Which has more atoms: 1 kg of iron or 1 kg of aluminum? See the pkb /(cc)g:mkykv,uh, eriodic table or Aycc,ukk)(gh:/ m vk ,bppendix B.

Name several propertkkj8m,4l 1ce iies of materials that could be exploited to make a thermometerecmk,l4 k81ji .

Which is larger, 1 C *2ifrazg: 59d 6tfg k6ok r)4jnu;msa$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium wit0v;u/v *bhcs; p gz-njh system B, but B is not in thermal equilibrium with system C, what can you say a;njpb*/;z- c0gvhvs u bout the temperatures of A, B, and C?

A flat bimetallic strip consists of aluminum riveted toemyx sl*d bmo;8e(dgb5,v 9 ;q a strip of iron. When heated, the strip will bend. Which metal will be on the outside osg e,oxbqd(5d9m 8bl;vey m; *f the curve? [Hint: See Table 13–1.] Why?

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

The units for the coefficient of linear ex0*pe 2lm0 miaypansion $\alpha$ 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 useds39ber +al;q m to control a furnace (or other heatingl;mqebs+93 r a 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 different temperatures.

Long steam pipes that are fixed at the eng4mhwgig-t:u20-.nxtfu9 s m1p pfm * ds often have a section in the shape of a nw0hm 4 tuiup-m:gtfg.9-*1m 2gpx fs U. Why?

A flat, uniform cylinder of lead floats in mercurj8 cf i jbc3 ad*o5/h-uo5c a5xvl23vuy at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glass thermometer is t nghq 47+vyqz/z:p;xfirst placed in a hot tub of water, the mercuryzqp yq;h4 g+z: vtn7x/ initially descends a bit and then rises. Explain.

A glass container may bbw l ) o7 h4kj3estl/y1o03cnnreak if one part of it is heated or cooled more rapidly than ad 7ce3/hwk03o n1l)l4jtosn ybjacent parts. Explain.

The principal virtue of Pyrex glass is9-giw0y vk uj 2k1d :g,a yjiocxajm 0(-gf;o/ that its coefficient of linear expansion is much smaller than that for ordinary glass (T,;ym:dov/a1gjx-ao j90jk 2igik (uwg cf0y-able 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather clb+.(o*+tud ;0-fexwtp lzh vmock, accurate at 20 $^{\circ} $ C, run fast or slow on a hot day (30 $^{\circ} $ C)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

Freezing a can of soda will cause its bottom and top to bulge aow 86 2d (e1dhuuz(dsso badly the can will not stan8uuha1ddewd(o6(s2 zd up. What has happened?

When a gas is rapidly compressed (s swfb-4. jv9jvbmr-mkn o((puh k*.d0 ay, by pushing down a piston), its temperature increases. When a gas expands against a piston, it cools. Explain these changes in temperature using the kinetic theory, in particular noting what happens to the momentum of molecules when they nk*wmf.okp b-jjm -vv9 d 4(0u(hr.bsstrike the moving piston.

Will the buoyant force on an aluminum sphere submerged in water increase-ss ll1cts li+1y +jb7 or decrease if the temperb7-sj+1it cl1 +sllys ature is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law fc.ktc4y d9c bi)ho(6tollows from kinetic theory and the relation between average kinetic energy and kt (d4ctoc 9bh6iy.c)the absolute temperature.

Explain in words how Gay-Lussac’s law follows from kinetic theoryg0y63 fidhuf)m qe+2f.

As you go higher in the Ea)7zs8 srwteh6, /qr ozrth’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 h4s rvzhr 1t/s0ave to leave the Earth and never return. The escape velo/ hzsr rv01s4tcity for the Moon is about one-fifth what it is for the Earth due to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere.

Alcohol evaporates more quickih o3j/;ic8 dm97djr m56ddwbly than water at room temperature. What can you infer about the molecular propertiescidd5mdw3m/i 7br8hdj 9j6o; of one relative to the other?

