Which has more atoms: 1 kg of:ia-y 4p y0:9flick/1wvs c ll iron or 1 kg of aluminum? See the periodic table ol slp kw4y:9fiv-ali:0cc/ 1yr Appendix B.

Name several properties of materials that could be exploited to makevwn-a uf72 ep1 a thermometep12fuv- a7e wnr.

Which is larger, 1 C ;v20xv 6jgi vk$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermaqxo,5l qlegd g 1j36i*l equilibrium with system B, but B is not in thermal equilibrium with system C, what can you say about the temperaturesd5j6xgl1l 3gq o *,qei of A, B, and C?

A flat bimetallic strip cpc g*;,olxg/1 fyue: bonsists of aluminum riveted to a strip of iron. When heated, /e g1by :c,fg oxp;l*uthe strip will bend. Which metal will be on the outside 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 coefficient of linear expabxr5+:w vv9y, l a4kjhuix; agpgb .6.79wpcx nsion $\alpha$ 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 simplern5*f,nv08h3 g4hp brj:ipx1jxc4 r a thermostat used to control a furnace (or other he5xj4pjr1x *fan,i0g :c hp38brvnh 4rating 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 ends often have a section in the shapej- o ayv26esvb54dcoj9vy 9z; of - dov; y9692ajco vejy4zb5vsa U. Why?

A flat, uniform cylinder of lead floa1 n1mgedx0c(m ts 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 fis1w*y cqmc4;kb wfsix:o)* 6qrst placed in a hot tub of water, the mercifwow:4k **cq)6s s; ybqc1xmury initially descends a bit and then rises. Explain.

A glass container may break if one part of it is heated;l7aazm e* -caf i*n*q or cooled more rapidly than ad ea*zn *ml-caq7ia* ;fjacent parts. Explain.

The principal virtue of Pyrex glass is that its coefficient of linear exeyhv4b;b o57rf k,q5 wpansion is much smaller than that for ordinary glass (Table 13–1). Explain why this gives rise to the increased 4qw7,;y5 eoh v kb5rfbheat resistance of Pyrex.

Will a grandfather clock, accurate at 20 s;14 djojt0y4g,:m fki s 8nlp$^{\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 sod z t2+sbztn yb))1; +eman8zeoa will cause its bottom and top to bulge so badly the can will not st ;z2+t)ztb)nb noe ym1 8za+seand up. What has happened?

When a gas is rapidly compressed (say, by pusadb cbi:o:b- 5hing down a piston), its temperature increases. When a gas expands against a piston, it cools. Explain these changes in temperature using tho i:5:bc-bbad e kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force on an aluminum sphere5ah9j lygo;kqju/ 9dei s;-y4 submerged in water increase or decrease if the temperature is increased from 20 iq9;ju9d 45yyaksgh;/-joe l $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinetic theoryd3 ,j,iw okmo. af24 *ciq*bhc and the relation between average kinetikj 3b**mw,o4h 2o,c .af qidcic energy and the absolute temperature.

Explain in words how Gay-Lussac’s law follows *)ah,nhatkis+57tuf from kinetic theory.

As you go higher in t) r5j1 tcj9z0cri,w- abc; 9jynrqr-whe Earth’s atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to the minimum s hyo u1m(ncpw 4(chk07peed an object must have to leave the Earth and never return. The escape vcn74h 0(u (ky p1mhocwelocity 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 quickly than water at room temperature. Whdc0 xy3vhfk )38m m, f d5c(m0ms2pvgmat can you infer80(p mm3kv sy 0,mhgv)cxcdd 3fm2fm 5 about the molecular properties of one relative to the other?

Explain why a hot humid day is far more uncomfortabh* 8q;vph;iuujdt ( r:le than a hot dry day at the sjpr; u u:th;qvih(8*dame temperature.

Is it possible to boil water a wl(4dle 9ba t3ed/ (tq:vdlp,t room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air hr*/ ku3r iy+/vazbv jv(9aa. temperature is the same but the humidity is different. Which ikbj/+h.yi 9ar vu (/ 3*zrvavas more dense, the dry air or the humid air at the same T? Explain.

Explain why it is dang2x1zl+fq hq ykxxpul)5 ,q -m3erous to open the radiator cap of an overheated automobile qlhq)-fk5 3 p2xl+x q,myzux1engine.

