Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the periog673 oxsp: cibdic table or ixpg7c6so3:bAppendix B.

Name several properties of materials that could be exploited to make a thermoa3ajft 3r2 rcows9)e(m ;8vw tmete)s2t9 ovr3jw3ca emwa t;(f8r r.

Which is larger, 1 Cuc w84 y30rj4xjwvf s3 $^{\circ} $ or 1 F $^{\circ} $?

If system A is in th -ov7m n4vhr(nd j8:hhermal equilibrium with system B, but B is not in thermal equilibrium with system C, what can you say about the temperatures of A, Bn(h 4m7dnvoh 8 jv:hr-, and C?

A flat bimetallic strip consists of aluminum riveted to a strip6jdadk;yt1 8f 8 w.opv2ho pu9 of iron. When heated, the strip will bend. Which metal will be on the outside of the curve? pta2 ud 6y p9wkvoh8o.81d;fj[Hint: See Table 13–1.] Why?

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

The units for the coefficient of linear expansio-v :zb bvl6i6xn $\alpha$ 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 .dnyu0419h 8gqnfhblsimple thermostat used to control 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 devb8h dy4ln0gnuqh9 f.1ice controls the furnace and how it can be set at different temperatures.

Long steam pipes that are fixed at the ends often hat 8d hv4cnim-fr-uj5 .ve a section in the shape of a U.mj4r-5 cihu- 8vndtf. Why?

A flat, uniform cylinder of lead floats in mercury at 0 c+ud5ea kmo/ e kodx;h2k)-5a$^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glass thermometer is first plf6o/lsql 9b9 fnm+cg7aced in a hot tub of water, tn69b/ocllg+sf 7q f9mhe mercury initially descends a bit and then rises. Explain.

A glass container may break if one part of it is heated or cooled more ra4dy-w4o x6 )xq m(cteppidly than a-dq4weocxp)(m 6 tx 4ydjacent parts. Explain.

The principal virtue of Pyrex glass is that its coefficient of 8xmpz) vf kq*7(xf2 jvey37cdlinear expansion is much smaller than that for ordinary p fkf()xvj3dzy72*q xe7mv 8cglass (Table 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accurate at 21) m yizyos6i20 $^{\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 anxe1g-mna /ri (d top to bulge so badly the can will not stand up a1e g-mx(/inr. What has happened?

When a gas is rapidly compressed (say, by pusm g129n 9 p9dec6 /x4kglnbjcyhing down a piston), its temperature increases. When a gas expands against a piston, it cools. Explain these changes in temperature g1/jlgc m 6 b42p99ykcne9xndusing 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 ap8(a+ n:k2tf h6adknq luminum sphere submerged in water increase or decrease if thk thqfa:2npk6 +d (n8ae temperature is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charlesv d2icnr2 )f6b’s law follows from kinetic theory and the relation between average kib dcirf)26v2n netic energy and the absolute temperature.

Explain in words how Gay-Lussac’s law followsd: , c4mc,*tjzh,ovb g from kinetic theory.

As you go higher in the Earth’s atmosphere, the m 1jxx)cdp+/i ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minixfl/g* e + mzkrb3.:almum speed an object must have to leave the Earth and never return. The escape velocity for the Moon is about one-fifth what it is for the Earth due to the Mgx*lf.+:kr 3l/ mabe zoon’s smaller mass. Explain why the Moon has practically no atmosphere.

Alcohol evaporates more quickly than water at room temperature. What can yoh1bx p:ntd:-bu infer about the molecular properties of one relatb1 nh:bxd: -ptive to the other?

Explain why a hot humid day is far more uncomfortaf/t+nq8s ur n-ble than a hot dry day at the same tempeuqn/srf8t -n +rature.

Is it possible to boil wat m,dan (sjxx/wh3y*e/rq5ti+er at room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperature is the same but 1vn+eqsn0 9zh w) bnsut3o,f 5the humidity is different. Which is more dense, the dry air or the humid air at +t9fo1b z)vuhn n3s 0 w,nsqe5the same T? Explain.

Explain why it is dangerous to open the radiator ((shj8xk;zr)o m 1bkccap of an overheated automobile en(k 1zcmsx)( kjob8r;hgine.

Why does exhaled airp t2gi4g;i987j9 awz m a6jmsv appear as a little white cloud in the winter (Fig. 13–28)?