Explain why a hot humid dayh+x(qa6sbe-i7-- n pa oswgf, is far more uncomfortable than a hot dry day at the same temperature. hqe+ ibsa--wf- ,op7 sxan(6g

Is it possible to boil water at room tpj6,wh.numqr1ca0b rp/3p d; emperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temper+b, -xhglku )kw4v q(sature is the same but the humidity is different. Which uxw,slkg h( 4-)k qvb+is more dense, the dry air or the humid air at the same T? Explain.

Explain why it is dangerous to open the radia;j - sxa5 no.dtn1 me,x,yjxr*v :cey1tor cap of an overheated automobile env e.exxnc5;:*j -r1n,m atoxy1yjd s,gine.

Why does exhaled air appjg mhh+ms:xh r7ij oj(/a2+j.ear as a little white cloud in the winter (Fig. 13–28)?

  How many atoms are ther:2g;toevz/z:o vb (eh,suq / pe in a 3.4-gram copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a xiidsxa:bn3bogj *a .0 q 4i5+26.5-gram gold ring compare to the number in a silver ring of aqa ii0:+jxbo 4s5d bxi3.gn*the same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. What is this on the Celsius sc trx y:l.2 k5uu8w*kmjale?8m: .*xk5 yukj2utrwl   $^{\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 )jf mthi66s. ,cx7jer3h2u3a n7vg xurecorded 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.h-t*l95b9vkiol4 ora 2fs(7j ul9 xxd 82 cm at 0.0 l4aslurxb9dhoi-ltv( 5 *9f7o 9 2 jxk$^{\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 nbt3,(r v9m)nddy+vz hr5o n)(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. 13ov4 av k 2z9do9e adz4da46j7z–29) is built of wrought iron approximately 300 m tall. Estimate how much its height changes 4a 67od24z z9zd ovav94jkdaebetween 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, rv)m0q+/bz0 suzpm wj4ivets that are larger 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 rive/0bqj m v4mup0+z zws)t 1.871 cm in diameter is to be placed in a hole 1.869 cm in diameter at 20 $^{\circ} $ C. To what temperature must the rivet be cooled if it is to fit in the hole?    $^{\circ} $ C

  The density of water at 4 e*g8 nch b6nv/$^{\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 c1 k +ft50pjdy7 /nqqwcm in diameter. What will be its change in volume if it i jf1cknt7+q/yq5p0d ws heated from 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim withj ak :2qnl:ru: 350.0 mL 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 z /b6vgxms5 w755.50 mL of 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 ringiocg,o+3k9 cm made of iron. At 20 $^{\circ} $ C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit?    $^{\circ} $ C
(b) What if the plug were iron and the ring brass?    $^{\circ} $ C

If a fluid is contained in a long, narrow vessel so it can expc;szbg0 ,tv9azwa36aand in essentially on 9za 0z3w,csa6t;vbg ae direction only, show that the effective coefficient of linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the changvv sv9rim8 ;4/ag istmtyqk/*10 z+ope in the density $\rho$ of a substance, when the temperature changes by $\Delta$T is given by $\rho$ = -$\beta$$\rho$$\Delta$T
(b) What is the fractional change in density of a lead sphere whose temperature decreases from 25 $^{\circ} $ C to -40 $^{\circ} $ C？

A uniform rectangular plate ov)lkee o21v; z5w69t jc jpzuj :-5kalf length l and width w has coefficient of linear expan vpzj9w z-:ko) e2vl6jta1juec l5k;5sion $\alpha$ 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 isotropicabrzh 9mmu7 0,e:x4cp 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 keeps perfect tim(*rg/pdsq7t wt yq,b0 e at 17/, swb0g(dq 7*yqpt tr $^{\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 8 i1kv(v(mc fe0.140 mm. The bu18evv ifc(m( klb has a volume of 0.255 $cm^3$ How far will the thread of mercury move when the temperature changes from 11.5 $^{\circ} $ C to 33.0 $^{\circ} $ C? Take into account expansion of the Pyrex glass.    cm(b) Determine a formula for the length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

