Which has more atoms: 1 kg of iron uoe8o+ ))nj jzor 1 kg of aluminum? See the periodic table or8j ju+eo) ozn) Appendix B.

Name several properties o1f3ob ;t( p nxjmtd(vj2,(ljaf materials that could be exploited to make a thermometevb( j(3pntjml,( ao 1xd;j 2tfr.

Which is larger, 1 C 2 vjbp2ce yuce5 ozmx3g9+85h$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with system B, but B is not lj- 6vejo; f4jin thermal equilibrium with syste;j4 6jfejol- vm C, what can you say about the temperatures of A, B, and C?

A flat bimetallic strip consists of aluminum riveted x q,4;jw o.zq*7d2qguro k5zwto a strip of iron. When heated, the strip wi wr2g q;x.dk4zouj7o,qq z w5*ll 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 line2 y(h6h *-xv rkjxc(klar 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 co:hh9 yl1f( dk*p0lxzm ntrol a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid mercury that conducts electricity when it can flow to touch both contact wires. Explain how t*0(m 9l1lz fphk :xdhyhis device controls the furnace and how it can be set at different temperatures.

Long steam pipes that aref ytxq.sas//5r9 fye+/.uuu y acy6q9j ; whi2 fixed at the ends often have a section in the shape of a U. Why?s yxi9ct2fq y +;wqru6auh/uysj/y/..5a e f9

A flat, uniform cylinder of l;h fx -jqegl: ,eww7*zead 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 thermometeri do:fn f-0s, g9gpnr6 is first placed in a hot tub of water, the mercury initisnno:dif09 f -pr ,6ggally descends a bit and then rises. Explain.

A glass container may break if one part of it is heated ob ,o6tby zmr2/r cooled more rapidly than adjacent part /mtoby26zbr,s. Explain.

The principal virtue of Pyrex glass is that its coefficieuzdo0a nqcx.-9kj 1c1 nt of linear expansion is much smaller than that for ordinary glass (Table 13–1). Explain why this givesc9kod0c xnj1q z .-1au rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accuratjkyufvd go.- wk5xg,-)3r g/ ca;2nyje 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 bot;:lj gmd6j + wjrpr:wrsz (g82tom and top to bulge so badly the can will not stand up. What pg::dg28l(szjr +j;rrwwj m 6has happened?

When a gas is rapidly comp/csdq; 1uw3p uressed (say, by pushing down a piston), its temperature increases. When a gas expands against a piston, it cow p; 1uuq/cd3sols. Explain these changes in temperature using the kinetic theory, in particular noting what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force on an aluminum sphere submerged in wat ntt1kwhi0at ) q6+4brer increase or decrease if th) qw t6k0tn1i4b+tra he temperature is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follows from kinetic theory *:a h7l9deyiwand the relation be* ly7i :9dhawetween average kinetic energy and the absolute temperature.

Explain in words how Gay-Lussac’s lwu2xb n/ik /mteo*b 8*aw follows from kinetic theory.

As you go higher in the Earth’s at5r9+ z:rhc p).xik dp jv,yuw9mosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refersb)cck5 mn-w8d8kp, x /y.i:i7 adyvrsqm-7 mb to the minimum speed an object must have to leave the Ear .8syd/m7b)7b5-c,ckk qyivxp :d a m-wrmi8n th and never return. The escape velocity 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 mjp,+5ftb0 kkat room temperature. What can you infer about the molecular properties of one relatkmktj b,pf+ 50ive to the other?

Explain why a hot humid day 009kzp;6 aa+k a*uahxazx )iois far more uncomfortable than a hot dry day at the s0xk;*u)zia+x 6ao h9az0p ka aame temperature.

Is it possible to boil water atn7+mkb z ut-e 9;n(5lgky8o va room temperature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air tempt7u xh1y2 f36zvxrh r4erature is the same but the humidity is different. Which is more dense, the dry air or trzft7v2 y h14 h6xur3xhe humid air at the same T? Explain.

