Which has more atoms: 1 kg of iron or 1 kg of aluminum? S9c)oi q *ij9dmee the periodic table orc iid 9oj)9mq* Appendix B.

Name several properties of matermr 47us+ 0tumvials that could be exploited to make a thermometer.v4rt07m s+muu

Which is larger, 1 C/,liu h /d4vdy $^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibriujtwlv 4r14.l 2z6ncu; w4 faarm with system B, but B is not in thermal equilibrium with system C, what can you say abf1r. ra24ulaw cw6vt4; jzl 4nout the temperatures of A, B, and C?

A flat bimetallic strip consists of aluminum riveted to a strip of irons :+ ne yv sq4ec7lbmg*e8bokh)-pz 18. When heated, the strip will bend. Which metal will be on the outs8)glzk7 8cmyq*bs s h1ev 4 ee+onp:-bide of the curve? [Hint: See Table 13–1.] Why?

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

The units for the coefk zke*.x6w/ar ficient of linear expansion $\alpha$ are $(C?)^{-1}$ and there is no mention of a length unit such as meters. Would the expansion coefficient change if we used feet or millimeters instead of meters? Explain.

Figure 13–27 shows a diagram of a simple thermostat used to control a f7 mfq9u0 iydw*urnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid mercury that conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and how it can be set at different t my9 *i0fuwd7qemperatures.

Long steam pipes that are fixed at the ends often have a section in the sh ef) cxuwgj 3drts :en4*minjbi1et5 /x0-7 ;tape of a U. Whe ntdcmiixft51nus* j; )bte:x0- j7rgew34/y?

A flat, uniform cyliss7.* h(wsvxl nder of lead floats in mercury 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 first placed in a hotdg 2m-+ rb7jq*.cp lz,do3it27*3efqga l vsd tub of water, the mercury initially descends a bit an ,m+3-.o7j2tr7ql gpeq*ldag*2cbz3sdv fidd then rises. Explain.

A glass container may break if ok,rsuo o0-b; bbr mn(*ne part of it is heated or cooled more rapidly th- k(ub,soob0mr ;nbr *an adjacent parts. Explain.

The principal virtue of Pyrex glass is that its coe 1jl*d rtlehinqoi 725wp-6e4/g n5zefficient of linear expansion is much2 /i6r5nw- ldi5 t*qh4 enje1polze7g smaller than that for ordinary glass (Table 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accucwo+h1 wml *b,rate 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 b cj t 9fw39ut8y1s3bband top to bulge so badly the can will not stand up. Wha1b 3j 3yb9 w8sutfbct9t has happened?

When a gas is rapidly compressed (say, by pushing down axt*ksla /3kp a+ain4 7 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 strike tnaks/4axp t k+37*ialhe moving piston.

Will the buoyant force on an aluminum sphere submerged in water increase or decr pt1e6xe.lkqx8uof , xw;;mt :07m qskeas;etf luqwes7mp.m8 tx;kxq16,o0x: ke if the temperature is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’0xnvir 2( yt/fs law follows from kinetic theory and the relation between average kinetic energy and the absolu(vxntri fy /20te temperature.

Explain in words how Gay-Lussac’s law follows frg) q0 t+z9c6qhv)t+ory xbne, om kinetic theory.

As you go higher in the Eartg b,r -lwd:*aeq4u)j sj.k :zdh’s atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the mini ty-vc3lh qx ./8vta g):ma+efmum speed an object must have to leave the Earth and never return. The escape velocity for the Moon vt a: /l8 thm)fe q.3cag+-yvxis 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 quicklrk-pkw5f1 nxp rwx7f 04d)qp1 y than water at room temperature. What can you infer about the molecular properties of one relative to the othx r-fd 1fn 5r7qk4p)w0x kw1pper?

Explain why a hot humid day is far more uncomfortable than o. w.;xyujx2qhtg; 61m(wduya hot dry day at the same txx u(6mw;y2 .1yqdo jg.u ;whtemperature.

Is it possible to bok; s8+lm1*a/d fppvnft; xkf: il water at room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the airaknm*( ha7mo 2 temperature is the same but the humidity is different2om ka*mn(a7h . Which is more dense, the dry air or the humid air at the same T? Explain.

Explain why it is dangerous to open the rz nraycvoh25.r k49a 4adiator cap of an overheated automobile enginr2 kz.v49ay choar45ne.