Why does exhaled air appear a+;wnmj0 pnnhw9e 7: dcs a little white cloud in the winter (Fig. 13–28)?

  How many atoms are there in a 3.4-gr9kiz )k1ern )2rfngu agr;9 +mam copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold ring compare to the number :* 4qu3 nyd0 vymzp-avin a silver ring of t0v pm-z4 :nu3yyq*vdahe same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°1+c zcczwwl :6F. What is this on the Celsius scale?w+c6zlcz cw: 1   $^{\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 temprp/ *epcqst2uy0+l b7eratures 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 alcoks7pee;e 1-h9o m9pcohol column has length 11.82 cm at 0.0;1e9eo mcpo s9p kh-e7 $^{\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 rn7fw xtwm2)* 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 approximately 300 m talj(vs v9zr0t-p l. Estimate how much its height changes between July (average temperature of 25z(- 09t rvvjsp°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 avr-zn34igf q7a dc):s x(s8jnre 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 rivet 1.871 cm in diameter is to (7s- znv:)8g3 qdjfaincx4r sbe 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 3b 6d h ze4btejkv/,)t4 $^{\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. Whae5 hh;ay;9d m4 td2f rn3poyw3t will be its change in volume if it is heated from 30 2 o ;yy3t4w;d3nh afrm59hpde$^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is3 -p5n2ne :mqk9i prpz filled to the brim with 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 55.50 mL of water at +1 /p ciqmw(.tre0lua20 $^{\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 mzi,y82ln .cc be 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 can 3dj)ban,4q -lfrk9 tt expand in essentially one direction only, show that the effectiv49q-bjrfntka3l),t d e coefficient of linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change i vw y.(mqeu68 )q(n 2hm)d+a jgx(thdjn 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 plat,l5 g1kn;at icp14qqc e of length l and width w has coefficient of linear expansicqn1 qkg 4ciap5;l 1t,on $\alpha$ 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 solida*s.kk; ewcxu +se+ k/6*nfmk, $\beta$ = 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 av;aho9 y0s55t6cxywis made of brass and keeps perfect time at 17a 9y506t5sx yhacow;v $^{\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 mmj/cib;8, yqeh/q3ezwkl+4 k m. The bulb cikw yb,q4 /83ekh ljze/q;m+ 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 whe. 6rc jq)pszf4el of radius 0.41 m is rotating about its axle on frictionless bearings with angular vej z4.q6p)crfs locity $\omega$ = 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. Holargcobv8x 9n:p7 rr947 coa7w much stress is required toxcp477 ra9ob:r 79 lc gvnr8ao keep it at this length if the temperature increases to 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of crossv u) jts5)ozt38b -n 7nrctf0z-sectional area 0.041$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diameter 134l(pm8nk8apjl my -9b).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 followinnc0m 06mbr;ltlha5* z g temperatures 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 the Fahrenheinoe.rz u7 remc)70 a7w:. qaqyt scale?    $^{\circ} $ F

  Typical temperatures 4p:,wvpxe eauf/i39k in the interior 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 any8,chfy /w mk6d a temperature f8 h6 ky/cywm,of about 20$^{\circ} $C is compressed in the cylinder by a piston to $\frac{1}{9}$ of its original volume (compression ratio = 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.    $^{\circ} $ C

  Calculate the density of oxygen at STPxz gu 1/s:ci4gnsgp u2a9g(hb4n;;qp using the ideal gas law.    kg/$m^3$

  A storage tank contains 21.6 kg of nitroon7(6f no *orbz k4b9vgen ($N_2$) 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 b58 yp)wo;p:,oh -gqh 2zd.nqta/rip -ja.xycontains 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 helium gas is a b)ypz7j2ktz96p) jb st 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 0sqho y9z. kihs8m3-rinside a 35.0-L container holding 105.0 kg of argon gas at 3hsys-. 3m89h ki0rqo z85 K?   $ \times10^{ 8}$Pa

