Which has more atoms: 1 kg of iron or 1 k;663jac0+dxc kfq( xn)sx*prxe l k3bg of aluminum? See the periodic table or Appendix Bx xcpq d k(fl 60bjs6e+x3c)rxna;k3*.

Name several properties of materials that could be exploited tky/+;/taipb,q/r x re/enm 9to make a thermometer.ty;+9 bper/exim/, /nqk t/ar

Which is larger, 1 C x5 hw bwo4f70. ui7lw705jte+sx mgbq $^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal ehstt s)cg08ugh ;5o4cquilibrium with system B, but B is not in thermal equi4csth5;c0go usth g8) librium with system C, what can you say about the temperatures of A, B, and C?

A flat bimetallic strip consists of aluminum riveteg43 ys3afek14* uchn38z xwwbd to a strip of iron. When heated, the strip will bend. Which metal will be on the outside of the curve? [Hint: See Table 13–1.] Wh4eh3c8w w*3bfzy1 us x4akng3 y?

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 coefficientqq *w kc)s*oc;+4)j2e jo rpcw 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 useggkw8cg.n: : k3zlr-5+w xzc rd to control a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of-c gg w53wx gk+lr8:zc:rknz. 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 are fixed at the 4i(mba+ lc +4kcy n),pqbs18de8ggfmends often have a section in the shape of a lnc 4b8eqm+ ky 841, ab)i( gf+psdcgmU. Why?

A flat, uniform cylinder of lead floatslzjx26zqn* b b, pi5)z in mercury at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-ir)kxn/9lz+x uq;p 2nqn-glass thermometer is first placed in a hot tub of water, 2ukz 9 q ;n+lq/nxxpr)the mercury initially descends a bit and then rises. Explain.

A glass container may break if onet-ruvm n0ajxp7f:8o6 part of it is heated or cooled more rapidly than adjacent parts. :t vpumf8o-67xn j0ar Explain.

The principal virtue of Pyrex glgk;j)e q8erg2t g,su/ ass is that its coefficient of linear expansion is much smaller than that for ordinary glass (Table 13–1). Explain why this gives rise to the increased heat resistance of P rsj)/e ,gtg; qekgu82yrex.

Will a grandfather clock, accurate at ; li7vj8*xnl 2et/qv3. .gbz7anx zne20 $^{\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 pt)g)s8(n-b263: jkzbvzp6gkx au ztcause its bottom and top to bulge so badly the can will not stand up. What has haat b3z:z-u6)8tg(2g p knszpb6kxvj )ppened?

When a gas is rapidly compressed (say, by pushing down a pwlvhemh q)p 8)wjd;),gt5re 8iston), its temperature increases. When a gas expands against a pim8l eghr ;) 5j,whdq p)8ewtv)ston, it cools. Explain these changes in temperature using the kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force on an aluminum sphere submerged in water incre xxuf: 5oy(2ik;9znnl ase or decrease if the temperature is u2fny5 ;:l(9kin zx xoincreased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinetic theory ankox4 t0iaki:u o.)o/n p3lj n-d the relation between average kinetic energy and t0 .n3xnoop aji/k)4oktui -:lhe absolute temperature.

Explain in words how Gay-Lussac’s law follows from kinetinuojng7esl7f9. w.jp5; x7r vc theory.

As you go higher in the Eartugyr*c d1 r:wc94q nz;h’s atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers tojaov n,*/zj- n the minimum speed an object must have to leave the Earth and never return. The escape velocity for the Moon is abou-oj/ ,*jn nvazt 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 wateo qj6cd 6 (z14nph6ojyr at room temperature. What can you infer about the molecular properties ofj (o6n1dzc pjh 66oq4y one relative to the other?

Explain why a hot humt8j+ y 2)axvmiid day is far more uncomfortable than a hot dry day at the same tempert 82 yajimv)x+ature.

Is it possible to boya;:up9b6/t(wve*azyb a sk+ yae6k5il water at room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperaturdznlh yoqo r+w*5 50)te is the same but the humidity is different. Wylnh*0) +twoqd55 rozhich is more dense, the dry air or the humid air at the same T? Explain.

Explain why it is dangerous to open the radiator cap of an overheated automobil,6 ofjcuo f,0fe engine.,f,foo0 uf6cj

Why does exhaled air appear as a likn*vovmw.d)b ;mk cun mx+0 ;t;cit)c09c(ckttle white cloud in the winter (Fig. 13–28)?