  A 23.4-kg solid aluminum cylindrical wheel of radius 0.41 m is rotating about i ;7hl ti9+kzctsl4 ro6ts9k6trlzc l 7oth4 ;si+ axle 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 the deze(v(z 3ke*w uvid ,p jeny l:5s)/;mxsired length when at 15°C. How much stress is required to keep it at this length if te:*n msz z( j;wi,ev u vx5)3/ed(lpkyhe temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sectio0wh52d eq+pxx nal 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 134.1229 nbw vljw4(2q 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 temp+bnuyppuqbdz9 3,6) v eratures 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 th9o y0tlba e4 c6d02irqt.hk1emperature on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth and Sun 1 rc5kied +h(9k3ybz pvl:9voare 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 temp wil*,xe)pi z,erature of about z*iwlp) e,x,i20$^{\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 usi::rj/,uju udp mt2wo5ng the ideal gas law.    kg/$m^3$

  A storage tank contains 21.6 kg of nitiuy hvcma 84-fc2u r2)rogen ($N_2$) 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 cwtz hnr+8y5l-)gz /k eontains 18.5 kg of nitrogen ($N_2$)
(a) What is the volume of the tank? $\approx$   $m^3$(“Round to one decimal places)
(b) What is the pressure if an additional 15.0 kg of nitrogen is added without changing the temperature?    $ \times10^{5 }$Pa    atm

  If 18.75 mol of helipgyn1 kp xyx:x 2fl:/zs7vo9q zco,:+ um gas 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 inside a 35.0-L contk* gcsd;)m1zgpf. x sc*xm0u/ainer holding 105.0 kg of argon gas at 38* *csm0k cp/ 1;d)xm z.ggufsx5 K?   $ \times10^{ 8}$Pa

  A tank contains 26.0 kg ofdjgvp;.n 9 hv9 +v)xpn $O_2$ 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 he p9f305n dpf7eahj /wrating the air inside the balloon, which makes it less dense than thee59n7p0r /adwjfp3h f air outside. Suppose the volume of a balloon is 1800 $m^3$ and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0 $^{\circ} $ C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.) $\approx$    $^{\circ} $ C(Round to the nearest integer)

  A tire is filled with air kj36 -yffwhs 4at 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 18dc, icijt 9rb3,7j)am.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 childfya +p((p-gy v’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 moleco/g ijw7hu ,dr2: xac8ules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 2 e 6vhcrx;;yq- 7dubo1.000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) molest59ycfgn , em2,    $ \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 lddvz(6 z4+ht-lcin :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 t*whay e76lm +breath you inhale that were also in the last breath Galileo took. [Hint: Assume the atmosphere is aboutt aehy7m+*l6w 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average t atmut259- s:q4wrbrtm0l+v xranslational kinetic energy of an oxygen molecule at STP2 ma95+t0vrtqum4xrb s:t -wl?    $ \times10^{-21 }$ J
(b) What is the total translational kinetic energy of 2.0 mol of $O_2$ molecules at 20 $^{\circ} $ C?   $ \times10^{3 }$ J

  Calculate the rms speed of helium atoms near the surface of the Sun at a tbf *5 t+ydqnf8emperat+*5ntb8yd f fqure of about 6000 K.    m/s

  By what factor will the rms speed of gas molecules i+x+1 yjwsxktz u u1ko .y.amgvwz+2x : )b5)ydncrease if the temperature is increaxy )uw :a1vxm5gs+. wk.x o2ub +1y+k)zdyjtzsed from 0 $^{\circ} $ C to 100 $^{\circ} $ C?   