Explain why it is dangerous to open the radiator cap of an overheated au72cq ;86tisstq(ovs h tomobile 7q (;oh6s8si2tsqc tvengine.

Why does exhaled air appear a3dhprdk.sw6z ,: k4 qzbzv9 5js a little white cloud in the winter (Fig. 13–28)?

  How many atoms are t,l23a ihyzq9w 5u bx5shmc6pd /2*j gohere in a 3.4-gram copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 4e00 tot os o:upeb8q-pa6 j2k26.5-gram gold ring compare to the number in a silver ets8u-o: 0p2q0 6 pbet 4ojoakring of the same mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to; w9 dlqo,ifz( be 68°F. What is this on the Celsius scale?id (o zq;wl,f9   $^{\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 and8uk0w3tn: f mj lowest temperatures recorded are 136 $^{\circ} $F in the Libyan desert and -129 $^{\circ} $F in Antarctica. What are these temperatures on the Celsius scale?high =    $^{\circ} $ C
low =    $^{\circ} $ C

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

  In an alcohol-in-glass thermometer, the alcohol c3xc-6kk r8mspolumn has length 11.82 cm at 0.0r mk6s-8p x3ck $^{\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 sl3d1bzf .c* frrabs 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 apphh/vo)k(-w4ud,,y wrs rr vr0roximately 300 m tall. Estimate how much its height changes between July (average temperature of 25°C) and January (a vh)dwr4(v r-howurk /,yr0s, verage 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 y(b :p,pn31vh5/kaq bwn1z vkare often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 c5kn bh3v/pb1(zvpn, y1 a: wqkm 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 41qblcxuu36 ) xq/ elj+ $^{\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 will be its change in volume if n:(2(sc2e zybw ejj,j it is heated from 302znjcsj:e,(jbe( 2y w $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is filled to the brim with 350.0 mL of waterlw7y c:zax7)k 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 55.50apn ,m x5.axb* vgv.-10skut o 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 ring made1t2rjc4a(ur 9g: rq dz 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, narn6 b,mhzde1mvw3 6 pou8*r;fm row vessel so it can expand in essentially one direction only, show that the effective coefficient of linear expansion is approximately equal to the nrh;f 8v1ume3 *6o bwmmp6d,zcoefficient of volume expansion $\beta$.

(a) Show that the change in tha;f u2s(wo4 ne)p0w fjl)yo9x e 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 width w h/t7- 6ot636hrji bm y zrjq(hwxjy 0p)as coefficient of linear expr6t3yb xzm q0oj6w7 t-/ jph(jry6h)i ansion $\alpha$ 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 isotu6 lt r28g d),ab4 5dhv7zm8kehlh(mqropic 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 grandfath+:8sn-6o tmz-fdwh:3 qowjjz er clock is made of brass and keeps perfect time at 1zhq j dwo nt6sm:w-j3:+foz- 87 $^{\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 thermomet 1+x 0ee*p tw/ynm-3tsm zi.lwer has an inside diameter of 0.140 mm. The bulb has a volupm n em3/ywl. 1i0extt-+ *szwme 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 x ir/e2*0fvc9mid )wmnawnw39* ma y: rotating about its axle on frictionless bearings with angu)nw yw 0ix3ai rd29:9e*n mmvw/ f*acmlar velocity $\omega$ = 32.8 rad/s If its temperature is now raised from 20.0 $^{\circ} $ C to 75.0 $^{\circ} $ C, what is the fractional change in $\omega$?   

  An aluminum bar has the desired length when at 15°C. Ho:ikh5lvd llt;*, pgl/x,ppe nf8o2 f- w much stress is required to keep it at this length if the temperature increases to 3v2 lk- e fl;pfog p5i8/ptlxd,n*l:h,5 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beabd2x,n)i 971 exrn.pxh hm 3vkm of cross-sectional area 0.041$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diameter 13n r2k2*o5uevk(*wcr4 mvnad ) 4.122 cm at 20$^{\circ} $ C is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 cm at 20$^{\circ} $ C. It is 7.4 cm wide and 0.65 cm thick.
(a) To what temperature must the band be heated so that it will fit over the barrel? $\approx$   $^{\circ} $ C(Round to the nearest integer)
(b) What will be the tension in the band when it cools to 20$^{\circ} $ C?    N