  How many atoms are there in a 3.4-gram cogtvp 3 f8vtql9/2 d0yupper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring compare to the nu /a:d+d*k5ra(fj jh6 0dyx ywbmber in a silver r:a add*hx+jryk b 6wfj5dy0/( ing of the same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. What is this on the Celsius sce mfwi5cbo1e 2,l)jp,ale?bi1ojp c2elfwm,) e5,    $^{\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 tempecb 7kp oc/*ds8ratures 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 ccex2 0sqyiz/. m at 0.0czey./2sx 0 iq $^{\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 sj:c q7/rzkz 42cvm jv(labs 12 m long (20 $^{\circ} $ C). How wide should the expansion cracks between the slabs be (at 20 $^{\circ} $ C) to prevent buckling if the range of temperature is -30 $^{\circ} $ C to +50 $^{\circ} $ C?    m

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

  The Eiffel Tower (Fig. 13–29) is built of wrought iron approxhm 3;c 5eyxow vr4p4je(m: ga.imately 300 m tall. Estimate how much its height cha;xpg5yhmo me4re 3v.a :4jc(wnges between July (average temperature of 25°C) and January (average temperature of 2 $^{\circ} $ C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.    m

  To make a secure fit, rivets that are larger iaq mlrr,u*), kly/ ru)n,qg :than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to beu) /qgy ,nimrr l, k:aul,r*)q 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 a2 v u3*4i0cyzs lrwqw2t 4 $^{\circ} $ C is $ 1\times10^{3 }kg/m^3$ What is water’s density at 94 $^{\circ} $ C?    kg/$m^3$

  A quartz sphere is 8.75 cm in diameter. What willktvux(0/efin 7ar3g3b/pm a + be its change in volume if it is hm7 xe3 0rtfp// gu aa3bv+(ikneated from 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 mL of waterd1yboo3d t4sr wsgn+b s79(w- at 100.0$^{\circ} $ C. If the temperature decreased to 20.0 $^{\circ} $ C, how much water could be added to the glass?    mL

  It is observed that 55.50 mL of water atuay 6 m:-0e+9ibspvim 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 be1qo l/z 0uj yt5z)(cl-stuz sv-0;j nh placed in a ring made of iron. At 20 $^{\circ} $ C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit?    $^{\circ} $ C
(b) What if the plug were iron and the ring brass?    $^{\circ} $ C

If a fluid is contained in a long, narrow vessel so it cansrf8s)ij4q :4;;,wlo a;gbi1 qjmfy h expand in essentially one direction only, show that the effective co; igqom1f4,qj j:8is h4b; rsyf ;l)waefficient of linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change in the d0znu.fxz8z )rensity $\rho$ 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 lkst+ k bd8uu(72mdtk5rru6 + rinear expkk5urd tm7d ks(bu+ r6+t 82uransion $\alpha$ 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 solin-)275 o8byd rj tosmq0me3j xd, $\beta$ = 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 g)sah-slqe3-da:4b g perfect time at 17 aqag e-h 4dbg:l-s)3s $^{\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 theruyv. df.y+ur2a)bd3uk /,t 1 cycsxm 6mometer has an inside diameter of 0.140 mm. The bulb has a voluys2)c ,u16ykt/x+v.rfcbmu d 3ud.ayme 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 04bf0lq*g sqh,2ey+i 9 zocaz-.41 m is rotating about its axle on frictionless bearings with anguz2 l9ehqsf zq*b- 0,ya4o+i cglar velocity $\omega$ = 32.8 rad/s If its temperature is now raised from 20.0 $^{\circ} $ C to 75.0 $^{\circ} $ C, what is the fractional change in $\omega$?   

  An aluminum bar has the desired length when at 15°C. How much stresx0m tzq: mkaxn f7(b4+s is required to keep it at this length if the temperature increases to 3xmm7 azq(kxtb n+:0f45 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-secgd v-i3 o(z(edw-hhy, 53plfs tional area 0.041$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diameter 13aig)q2 9jb/ofti oxt ,gu 9r*04.122 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 tempera+vx*nne9+cr)xb 8; f 4 ffrbhttures 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 t.b0t y2dpjyf6 -d3x wghe Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interjqp a 77+:rswciw-s1kior of the Earth and Sun are about 4000$^{\circ} $ C and $ \times10^{6 }$ $^{\circ} $ C respectively.
(a) What are these temperatures in kelvins?    K    $ \times10^{ 6}$K
(b) What percent error is made in each case if a person forgets to change $^{\circ} $ C to K? $\approx$    %(Round to the nearest integer) $\approx$    %(Round to three decimal places)

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

  In an internal combustion engine, air at atmospheric pressure and a tg b/3fy2 e 8te0h 8w6kyhwe9zuemperature of aehhe96 beft28 3y/ ywg0kw8uz bout 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 idel7ry-7q (inp c yz4rn8al gas law.    kg/$m^3$