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

  Twelve molecules have the following speeds, given in units of km/s: 6kgd:uk-jt .x yi +;6zg, 2, 4, 6, 0, ky+t.6 giu;x kd:g-j z4, 1, 8, 5, 3, 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecm:jbs(5ow8 mg6 x p5xgules 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 while its volu.nyvvoxs 1sohqrpch;izr/.) z/k4 : 5me is held constant, by what factor doehn vz.:/1) hz/ rori ;k sq4ps.yovx5cs $v_{rms}$ change?   

Show that the rms speed of molecules in a/: zlt qhxnlnn/n+ 24o 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 temperat x:w ra6x(6kafya7u 2rure, the ratio of their 6xf y(aa:aw uk7xr2r6rms speeds is equal to the inverse ratio of the square roots of their molecular masses.

  What is the rms speed of nitrogen molecules contained in an 8.5vx k7getd:kt-gb9,7by 7lkt +$-m^3$ volume at 2.1 atm if the total amount of nitrogen is 1300 mol?    m/s

  Calculate (a) the rms speed of an oxygen mopvx1-rvkiq j;l0 w6 :olecule 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 distancex4a3sf,pw5-lf: /7tzr 0wp dls r2j cr between nitrogen molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms spee5 i8)3hvxansp/h3nce ty 5g,g d of an amino acid whose molecular mass is 89 u in a living cell 83v pyx5sh)h/tgc35 eig nna,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 g( d9 ud;.d2m7fdg9dnv5nbbn can be written P = $\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of urani0 d 4v-ujfnbm2jlek 55um, $^{235}$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 phc /pw 8t3us;h xx,kw0wases 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 p8m-)myv u4kbzressure is 0.01 atm and the temperature is (a) 908mmky4vu) b-z $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (apk4eb 7; : hvh4ercrhx-proximately) if the humidity is 50% on a day when the temperature is hk4 7ev eh4;:bx hr-cr25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a ;gx/njoinrgtoqa q1d5.pesn1w8* (7 place where water boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mountains is 0b 9b(5zqyazlv 88 rz5b.72 atm, estimate the t bvz8r8b55a zlzbyq9( emperature at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a dayfu8z7j u mjx0mf8+4xk when the partial pressure of water is 530 Pa and the relativuxmxj8 j fk4z8+f u7m0e humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water*9bzcru3 k1 10tjqq lv7enc3h on a day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate presj7.1m ;-4(buiuj ;m pajul qlzrr b1w2sure inside a pressure cooker if the water is boiling at a temperatb jllw7 z;jai2pmmu14r.uu1jb- (q; rure 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 volume 68062i50(fkom sml 5ad nm( nc2ekclqc92$m^3$ 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 9b9f n,*c)c wo2t ufkiyozk /75 $^{\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 moqq4mn.z tl h*kb 1*zt(cs(w z8oepo8*lecule (see Table 13–4) to diffuse a diw(*zzh e**.tqtno8kbclq(4 z1so8 pm stance of 15 $\mu m$ in water at 20$^{\circ} $ C if its concentration varies over that distance from 1 mol/$m^3$ to 0.4 mol/$m^3$ Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u. t $\approx$    s ([color=rgba(0, 0, 0, 0.85)]Round to one decimal places) $v_{diffuse}$    $ \times10^{ -5}$ m/s
$v_{rms}$    m/s

  Oxygen diffuses from tho*p4wtfu9 g.r e surface of insects to the interior through tiny tubes called trac4op9 wrg.tfu* heae. An average trachea is about 2 mm long and has cross-sectional area of $ 2\times10^{-9 } m^2$ Assuming the concentration of oxygen inside is half what it is outside in the atmosphere,
(a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20$^{\circ} $ C is about 8.7 mol/$m^3$ then $\approx$    mol/$m^3$(Round to one decimal places)
(b) calculate the diffusion rate J,    $ \times10^{-11 }$ mol/s
(c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $ 1\times10^{-5 } m^2/s$    s

  A precise steel tape measure has bee.8jgs s6 hv(;x sgab9rn 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 calib .1a geeph3i8wrated 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 j *w3v anbpvy5e)):aomuch error will be made in j w)y pa)e n:vvb*a5o3a recipe calling 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 is initially 28 at*fxr afd:v/)i m. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the original gas remains in thdx)v f i:/*frae cylinder?   

