzt l2;;z.c 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 at 18.:3pkno4i;u qj4ur ,+p 7tq vfx0 $^{\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 escape h2oxxh,9o7 zk/4uun h)1jx5yqh g2 ebs a child’s hand at sea level and 20.0 $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number of molebljqfb dft7nm7c.4 wvi. : 82ucules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.000 L? 9b298d o, tnx yxai+6tru7glzz /ok w1yg74 ozHow many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number ym9;bx- m)i-tu/bkc v3*vt lrqq-z j 9of (a) moles,    $ \times10^{22 }$ moles and (b) molecules of water in all the Earth’s oceans. Assume water covers 75% of the Earth to an average depth of 3 km. $\approx$    $ \times10^{46 }$ molecules

  A cubic box of volume 5.1jbmy8 t6u 9(j:km8(b/bscomye k 3 ul4$ \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.hg 8dp23j7hoeiz+u7l 0-L breath you inhale that were also in the last breath Galileo tool8hp g77 heji2dozu3+k. [Hint: Assume the atmosphere is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic enead c-b7 9xvm,h/q1obergy of an oxygen molecule at STbva-m1dqc b e9 /xh7,oP?    $ \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 S/ez e,hjlh5tb:o bn*neh5 4r 5un at a temperature of about 6000 K5r/h j5nel, h n* 5eho:b4betz.    m/s

  By what factor will the rms speed plr,/d :tt8xt: jh;fhrhe - 3zof gas molecules increase if the temperature is increased from 0etf tr8:lhjh;p -3z r:/,hdtx $^{\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-t4ja 7z +w zu7vltly7, 4, 6, 0, 4, 1, 8, 5,+ l y77zav7wt ju-4tzl 3, 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of moleculr :fjb(. xft ultcr,+.es 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 doubled wht y0sots++re* z23dycer+ 9m zile its volume is held constant, by what factor d+ ydss+2r+z 9yc0*ttr3z emoe oes $v_{rms}$ change?   

Show that the rms speed of mole+g o/;,kx6hwoolqf xbke /e-6cules 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 rah 27ugiox w,mtiq8 t;(tio of their rms speeds is equal to the inverse ratio of the square roots i twmt7ug (ihox 2;,q8of their molecular masses.

  What is the rms speed of n d4yf s/2av)r*pko4g ba*f0bditrogen 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 an3uiapb/ ak4+h77zxmj oxygen molecule at 0 $^{\circ} $ C    m/s
(b) determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collisions with other molecules.    round trips per sec

  What is the average distance between nitrogen moleculesj latds*57*cy at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose mole zhzco3rc),; ncq9s+k cular mass is 89 u in a living cell)9zrn 3cc;s k,zhq c+o 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 written P = w( z2:/a7uvyf js h*be(1 kpkm$\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of uranu gdma-mlmo0gw . i484ldmp, 0ium, $^{235}$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 whahzr)* bx r-l1))hlht vt phases can $CO_2$ exist? (b) For what range of pressures and temperatures can $CO_2$ be a liquid? Refer to Fig. 13–21.

Water is in which phase when the pressure is 0.01 atm and the txbq5r*oq w19remperature is (a)91xqbor *q rw5 90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if 3nt+wfr43dg xe w x w6waxyeik97p*59 the humidity is 50% on a day when the temperature x7 gw6 r eexkafiwn * 4wdxt5y399+wp3is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where wat+hdesnt g69bz,n+ 5i uer boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a pa cen5dg ey3(v9 /ztjosf2zi,3rticular place in the mountains is 0.72 atm, estimate the temperature at which gz 52/3co (syidvztj3ef,ne9water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure of weob /wl* iac46mhn-s 7ater is 530 Pa and the relative humidity is clae6ih*-w/ o4ms 7nb40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of was (jt6nhhkq5/b -- izlter on a day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure i1jxfx u0/n3k anside a pressure cooker if the water is boiling at a temperature of 1xja3/0 nfk1 ux20 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a room r e-vfm-p:-f*skas(zof 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 hw7e:.ya 8 vum9jdn 6hpoint 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 mzfrr 2ox4z6mgke 4ma 4o)kc0 6olecule (see Table 13–4) to diffuse a distance of 15 zg2 k6cxm0zo) r4kf6 4me r4oa$\mu m$ in water at 20$^{\circ} $ C if its concentration varies over that distance from 1 mol/$m^3$ to 0.4 mol/$m^3$ Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u. t $\approx$    s ([color=rgba(0, 0, 0, 0.85)]Round to one decimal places) $v_{diffuse}$    $ \times10^{ -5}$ m/s
$v_{rms}$    m/s