  How many atoms are therdbwbf,j01cu+b g xgimn*+scp /z .0d9e in a 3.4-gram copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold o//ebqj5il -fring compare to the number in a silver ring of th/qf j 5i-eol/be same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68h.6v o 8jw5 6skvhre pb/1i;cn°F. What is this on the Celsius scale?v8ec h.56;wbh/vspk 6 1jiorn   $^{\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 te 3a*m3zhey,ro6ai p( emperatures recorded are 136 $^{\circ} $F in the Libyan desert and -129 $^{\circ} $F in Antarctica. What are these temperatures on the Celsius scale?high =    $^{\circ} $ C
low =    $^{\circ} $ C

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

  In an alcohol-in-glass thermometer, the alcohol column has length 11.82 cmv m-mp1ka)0ojg k4)vm at 0.01m0g v-v aj4m) pkom)k $^{\circ} $ C and length 22.85 cm at 100.0 $^{\circ} $ C. What is the temperature if the column has length
(a) 16.70 cm,    $^{\circ} $ C
(b) 20.50 cm?    $^{\circ} $ C

  A concrete highway is built of slabs 12 m long (20xvw22 )rkxp8,:knzfjnn d. *l $^{\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. 13–227bi s,if7 /4xibg9-kox ;lrzsykya3 9) is built of wrought iron approximately 300 m tall. Estimate how much its height changes between July (average temperature of 25°C) and Jan7k,3bz7xyx/i ;i4 y sif-bkrsog2l9auary (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 usel7(q l/lv7 xied and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter llx7 7e vql(/iis 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 at 4bl-c lv6c. q 5x(gee2o $^{\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 i2cu6 8tsnk gk3n diameter. What will be its change in volume if it i6 cu3k2tsgkn8s heated from 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 ad+jm4sdk92kr:0ux p .3-gu ounoo h5mL 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 cet v bcskni 101nys i)sjh-n5,n: (q/wp:wk8of water at 20 $^{\circ} $ C completely fills a container to the brim. When the container and the water are heated to 60 $^{\circ} $ C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container?    $ \times10^{-5 }$ /$C^0$(b) What is the most likely material of the container? The density of water at 60°C is 0.98324g/ml.

  (a) A brass plug is to be placed in a ring made of iron. A jec(z+u7a, bxt 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 cagrh1:o7b4n;hk 4j z iln expand in essentially one direction only, show that the effective coefficient of linear expansion is approximately equal to the coefficient of volum ozr71l:h g4;nk 4hbjie expansion $\beta$.

(a) Show that the change in the densityn ns,l)q9;ff j ik .axz7fbn+3 $\rho$ of a substance, when the temperature changes by $\Delta$T is given by $\rho$ = -$\beta$$\rho$$\Delta$T
(b) What is the fractional change in density of a lead sphere whose temperature decreases from 25 $^{\circ} $ C to -40 $^{\circ} $ C？

A uniform rectangular plate of length l and width w has coefficient of l9ittpt 0t-to 3sjl-;d3 .vzp emff.n4 inear expanstn. mz.i3;e tt-4lff3ot-spd p0j9 vtion $\alpha$ 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 iso-fv-do9j6 )tym y4r fmtropic 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 nen2 (f ihvi 7(7avq*i8)gonxmade of brass and keeps perfect time at 17 iaxin2qon(7efivh8n7v *( ) g $^{\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 thermomete ltz6jhx4 v2qu+a2re ,r has an inside diameter of 0.140 mm. The bulb hahreu la2,64v x+tqzj2 s 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 ra 3(/ ps7quqpb b/rs+zndius 0.41 m is rotating about its axler3 pb+uq(/bp7qz ns/s on frictionless 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 th.2 l8abbm2 tcue desired length when at 15°C. How much stress is required to keep it at this leabbtu28lmc2 .ngth if the temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam o ijm(f,g v/oy*be-d+v f cross-sectional area 0.041$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diameter 13ssn.6ty.5o.gq qp w0n4.122 cm at 20$^{\circ} $ C is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 cm at 20$^{\circ} $ C. It is 7.4 cm wide and 0.65 cm thick.
(a) To what temperature must the band be heated so that it will fit over the barrel? $\approx$   $^{\circ} $ C(Round to the nearest integer)
(b) What will be the tension in the band when it cools to 20$^{\circ} $ C?    N

  What are the following temperatures on thejfw6 gu 3r6e jp58+rzo 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 zy7ed0gg ) v85c+leep temperature on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth a4tlos :ut7 nyur9af9s:ow8 -znd 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 atmospheric pressure and a,8am1s8 0c2bnjw w qot temperature of aboutna1sj bww,otc8 q m208 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 4bpbn;9l9g -re h ugr:-xf1p) n3vigkusing the ideal gas law.    kg/$m^3$

  A storage tank contains 5 *up639jmifi /m ;h9rnms lrw21.6 kg of nitrogen ($N_2$) at an absolute pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by an equal mass of $CO_2$    atm