  A tank contains 26.0 kg2,fn9:oihe(w nmmlx 8 of $O_2$ 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 itsq:7egj/ ud4;rhka x 6z buoyant lift by heating the air inside the balloon, which makes it less dense than the air outside. Suppose the volume of a ball:uzjq agrd6k h47xe ;/oon 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 a8t/ 5h ctu dyi4,z9jiqt 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 (u 6eqz u /lxr8d2nk*s18.0 $^{\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 w5zmk 3 ,co rvzyvyjk2j+38,x wgj( 2sa child’s hand at sea level and 20.0 $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number of molecule)oud0+suxuewb3c6 v+1 dc0g es / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.000 L? How manyc1wsvr;zk80kpw n, p 5 molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (aq.gk*fd )g 2x v*mgqt1reli-,) 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 vzl8b cmy-23m-2jsr qe 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 breath you inhale t zs-s rxfaw/ee/ q0kdx;wk+ 6)hat were also in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high ana/-kzx0ew;xqse) +dfwrk6s /d of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kizkv,- o s/lz nwlh5n/nv;xv3;netic energy of an oxygen molecule at STP? z5 v wsv/n;ox-n,hv/l; k l3zn   $ \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 sdig42oa a/is- urface of the Sun at a temperature of about 600 -i2/iagda4 os0 K.    m/s

  By what factor will the rms speed of gas molecules increo0w8dx:k ;0qb y4cntj ase if the temperature is incn:bq jd8y;k0ctxwo04 reased 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 follohui5, f9we :s8ddjg r:wing speeds, given in units of km/s: 6, 2, 4, 6, 0, 4, 1, 8, 5, 3, 7, and 8. Calculate the rms speej ws98:eru ,5:ifddgh d. $v_{rms}$ =    km/s

  The rms speed of molecules in a gi et*6 wu ,-kcaqtxl7-as at 20.0 $^{\circ} $ C is to be increased by 1.0%. To what temperature must it be raised?    $^{\circ} $ C

  If the pressure of a gas is doubled while its volume is helxhw .txh bvv(,+us3 7ld constant, by what factor do lwhvhbu3(t ,xx7s.+v es $v_{rms}$ change?   

Show that the rms speed of molecules in aruidtb p21 73y 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 galeb;0nbez sx z9 *ul059ezif3ses at the same temperature, the ratio of their rms speeds is equal to the inverse ratio of the square roots of the5u9 zs0 lx*e;if n9e0zz 3eblbir molecular masses.

  What is the rms speed of nitrogen molecules cy, jv;rh2s p9m,5+.0rmh p q5vtlzvbaontained 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 oxygebyun9o v o6+m2khja04 n molecule at 0 $^{\circ} $ C    m/s
(b) determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collisions with other molecules.    round trips per sec

  What is the average distance between nitrogen moleculire ;elp pdau h59 /lmk(a-4c4es at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whe, rzv7)uo4 6tp uzh7gose molecular mass is 89 u in a living cell at t hepuzvoz)4ru6 77g,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 pressurv1. zk h5g*obde P of 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 uraniu l-d:0sl x(lw 0r/igntm, $^{235}$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 press3mga ;kwa3h d ))lk2fkure, in what 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 preskol:b;: d+edrs4;x 6 hzi1 dfnsure is 0.01 atm and the temperature is (a) 90ki;f;+6zsdh 1o drx n:: 4dleb $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the hu16wjhmm f+ pa1midity is 50% on a day when the temperature is 25m hm11 pj6aw+f $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where water boils52tdv,a9p ixj ( b.mrw at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular placm(:t jk7uq1i gdu6 jh3* g;bbhe in the mountains is 0.72 atm, estimate the temperature at which :*jmh q61u3 i ;d( bhgj7tgbukwater boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day whroi d-+-/b xtk (cr5qyen the partial pressure of water is 530 Pa an-qb o(/ytxr c-5d+kird the relative humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a day when the t)rmtwtp k4)c 1e.jgquf/k-.nemperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside a pressure cooke6oqcn4 b(r 4xkr if the water is boiling at a t4bc( rx4koq6n emperature 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 volumltjx5vo* p6 fv v8o9( 3s/bebn1ljnn9e 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 poin; fa1p2skiivtx g8bj +ths)-3 t 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 molecul: bk;yiwfn8o*e (see Table 13–4) to diffuse a distance of 15w* f;: nyk8bio $\mu m$ 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 th*km c ec6+nyk-rough tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-sectiokc-c ekn*+m6ynal 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 be+c,d+o h qftp5gn- o*ken 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 measureml+k71tyd hc vg;k; 9 b1yr*gl 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 tempzbo o5nj9 i: cedy6o2lb0 )6izerature. How much error will be made in a recipe calling for 300 mL of cool water, if the water and theobe l i:zz2o5ni)cb9do6 6jy0 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 i.v6dq)v7 ejjinitially 28 atm. After many balloons have been blown up, the gauge pressure h)qi 7dvjv6 j.eas decreased to 5 atm. What fraction of the original gas remains in the cylinder?   