  Oxygen diffuses from the surface of insects to th9 m:xt bd+nehk8ihjs-d(. -1b1kdlpe e interior through tiny tubes called tracheae. An average trachea is about 2 mm long and has crossd-tseb(l-i hmkdhn 9xe+1pk8b. :1dj -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 hadx .0a 6c4ayect,qs( ls 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 cali)jjg6 -5wfhcr v t:*pqbrated 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 much rte caiw,a06( :9uwuy error will be made in a recipe calling for 300 mL of co,aureicyu(ww t:9a60 ol 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 ini .m5-zwek72oamm8gdbtially 28 atm. After many balloons have b -mb. 5kmd8mzg72aoeween blown up, the gauge pressure has decreased to 5 atm. What fraction of the original gas remains in the cylinder?   

  Estimate the number oylj8m 5wnsv)-d /wm,kf air molecules in a room of length 6.5 m, width 3.1 m, and height 2.5 m. Assum,n v/lkmw8jsdw5) m y-e the temperature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of matter is about onek59 l.9l nvnrk4 akw 44waqyb. 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 b,:/ k 7u3 p* t3vah+ivgz jpdjq*dlee0g7 ,knusing the best available vacuum techniques is aboevq*gk3pae: ,/ 7ntjgpk i,3dvj d+ l0uz7 h*but $10^{-12} N/m^2$ 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 m below theli2 wp5p4+n hr surface, to what volume would his lungs expand if he i24h+rl 5wp npquickly rose to the surface? Is this advisable?    L

  A space vehicle returninno/ttb dl4y5/ g from the Moon enters Earth’s atmosphere at a speed of about 40,000 km/h Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond tyn4l bod/t/ 5to 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 idealod-*8x5z /, pv:zmfrtgpcwb5 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 770mwjyp;yg3bg w 3/gt:t0$^2$ (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 atmosphetcq8o+ccduy*twa w +)v;ai . )ric pressure at the surface of the Earth, estimate the total number of air molecule.8ov cqy aciu) awd;t*+ +tcw)s in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speek6tt7 h3e eqw nh-)8dzd 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 rxoy)+6-ov n kof 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 pressurrk-+ o6y oxvn)e, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mercury cyc tvj(+a-d ;z(r:yv 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 gasolin88 xtr t-bye 8jzdj,+ ews+lg29man,ue at 0$^{\circ} $C is 0.68$ \times10^{3 }kg/m^3$ What is the density on a hot day, when the temperature is 38$^{\circ} $C?    kg/$m^3$
What is the percentage change?    %

  If a steel band were to fit snugly a q1x8z93juo,xx/mp w fround 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 jluaj-r+.+yvh/t4s / teg (ry8c g8hz 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,or.ty5xds3 + r 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 +1v 7m g:bvoe cxykjjq;.x0.k charged, 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 Eaa;ol4zcj*vgt 9 2vqi3rth is $ 1.12\times10^{4 } m/s$ so a gas molecule travelling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field. At what temperature is the average speed of
(a) oxygen molecules,    $ \times10^{5 }$K
(b) helium atoms equal to $ 1.12\times10^{4 } m/s$    $ \times10^{4}$K
(c) Can you see why our atmosphere contains oxygen but not helium?

  A 1.0-kg trash-can lid is suspended agains*f*8i7j v,ki4mylc no t gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, assumf i8c*4k7m,jl*ni yo ving they have a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-d ,:o16 e oxj3cs7ouw-e bswy5qiameter (spherical) 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 w,uje6qo5o cs1bo- 7y 3s:wxe as a perfect gas. How large is the bubble when it reaches the surface?    cm

  Calculate the total water vapor pressur lk*-i,c*pxr fe in the air on the following two days: f-*p*x ,i clrk
(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 de8 rd/amqi5 ot7nsity of iron at STP, and when it is a solid deep in the Earth where the temidt8 mqr o5a/7perature 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 p:p g bv,vo39xlk md09show that, for an ideal gas at constant pressure, the coefficient of volume expansi: ,bpl3vx9 9ovdmk0pgon 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.