  A storage tank at STP contains 18.5 kg of nitrogz (6ec4( uy3,eprlc wben ($N_2$)
(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 gasjyk easn5 yq0bzd9 42- is at 10.0$^{\circ} $C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions.    $m^3$
(b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.    $^{\circ} $ C

  What is the pressure y c l0yr6rlge ;6iw:w*inside a 35.0-L container holding 105.0 kg of argon gas at 385 K?0gw;eli *:cr wy66r yl   $ \times10^{ 8}$Pa

  A tank contains 26.0 kg of wbj2;wna)/9l c4t 5d slp )hhf$O_2$ 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 itsqci /(+9 +a ts3pkwucz buoyant lift by heating the air inside the balloon, wh s/p(39uitzckwa + +cqich makes it less dense than the air outside. Suppose the volume of a balloon is 1800 $m^3$ and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0 $^{\circ} $ C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.) $\approx$    $^{\circ} $ C(Round to the nearest integer)

  A tire is filled with an., ozxi-h p7gk )3wofir 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 1nc,t i8o(csy)x 1(9gpww7 yff 8.0 $^{\circ} $ C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 50.0°C, what will the new pressure be?    atm

  A helium-filled balloon escapes a child’s hand at sea level .gfi, mb7 9s6 fglhaq2and 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 mole9jc)if ny a,)-) oig ib)ujr,icules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.000 L? How ma .nxvku9a 5j*gny molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number o6ddwk6oi.h7hruh u btt * mvk z*0n/.5fu(a 9wf (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 5.1pct4:y 8lm1vh $ \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 in5z,6ozrbh mdn 9rt k;5hale that were also in the last breath Galileo took. [Hint:dbhzokrm,r56; 5 n9 tz Assume the atmosphere 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 ovw ;v0fj:28i2 jkxwux + jiq1STP? wjf21ui ;wj k2+ xv8jvx0 q:io   $ \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 i5dk fi85; ks/rzfeb ;. 3teo*olwxl+near the surface of the Sun at a temperature ofolflx+8t 5 ebi35zd;wrfi.o* kk;s/e about 6000 K.    m/s

  By what factor will the rms speed of gas molecules increase if the temper-klxm dv gpl6v6/x5fkf ip-8 /ature is increaspv-kxilfdv m-x / plfk85 /66ged 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 followin gz .5vdnxypep 8*8wqf.suv;(g speeds, given in units of km/s: 6, 2, 4, 6, 0, 4, 1, 8, 5, 3, 7, and 8. Calculate the ;exs8v(z.qpf*pv5.8ngu dyw rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in a gas s9xmxuecpxvfhv m )tmhqd8-6m -74 ;:at 20.0 $^{\circ} $ C is to be increased by 1.0%. To what temperature must it be raised?    $^{\circ} $ C

  If the pressure of a gas is doubled while its volume is held constant, by 5q h 96fj9pv5(jb hnxf2b go1dwhat factor doh9(fvnd2 j6f o5gx 5hbjbq91pes $v_{rms}$ change?   

Show that the rms speed of molecules in a gas is given bye-m(g d0s-g-q,nh vsi y; y9xj $v_{rms}$ = $\sqrt{3P\\rho}$ 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 rati*omqu ;yu r/o zqnu/(2brrr1*;-ryvyo of their rms speeds is equal to the inverse ratio of the square roots of their molecular masseb yy*uy(; uorqm/;2q1 ounvz/r*-rrrs.

  What is the rms speed of nitrogen molecules contained in an gbamp gl ;pina+ j-/9n7.s.eh 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 molecule at c6hfii *ny no9: 3.ha+o1xyj u0 $^{\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 molecules+-t /xbwtr0)6c2n oxkllci:tf hy4 j. at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amihrt3 :t 2b2 10l .bavimcaywj,no acid whose molecular mass is 89 u in a living jl 2:irwt 2y bacvmbat1,3h0.cell at 37 $^{\circ} $ C.    m/s
(b) What would be the rms speed of a protein of molecular mass 50,000 u at 37 $^{\circ} $ C?    m/s