Why does exhaled air appear as a l ixh09* zuq0njed yfb/dj r++.k1m;rpittle white cloud in the winter (Fig. 13–28)?

  How many atoms are there in a 3.4-gram copper pennyh+bywcu;iv4r fkr7mjx (7 h((?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring compare to thabt,ajr x. p-n,j2(ji uiuc4n oo d)./e number in a silver rin)jacpr ,x.oju d(in/no2 tu. b a4-j,ig of the same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. Whla evrsdz,.l9m (9-9 lh 0kdcjat is this on the Celsius scale? (.mv9d0lkrclhj e9sd 9-lza ,   $^{\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 reco9 caq)whkz6q4kdlm* 5rded 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 cm axy 5k u-/njpd)a4kop;t 0.0 -)ap4 /jup 5 oy;xdknk$^{\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 eoqiuk2flk wmu/ )8s6b8+)leslabs 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 onh 4eeeb8f;q ,1j h fnu5-*ghapproximately 300 m tall. Estimate how much its hef4n;b1 nhh-h8e,e *j5efuoq g ight changes 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 than the rivet hole are o 8j ij0tyehw8vv,) ;gs )ij1svften 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 be placed in a hole 1.86jeyv0t8i ;, w)v)hgjis 18jvs9 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 m (1m3r ub*cug4 $^{\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 wilm8 o,7t.slalo.pi 11 x )oqzjcl be its change in volume if it is hes8i 1lpm..j1oqa,t7o xc) olzated 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 water at 100.oj/4*f wbtd n;mz8*fk0$^{\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 at 20mi2 e jub0pox/:zp/k8 $^{\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.bnui:q9xtm lqi-:g:* 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, narropx, r.qi6pzpi/d m0l /w vessel so it can expand in essentially one direction only, show that the effectir , p6x piq.zm//idl0pve coefficient of linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the changnl 7x 9 c.; *mpljcxi;ef3b0jze 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 of length l and wif a)q 5*,yytkidth w has coefficient of linear expansio *5 ykfi,qa)tyn $\alpha$ 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 soq dq xm 1b5i7d.vm*3golid, $\beta$ = 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 time -v g8u9wgxs *i.xu +zwat 1w +.9-uxsgz i8uxwv*g7 $^{\circ} $ C. How much time is gained or lost in a year if the clock is kept at 25 $^{\circ} $ C? (Assume the frequency dependence on length for a simple pendulum applies.)$\approx$    min(Round to the nearest integer)

  (a) The tube of a mercury thermometer has an inside diameter of 0.140 mm. Tdd*mx /2p 5zjuhe bulb has a volume of 0.255 d/* m2juxpzd5 $cm^3$ 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 r sxqr7-bv2ujfbc7wc020(q fiadius 0.41 m is rotating about its axle on frictionless bearings with ri7f (0ufsq 2 wbq720-bcv jxcangular 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 dest2k c1ie w7wj5ired length when at 15°C. How much stress is required to keep it at this length if the temp5w7k t1eji2wc erature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sectional area 0vm48j.qy06oju o7 bz/ xot9ln .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 134.122 cm adtx7tpf ;+ +hst 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 tem( 0 /il5t zg4lw(huqogperatures 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 te*(zis gn yrd9/mperature on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth and ne j iu/v+*8dySun 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 atmosphelmz 6 dg2 od,: n) j3aebdjgcn((jmc9/ric pressure and a temperature of about 23:njjm gjc d gde(a6(9),olm2n bzd/c0$^{\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 usiwqohj-pax) 3c: s1 is+ng the ideal gas law.    kg/$m^3$

  A storage tank contains 21.2obbod-4:5ff jy , ufc6 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 tla ,w6e;xxlb 6s-/fu contains 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 heliu+k+ 2ukpc7l 1 ,oac7eexmqgpcf07ww:m 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 container holding 1ffaomzj rga 4y2-;o h7o: *q3i05.0 kg of argon gas at 385 K?fah-rmaq4z ;oiyf* 7o3 2 :jgo   $ \times10^{ 8}$Pa

  A tank contains 26.0 kg xmo zgpv0 64)inz1j :s3rgh:mof $O_2$ gas at a gauge pressure of 8.70 atm. If the oxygen is replaced by helium, how many kilograms of the latter will be needed to produce a gauge pressure of 7.00 atm?    kg He