  A storage tank contains 21.6 kg of nitrogen (rh9l oa x24w63:npkcz$N_2$) 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 nitrogen kwo,;xim .k+5zwg0wx ($N_2$)
(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 is2.fk d clk-ji; at 10.0$^{\circ} $C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions.    $m^3$
(b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.    $^{\circ} $ C

  What is the pressure inside a 35.0-m9cwo (gte ;(gL container holding 105.0 kg of argon gas at 385 ge( 9om(cwgt;K?   $ \times10^{ 8}$Pa

  A tank contains 26.0 kg ozx v04h1ps6s qb pp96ef $O_2$ 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 achi+8hozsgfc :a 7eves its buoyant lift by heating the air inside the balloon, which makes it less dense thancs g7:fahz8 o+ 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 aira3fm6lo+)jiapuq3 4i 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. u;kw:zs qsxd9 8ia0r70 $^{\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 w ws xa1s68ajf)7f5vn 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 mo brql8d7r7k2)zme0ym lecules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.0002t*lbg1.lfih bk tna:e1i 2 e2 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) suq8l:.f,zmh xva7)q 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 volum/fly j* d3e : c.s11b1gavfzjke 5.1$ \times10^{ -2}m^3$ is filled with air at atmospheric pressure at 20 $^{\circ} $ C. The box is closed and heated to 180 $^{\circ} $ C. What is the net force on each side of the box?    N

  Estimate how many molecules of air are in each 2.0-L breanh u+ 81j jsxgoh3c6*dth you inhale that were also in the last breath Galileo took. [Hint: Assume the atmosphere is ad*+ 1 nxsu6c ohh8jgj3bout 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic ene018xrj8w i yp2rykto 0rgy of an oxygen molecule at STtjw28ip xy1rk8o0 y0rP?    $ \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 surf+.4of k+;h nsydiu3sz ace of the Sun at a temperatu4 +h.u;zf3 soik +syndre of about 6000 K.    m/s

  By what factor will the rms speed of gas molecules increase if the tempert6+dhq h)a:k kmg-o c(ature is 6(+kct:qo-m )kdgahhincreased 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 unitsyqthr 3 h9kix7x3z*s7hw n, q( of km/s: 6, 2, 4, 6, 0, 4, 1, izts7w ,7qxhkhn*3hy(9rq3x 8, 5, 3, 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in a gas at 20b1fp wuw):a* r.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 whkun :l) i/bg9xile its volume is held constant, by what factor does 9)xgukb: /inl $v_{rms}$ change?   

Show that the rms speed of.4k lceo eaq*2 molecules in a gas is given by $v_{rms}$ = $\sqrt{3P\\rho}$ where P is the pressure in the gas, and $\rho$ is the gas density.

Show that for a mixture of two gases at the same temperature, the ratio of thei8 kat d,h(he,fr rms speeds is equal to the inverse ratio of the square roots of their t e,8hk,afdh(molecular masses.

  What is the rms speed of nitrogenq)yc5 8m gq+ww 5r7ixg 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 oxyo-e (tug6(gj8txx aj 4gen 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 nitrlr:b t8o;/2fnr k pp;aogen molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose molecular massi:k5e+u d gk*r is 89 u in a living celk+i5 :rk*gue dl 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 = k u+2++hbl4z lge.okjuzj5z9$\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of :pgpf5g3nv4) v7n zsm(q fx :juranium, $^{235}$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 pg nramx0r 9f3et9 9.gvhases 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 prz7+mfw3),aq xpd*jnvy k1;zn essure is 0.01 atm and the temperature is (a) n1f7kp ;yx) zwvzqnd am3+j,*90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50%lqhjbk; qhy+//nf9 5v on a day when the tempera/9 f/v+qbjhk5 hyqn; lture is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where wa 9yg5wv: ev-bjter boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular pl,4 itvb.3ng rpace in the mountains is 0.72 atm, estimate the tpgivrt3b n4,.emperature at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure ofjhf7 0y;-lr9l4hg6neux me 2ua s:k 4x water is 530 Pa and theg9e ur:s-4h xul 7lak;j6e2ny4xh mf0 relative humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a day when the temperature au1: 1 tquydr(-gbdy3is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate ppkco2qh qglb9 lc-or :q05kc/ fp*7 l-jh+gg-ressure inside a pressure cooker if the water is boiling at a temperature of 1c q5*l97hgjg /-q-qfc2k0:p rh-pgck+ol blo20 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a roomte yeg .o)4lc, 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 dexbdrh5pmqe46+ n / oi6 93y*m urnhgz9w 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.c*du9i;p hketm -ml3 (see Table 13–4) to diffuse a distance o- kde.ui9;p3h* tclmm f 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 througje,i96*icqrh h tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-sectce9rq i*, hi6jional area of $ 2\times10^{-9 } m^2$ Assuming the concentration of oxygen inside is half what it is outside in the atmosphere,
(a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20$^{\circ} $ C is about 8.7 mol/$m^3$ then $\approx$    mol/$m^3$(Round to one decimal places)
(b) calculate the diffusion rate J,    $ \times10^{-11 }$ mol/s
(c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $ 1\times10^{-5 } m^2/s$    s