  What are the following temperatures on the Kedy3exfsm9a,)0vg k 4plvin 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 Fahrent8(0 b rvwcbn5heit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth and Sun are about 40069cpm( e6og+ uu p-jxs;qw*zo 0$^{\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 temperatu39qd;lqu4ac*apq9rjm l9+gyna. 9zgre of about 2*9nz94 lgdyrg.m a 3ual9pqcqqa+ j 9;0$^{\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 densityxeil0h *iovlm: c1 /tp9+ hue, of oxygen at STP using the ideal gas law.    kg/$m^3$

  A storage tank contains 21.6 kg of nitrogenzom pm j2f837ovkq6 f) ($N_2$) at an absolute pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by an equal mass of $CO_2$    atm

  A storage tank at STP contains 18.5 kg of nibh +b0a,lmzf,q j*z c)trogen ($N_2$)
(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 at 10k)uha- iuv0(mk h91gd.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 105.0 kg of argx1m;h, zniz;i on gas at 385 K?i;1n z,m xzh;i   $ \times10^{ 8}$Pa

  A tank contains 26.0 kgh7,y1jki e ou3e mbl95 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 achiev1ftpqd jazq*4ts. 5h6es its buoyant lift by heating the air inside the balloon, which makes it*aqftdjs1 h6 t5pqz .4 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 airo)y u+ g1p9esm ioju)- at 15 $^{\circ} $ C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 38 $^{\circ} $ C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained?    %

  If 61.5 L of oxygen at 10xcis0qhm sqd(8* f: hxm x,2w8.0 $^{\circ} $ C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 50.0°C, what will the new pressure be?    atm

  A helium-filled balloon escapes a child’s hand at sea qj+s .jqjtmw+ (bh() ylevel 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 molecules 5tpph7rpb7o, / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are there in 1.000r0fox tch :g+y:5rq)zej( 1ty ax6wj3 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (a) molesww;d,tc65d,-ru gxe shr (1k y,    $ \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 volumeaw,t ) ib0wcg( 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 ai llbk)y0qbag)f/4q4hjp ,t6i r are in each 2.0-L breath you inhale that were also in the last k4i6g) bb 4jh,/l qtp0ylaqf)breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kineti czcnz6)991 n gg*kgwcc energy of an oxygen molecule at STP? wg9c zgg 19)*n 6nzkcc   $ \times10^{-21 }$ J
(b) What is the total translational kinetic energy of 2.0 mol of $O_2$ molecules at 20 $^{\circ} $ C?   $ \times10^{3 }$ J

  Calculate the rms speed of helium atoms near the surf nh b*rc7ay6y/ace of the Sun at a temperature of y6r7 ynb ac*h/about 6000 K.    m/s

  By what factor will tha01z/2dc9ar q n,brx f4stk e4e rms speed of gas molecules increase if the temperature is incr4frd2 bt0n/s1kq 9rc, 4zeaxaeased 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 uni6n3)x fqex07h 1ij krrts of km/s: 6, 2, 4, 6, 0, 4, 1, 1rf6 e )ikn0rq 3jh7xx8, 5, 3, 7, and 8. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in a gas at q1dyy 9p7mwwgn 5*sw* 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 u+lk xmx;4p1edoubled while its volume is held constant, by what famk 4+uxxp1;l ector does $v_{rms}$ change?   

Show that the rms speed of5-l)two utm qxh ro,5) molecules in a gas is given by $v_{rms}$ = $\sqrt{3P\\rho}$ where P is the pressure in the gas, and $\rho$ is the gas density.

Show that for a mixture of )hjyqq8xx g06ec-u2e two gases at the same temperature, the ratio of their rms speeds is equal to the inverse ratio of the squaq jhe2xc)x0eu8 q6gy-re roots of their molecular masses.