  A hot-air balloon achieves its buoyant lift by heating the air insidei-q+9.l ivc xi the balloon, which makes it +i c -9viiqlx.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 air at 15mpzd t+la35 ;v $^{\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.:ts9 9zwduuom-j 5+)dh g 9hbj0 $^{\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 ballooncrs5rv msy+ .4 escapes a child’s hand at sea level and 20.0 $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number ou7 ilfypojwmn .p(9r3i9) bg -f molecules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.-f skiiv)+mkj : imi5(000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) molr:e6/hr vmh0res,    $ \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.jrvxz 9:fq t0:1$ \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 is3uy a+o2/g7 5e6z xs j- robcd6(fepcn each 2.0-L breath you inhale that were also in the last breath Galileo took. [u2o63- azr o 6sx(+bpf5/ecjc7 seg ydHint: Assume the atmosphere is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinj u9c /j2jw.mzetic energy of an oxygen molecule at STjj.w2zc9 /m ujP?    $ \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 nearjuf:5 bzax8. xjm 2zi4 the surface of the Sun at a temperature of aboutz 2uz.8xmijb4ajxf5: 6000 K.    m/s

  By what factor will the rms +krnip5xu4c 3sgjmz 4lofe9. 0ab. h(speed of gas molecules increase if the temperature is incigmkp3 fu jh+.sc0. or 9lb(445ax eznreased 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 unit4n4x6su.7y ( wbg rsciyl9sq 1s of km/s: 6, 2, 4, 6, 0, 4, 1, 8, 5, 3, 7, and 8. .s64y4n7cs1 bxilq su w 9ryg(Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecule-t5u 1)uq tc47azkgo 1: kbsw1tl+cut s 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 volume isnw+:1qx) .xm+iz e mk54bveak held constant, by what factor dov k+5i :x) kbaqxm4we.nm +ez1es $v_{rms}$ change?   

Show that the rms speed of molecules icbn2+i3 qk(ec n 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 o7v ubx4wj4:3 5q a)-mkfjkrinf their rms speeds is equalw4 afjq)i rk j-:unxk m5b47v3 to the inverse ratio of the square roots of their molecular masses.

  What is the rms speed of nitrogen molecules contained in bt62o 2oi u (qmnumx+ear/ :u9l0rc/xan 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 oxyk rjdyo q)l1xflx,v 3;n4sg+; ky+r9hgen 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 nitrogaiba ql5iy+;;ng16e e en molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whose molecular mass is 89 u in o (ehch*+jt4x2 h7q: lxjszs-a livj*est- l h +47h xqj:sh2xco(zing 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 o 7p53:tn io+jf0qod nxf a gas can be written P = $\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of uranium, w2e *a0nab;i( oe4o;mnfzlz, $^{235}$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 whlw( t6uki oz(6o+uddo/o6w. jat phases can $CO_2$ exist? (b) For what range of pressures and temperatures can $CO_2$ be a liquid? Refer to Fig. 13–21.

Water is in which phase when the pressure is 0.01 zjmkc 68q22q uatm and the temperature is (a)6cqq8kmu z 2j2 90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50% on a day when .:d kp1e )hadothe temperature is 25.:k)aep1hdo d $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where water boils at 96 rpz: lehs7(y0 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mountains q +:syjy0hy-y is 0.72 atm, estimate qyjy +:0-h ysythe temperature at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure of water is57t7jsnju kngn, p8koxni(2 5 530 Pa and tnx(kn5,pun7 j s7jiokg 5 82nthe relative humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of 3*s(+0cq)mkhlo gvx pwater on a day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside a *sv5vl8 2oy0j ) f,xlykjlf 6ppressure cooker if the water is boiling at a temperatuov xp,*l2vy8)lsyfjj fk 6 5l0re of 120 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a ro o/ ow0w mae)tb*z)+dmom of volume 680$m^3$ at 25 $^{\circ} $ C is 80%, what mass of water can still evaporate from an open pan?    kg

  Air that is at its dew point vx5 s(www+/i3)r4+gucz z kckof 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 fomi.,54f i cikb;afdes1/cf 0wr a glycine molecule (see Table 13–4) to diffuse a distance of 1 /0a45midk,1fi fwcfic.esb ; 5 $\mu m$ 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 surfbyfpon/ic56: c( dxg+c*y4 wa ;n .rlcace of insects to the interior through tiny tubes called tracheae. An average trachea is abocx4c.id; yl:5 rag(/cn oy *np6fc+w but 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 measurea0 sd-iz9ge /d 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 mebqp9 vn5- 5+b yezwu/f g)lu(casure 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 Pyrex measuring cup was calibrated at normal room temper1f+s1 d+horj tature. How much error will be made in a recipe calling for 300 mL of cooljdot f1++s rh1 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 atm. After*jdwh;y4* xmr many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the ormd*r4 w* xyhj;iginal gas remains in the cylinder?   