  Estimate the number of air mole7g33cc e/ay0e sq+d5 enut3w e;g1zkicules in a room of length 6.5 m, width 3.1 m, and height 2.5 m. Assume the temperaec3a5gngceiu/3q y w3 ;0tz17kes+ edture 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 att0 c;m tuxq1 p/8lnfs-q6( ;wm 5lwejnom per $cm^3$ mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).$v_{rms}$ =    m/s    $ \times10^{-22 }$ atm

  The lowest pressure attainable using the best available vacuumo+xkvmbn;/e (n:/ pqjf9 l ,tcd4qd9f techniques is about m t d bkd f:9evnfn4/(q,+cjl9o qp;/x$10^{-12} N/m^2$ 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 lu3x 8yqh-3bbmgqs 6om;ngs to full capacity of 5.5 L when 10 m below the surface, to what volume would 3h b8-x;qg3o6qb ymmshis lungs expand if he quickly rose to the surface? Is this advisable?    L

  A space vehicle returning from therpzmpy 3.dk; : 6 mw,7*zgcirj 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 to what temperature? (Because of this high tempe3j; .z* d7:6czgymmppirw, rkrature, 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 ideal gas is increafja;5 *so ojr-sed 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 77x*x 3uim 5x4e:.ol6 t mqw.ety0m$^2$ (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 pressurh-xr+2nou0v d e at the surface of the Earth, estimate the tota n0vh +u2o-rdxl number of air molecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen molecules contained in a 7me*w k 5a zg 9fabhq16o4d:q1a.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) 8w 2hvevm.t22 r )uc othyp*8t7bfxe pressure = 2000 psi (13,800 kPa) and at T = 259K How long will the cylinder last if the flow rate, measured at atmosphe8 yht.opwxb7t2ev)c*u) 8rh ve t 2mf2ric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mercury3 e*z4ropjb w*c-r e9soik4 *z 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 gasolinoi x+ j0f xzbfnh7(h- o/r/619dxcibye 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 around to48xdyq xc.5qhe 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 onduaf:-**fl g vto 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 the 18 ig:idr9flua- kke2e7: 5q;q m$^{th}$ 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 cg6du. g6keqrbq/e i;7harged, 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 thv5 l,d;fq- rsznxn2 *de 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 susic;r;h d:)sbc, 9nr (6lchrz j7n; uikpended against gravity by tennis balls thrown verticczh96 bnir)r(h7c;:ids rnku j ;,; clally upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diar5z cpxzqu k+p 6yw2;9meter (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 z ;5 pc+ 62qkpyx9uwrzbehaves 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 followik biy bs8.6qir 5ydt, 6j,s/qfng two days: qb,.t8b,y jf6/ir dq5ks yi6s
(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 the5:sq) v x6cy ewev7-qc density of iron at STP, and when it is a solid deep in6 e- v cxsvw7:q)q5yec the Earth where the temperature is 2000$^{\circ} $C and under 5000 atm of pressure. Assume the bulk modulus (90$\times 10^9N/m^2$) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.    %  ----待选择----decreaseincrease 

(a) Use the ideal gas law to show that, for an ideal gas at constant pressure,*u8 ctvikgldih2,h3( the coe8di(3iu, t ghck v2h*lfficient of volume expansion is equal to $\beta$ = 1/T where T is the temperature in kelvins. Compare to Table 13–1 for gases at T = 293K (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P where P is the pressure.

  In humid climates, people ae-ylz6;bh.hkb ( p0;c2m/hrhbje. rconstantly dehumidify their cellars to prevent rot and mildew. If the cellar in a house (kez;a6br bc k/h e0jrhhh-pl(2.;yb em. pt 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