Show that the pressure P of a gas can be wriu:)tqg9 qx srs67r;:tpg mjk0tten 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 ura( iralzoy u 1a 1d-.(a1i72w w8aeaw+hd2dwetnium, $^{235}$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 pha9ba;hl(khw6mwe 1v 3 jses 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 pressuo he:e/ .gs8eqp 6*puxre is 0.01 atm and the temperature is (a)s8 e hgp *xpe6.ue:q/o 90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50acowfe dpsvd2 /jb- 5wgvg z)x1/.*4f% on a day when the temperature is-wd bs5f a1*/g/d of2vw x.gzc4pvje) 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a mi5l (fu +5oqzplace where water boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mountains is 0.72 at 6 z6i3p+ cgkr75xbbdr26hkwq m, estimate the temperature at whi56rc wr3d +qkk6xh6bbp7 2zgich water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature q/.9 . v2 sbqdvafvhf+ qoq3inhcb 972on a day when the partial pressure of water is 530 Pa and the relativ932 n7bh2c vfqbf+qqo h s.dvai./9v qe humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on e: dqld(1/ vgga day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pri 8 )jq4 inpz-h1g-wjhessure inside a pressure cooker if the water is boiling at a tem-hw -4 qij8pz1hn) ijgperature 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 volumew: 0u7cg.oeqx6peuf:fujm:: 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 of wd:486i**ia uxbyzq m 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 Table 13–4) to diffuse a drq :/ibrh8 l ..frhu;yistance offrl/ r;hy .ib8uh.:q r 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 to the interior through tiny tube :g58k ckr+jbk;/inzsz h6alb,v+ :zws called tracheae. An average trachea is about 2 mm long and hasr:+zkav;wb8h: zic /+ nzbg 65jkkl,s 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 meas nuuu7ws3lo9c;hl 01hure has 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 calzhcz.ajgk 0s: tyva m(cb.4b)h9 ogx; ue63.fibrated 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 mucyqpu hjw/c -/sf n,tv,;i n 6sy.i29yvh error will be made in a recipe csnhys ij6ycu9v2/ y v ,,q/fwtpn-.i;alling for 300 mL of cool water, if the water and the cup are hot, at 80$^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a helium gas cyltx,5li)+1dtcr h, c84rvog geinder is initially 28 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. Wht l5)c t8ier gg4,h,+xrdv1ocat fraction of the original gas remains in the cylinder?   

  Estimate the number of air mod+qh r7x.4ptg (3jd eot8xch)lecules in a room of length 6.5 m, width 3.1 m, and height 2.5 m. Aop t+d et c4xd)8jhxg 7hrq3(.ssume 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 one atom per(taix.-t5qx iy*a9fv $cm^3$ 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 7nnhe. x*c ,+w.iumd tbest available vacuum techniques is about n*+im.twnhx e d.cu7, $10^{-12} N/m^2$ 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 lun9b 9t 20owiucags to full capacity of 5.5 L when 10 m below the surface, to wha 0t9 b2cui9woat volume would his lungs expand if he quickly rose to the surface? Is this advisable?    L

  A space vehicle returning from the Moon enters Eartce pjuon4cke0,* ob*2zh7,i mh’s atmosphere at a speed of about 40,000 km/h Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of 0n e2u* 7 ,b4cohz*,okmpcijespecial materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)    K

  The temperature of an ideal gas is increased from 113ugj2edt5b0har7 o 3u+y4j vv0$^{\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 nv fg5nl.f l6cv o*:nzrs3.w5l tkl .-of 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 2 i:akam df42nof the Earth, estimate the total number of air ma2ia:nd 4k2fmolecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen moleculebfwpb750qs. yo il i)/s 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 a hospital has gauge pressure = 1hstiok-( )n3n efdt a.gi*0n2000 psi (130fneki*n( .) tthn31dioa -sg,800 kPa) and at T = 259K How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mercury krn:: o4 vkol8at 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 4u7 u7a azycl+j71wiaat 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 around the Ep7v y0y/ltr sol5-t5f arth’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 av+ pyphv1- xv3(bk:njar 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, adoptw:m24-c gzyn rq6y tp ),wgj:qed 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 fu ye+9fgrna,bxuy0j2zr q81r(lly 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 thegum4b-z2bf k6 Earth 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 a9vxv(*14n/ihmwvt p3hyjr1 pgainst gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebou*hwpmry 1n3vvh vp x /1i(49jtnd from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diameter (spherical) bubble of air from a dc s6m2 yw/0b9h,f:,v alxenuqepth q/xwc2 e,f,l ua m 6n9:0vsyhbof 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 reaches the surface?    cm

  Calculate the total water vapor pressure in the air on the followifioxmg8;)5 0r/ldw av0efwu 4ng two days: 4mxarglf0ofu;e dv0 w)5w/ 8 i
(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 denm9+0tzy0u a- b j0dj1oppkp/esity of iron at STP, and when it is a solid deep in the Earth where the temperatur+ 0zpo pt k900 /ym1jpduja-ebe 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 consts ipyy26 me6 oy541rwkant pressure, the coefficient of volume expansion is eqeyi5yk omsy146 rp26wual 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 ths89b+ae :fouweir cellars to prevent rot and obw9fus+a : 8emildew. If the cellar 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