  Estimate the number of air molecules in a room of length 6.5 m*- qp k12hbtxpt s;rk-7wpvg5, width 3.1 m, and p5q2ksk *pxw-t p7 rtg;hv1b-height 2.5 m. Assume 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 g7msrti*9z gl ;p4rd.$cm^3$ 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 d,9a5pj.rikhbest available vacuum techniques is abouk5 a9,.dpr ihjt $10^{-12} N/m^2$ 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 lungso(vgqh1 y j63z to full capacity of 5.5 L when 10 m below the surface, to what volume would his lungs expand iqvjy3( ohg16 zf he quickly rose to the surface? Is this advisable?    L

  A space vehicle retu.a ux)ghly8l6 rning from the Moon enters Earth’s atmosphere at a speed of about 40,000 km/h Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, the l. yxlhga8)6unose 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 iov 9n h8 o0al3au oly73g4r,lencreased 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 f(i ov4s9kj8yzgrtf n,(7fu * 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 scby3) 31izns . (- pdc6iunfcfurface of the Earth, estimate the total number of aipd6 1)c(ni-3n.fccuf 3ysib zr molecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen molecul sx mw 8n,1:.va4 udihxvqf)g4es 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 oxyge4z268vgr zf+oj r+fanbq+ wz 6n used in a hospital has gauge pressure = 2000 psi (13,800 kPa) and at T = 259K How long will the cylinder last if the flow rate, measured at atmospheric pressur ab++6jo 4zn fzr6vzgq2 w8r+fe, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mercury ateo(q t7ldd25xrhj0;qjh ;nd- 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 at 0 sul1c6in 5q4d$^{\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 Earth’s e:9abxk*f otxt,a )sf2u9bw 5lquator 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 avoyqze 41g)pz4s,u1x 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 standzlq*z2 jsfk1. )k6o ,p5virxsard, adopted in the 18$^{th}$ century, was a platinum bar with two very fine marks separated by what was defined to be exactly 1 m. If this standard bar was to be accurate to within $\pm1.0 \mu m$ how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion for platinum is $ 9\times10^{ -6}C/^{-1}$. $\pm$ =    C$^{\circ} $

  A scuba tank, when fully charged, has a pressure of 195 a- x1e wtzio6n+tm 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;hl6h0s,kptqx82uc v e8fj, k 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 suspended against gravity by tennis balls thrown 8ja -yz tj8 doev.5b/b+ aa6a7cq/tagvertically upward at it. How many tennis balls pert eja8ajoq aybz /5acv-bd/g.6t78 a+ 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.swh 80r( e dji(aawd9.xj/p)a00-cm-diameter (spherical) bubble of air from a depth of 14.0 m in a lake. Assume the temperature is constant at 298 K, and the air behaves as a perfect gas. How large is the bubble when it reaches the surface?)8 sdxi0j.j(/aae (daw p r9wh    cm

  Calculate the total water vapor pressure in the air on the following two dayjpn1m:+7 3.trsg9th2/dddaw9jqt tcs: 71m 3.t/qd sj +2hrw9 jcd9gd atp:ttn
(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 density of iron at STP, rw r7vrlp -nbaf6m 2 xh9w89,rand when it is a solid deep in the Earth where the temprb whw7nvr-x8mrlrf 92ap,6 9 erature 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 angud ayb*34f- b du aw+2zn2xr5 ideal gas at constant pressure, t*z n+b -3agdbfrx w uy42adu25he coefficient 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 constantly dehumidify their y 5osma:dbl3ogf1dxk,t)w mvm m:q*2(7env9 cellars to prevent rot and mildew. If the cellar i*y2xq1e :79dgnm fdmb mvowm(5:tv3 k ,osla)n 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