  Estimate the number ozh1c/sc-lx5ne zj v56.a/ bjyf air molecules in a room of length 6.5 m, width 3.1 m, and height 2.5 m. y5l- xn1jzbc / eza6vj/ch5s.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 abou98 qfuy,m:a c xrpd;2 xoa ;zq s*aqwa58bt.m;t 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 atta bgfuopu qn37 sls64(-inable using the best available vacuum techniques is abounl (uo3 sf-qbg 76pus4t $10^{-12} N/m^2$ 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 ojwbn s js(1*4yf 5.5 L when 10 m below the surface, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable? jbsy14j* sw(n   L

  A space vehicle returning from the Mooidg8 ay(da2l+ n 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 nose of a space vehicle mustlda8i 2ga( y+d 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 i*vppn3csd6)v q )h p(olu0oi ;deal gas is increased from 110$^{\circ} $C to 360$^{\circ} $C while the volume and the number of moles stay constant. By what factor does the pressure change? By what factor does $v_{rms}$ change?$\frac{P_2}{P_1}$ =    $\frac{(v_{rms})_2}{(v_{rms})_1}$ =   

  A house has a volume of ;l74r*zbhp)rbhq z:b 770m$^2$ (a) What is the total mass of air inside the house at 20$^{\circ} $C?    kg
(b) If the temperature drops to -10$^{\circ} $C what mass of air enters or leaves the house?    kg

  From the known value of atmospheric pressure at the surface oteg3f9 cc(+r2nqj wdm1-,ntt*khg 0of the Earth, estimate the total numberj ger9kdnot,tqfh3c*m+ntw 2(1cg- 0 of air molecules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen mi-j6zt/ e3g/iifq e;,zc sye t1v8q9n olecules contained in a 7.6$-m^3$ volume at 4.2 atm if the total amount of nitrogen is 1800 mol?    m/s

  A standard cylinder of oxygen used in a hos;ooiwvtj /)-w pital has gauge pressure = 2000 psi (13,800 kPa) and at T = 259K How long will the cwj itwov)- o/;ylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a j4d idje.5dr39h wx u;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 at 0 o.3mu y t ,68mh6mxpsxn,dr.d$^{\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 theasz ampb)p7mf8 om5lk01c8 z6zbw o) 9 Earth’s equator at 25$^{\circ} $C, but then was heated to 45$^{\circ} $C, how high above the Earth would the band be (assume equal everywhere)?    m

  A brass lid screws tightly onto a gle3i 9d/zfywsh0y r7-cass 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*seq3l ;29dnsz.lkxp 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 charm k4a k syrui1yx102(iged, has a pressure of 195 atm at 20$^{\circ} $C. The volume of the tank is 11.3 L.
(a) What would the volume of the air be at 1.00 atm and at the same temperature?    L
(b) Before entering the water, a person consumes 2.0 L of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last?    min
(c) At a depth of 20.0 m of sea water and temperature of 10$^{\circ} $C, how long would the same tank last assuming the breathing rate does not change?    min

  The escape speed from the Earthw ;o tdbugo0f/ ,epl9n)(d-qn 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 suspend2dxw *tcu opt:t7,s x4ed against gravity by tennis balls thrown vertically upward at it. How ma, c4* xut27 d:tsxwptony 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-diameter (spherical) u5fyfw01ar :jbubble of air from a depth of 14.0 m in a lake. Assume the temperature is constant at 298 f uwraf:jy05 1K, 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 following two days iu 55 1nor,ky+vvevy(jwd +c): ndy i,uoey5wvkvvc1(r)j 5++
(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 da9mh9hf(. g gh1rik ,.c at:apensity of iron at STP, and when it is a solid deep in the Earth where the temp.a , fgkh9(r:ht9a h i.g1mpcaerature 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 cons/01vg)*mps vwl* c)lws)4 penm v,lbvtant pressure, tl )wpg* lnepvcsm41smw* /v)v)0l,vbhe 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.