  A precise steel tape measure has been calibratedu:vau k 4oqu2+ 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 calibrated at+qa:1d ih8r *yrkjav5 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. 8 cvn :jnoo,re.m2ve n-fm1-wHow much error will be made in a recipe cav.e1 :nnn-fmr2jec- o,vwm8o lling for 300 mL of cool water, if the water and the cup are hot, at 80$^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a helium gas cylinder isp udy(/. qys;x+sm .naql7mv ( initially 28 atm. After many balloons have been blown up, the / qs.amqs(7 y+d(vnlypxu;.m gauge pressure has decreased to 5 atm. What fraction of the original gas remains in the cylinder?   

  Estimate the number onzoo hmfw ui)-+3j;k-f air molecules in a room of length 6.5 m, width 3.1 m, and height 2.5 m. Asou+z)k- n owi fj3-m;hsume the temperature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of matter1ey 98ed)q viln5t ;cd 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 thgo j tvev.)**9 ak4qske best available vacuum techniques is about 4okgtas qv kv9.e **j)$10^{-12} N/m^2$ 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 bek*vobf -1(:x adr)j* utcvqv 1low the surface, to what voluxv*j1t(rk1ab)v*q ocu: v -df me would his lungs expand if he quickly rose to the surface? Is this advisable?    L

  A space vehicle returning from the Moon enters Earth’s atmosph7w0qf y 0bfyl2ere 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 vehicl 0f7l2wyfqyb0e 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 ideal gas is increased from 11,z7wc 07pawge 0$^{\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 770kaxo b1;yg,k(u j.e*d.qmkq; m$^2$ (a) What is the total mass of air inside the house at 20$^{\circ} $C?    kg
(b) If the temperature drops to -10$^{\circ} $C what mass of air enters or leaves the house?    kg

  From the known value of atmospheric pressure at the surface of the ur 455p 2qouplsu39iiEarth, estimate the 52i ps945lu oi pruqu3total number of air molecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen molecules contained23 3 ;tffvg e*q6r8hb,fdltd frq+w1 k 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 useqmp4t*f3+l sxqkq..(q- o4 tsv*91ayrncxq b d in a hospital has gauge pressure = 2000 psi (13,800 kPa) and at T = 259K How long will the cylinder lxos x(*m41ql.-fpv tk*.q rq c4qnqsa+t by93ast if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats i0nt lefn8cs )a s4d-)hn a bowl of liquid mercury at 0$^{\circ} $C. (a) If the temperature is raised to 25$^{\circ} $C, will the cube float higher or lower in the mercury? ----待选择----lowerheigher 
(b) By what percent will the fraction of volume submerged change?    %

  The density of gasoline aq zjf(d yb8n1 ,yj-4wvo:cg)kt 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 tz3g;jq; qt-r bda)sh7 he 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 onlmup5 nwj);/3ez+ e ub,wc2d mg:s0b cto a glass 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 k0zoh*g:a a:ibu. *nkthe 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 ps t :gag7 )-cew7d+lyfressure 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 vis3mvs9f.h - the 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 suspen a2kfm5h*zha- ;cpqy0 ded against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they hcakmz q0y h;2-ph5*fa ave a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releases a 3.0ze7-h2b-eh c1dfnpbd nf() .f0-cm-diameter (spherical) bubble of air from a depth of 14.0 m in a lake. Assume thecb-hd e.fbzfn)2n-7( 1d f peh 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 followin s xr.:;g.km0klhpy. ag two days: xsm;pa:0..r gkl.yh k
(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 differencedos5 4cw9hcgtegi-4u 9zk2e yu y8h6( in the density of iron at STP, and when it is a solid deep in the Earth where the temperature o9k8ugh9i6z2cc-e( 4sywhdt 5 4e u gyis 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* ,xk l2dj2pbs, for an ideal gas at constant pressure, the coefficient of l jdp2sbx k2,*volume expansion is equal to $\beta$ = 1/T where T is the temperature in kelvins. Compare to Table 13–1 for gases at T = 293K (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P where P is the pressure.

  In humid climates, people constantly dehumidify thei2unknx.e k+ g;r cellars to prevent rot andx+k g u;.nnk2e mildew. 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