  What is the rms speed of nitrogen molecules con zz )gue/ d0dbs*h6 by(z;e2kh f0g8xntained 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 oxygen molecule a(gyw: u qacy 6o8g qkhh/u8/ )hq/p7jqt 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 nitw pbs5i9b7 y gyi9w/j bp57tp2rogen molecules at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms spee r04ba3,yp hped of an amino acid whose molecular mass is 89 u in a living cell at 37ybpa4 e,3p h0r $^{\circ} $ C.    m/s
(b) What would be the rms speed of a protein of molecular mass 50,000 u at 37 $^{\circ} $ C?    m/s

Show that the pressure P of a gas can be wcu 3mcazs7)y5 v+c ty3ritten 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 7d/*v,qgq:5 bsqtvy1 c zu5ou uranium, $^{235}$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 pha.;x z*k8o4o:u hlxexsp9xx; xses 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 0.01bxtaihk (8 2o.0x0cnt atm and the temperature is (a) 0chtxkbain08t. 2x(o90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately).o)vxuqgzc 4k77 d/;h;9 a qys8wmgut if the humidity is 50% on a day when the temperature is 9o.xz477/q hv;u; )gdc 8 gs wyqktuma25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where water hy6jdu4eei jsc a.(*8boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mountains is 0.72 atm, esttb 9o z0mij06i0np *uximate uip9xb6nom jzi0t0 *0the temperature at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pressure of water is 530 Pa k1 tpe( :- yw,nb5p- gfn6hkdcand the relative humidity is-kn :,(cbyt6f5 -1kgdwh nepp 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of water on a day when thek(4mdg ,xz6u ka8cso -xgs9xq cb;+5o temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside a pressure cooker if9w i-jy;r b:c h1zpd)f the water is boiling at a temperature of 12d )zi c1f9-h bjyrpw;:0 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a room of vid wbpl,,;,h,-hlkc/d9htp m olume 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 v)paxkq-em 1+s6ws7-n +arpq 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 gl1z5utgy1ho*e o)p:l lsv)e m9ycine molecule (see Table 13–4) to diffuse a distanceolt em*hy:5og u9zespl1) 1)v 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 the surface of insects to the interior throxrvp4 2wshes5se iew* w0+7i; ugh tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-sectisxhw2 p 47+wvreis*e we ;s50ional area of $ 2\times10^{-9 } m^2$ Assuming the concentration of oxygen inside is half what it is outside in the atmosphere,
(a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20$^{\circ} $ C is about 8.7 mol/$m^3$ then $\approx$    mol/$m^3$(Round to one decimal places)
(b) calculate the diffusion rate J,    $ \times10^{-11 }$ mol/s
(c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $ 1\times10^{-5 } m^2/s$    s

  A precise steel tape measure has been calibrated at zuz. e)f0u ae520$^{\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 meadewc t7v2p;)kkmp * :msure 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 bqcv/:(u:pdhkg 3vc8. qojv . normal room temperature. How much error will be made in a recipe calling for 300 mL of cool water, if the water andvcc/:(u3vdk p.q:.o8qv b gj h 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 initia7c9 mtnjk27ia lly 28 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the original gas knitm7j 927acremains in the cylinder?   

  Estimate the number of air molecules in a room of lengtvui*e2 1ebv5u h 6.5 m, width 3.1 m, and height 2.5 m. Assume th15be*vv2uei u e temperature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of matterk4 r1 nd+y8 3;ydxgopq is about one atom per $cm^3$ mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).$v_{rms}$ =    m/s    $ \times10^{-22 }$ atm

  The lowest pressure attainable using the bxixuf:n rkh81in62j5z./ m e;zu nmr/ est available vacuum techniques is aboxi/:k5u1rru eznmz i.x jnh68 2/mn;fut $10^{-12} N/m^2$ At such a pressure, how many molecules are there per $cm^3$ at 0$^{\circ} $C?    $\frac{molecules}{cm^3}$

  If a scuba diver fills his lungs to full capacity of 5.5 L whbevlzjjg :54e ery8 om,jl hhwa8x86x;q2/1 len 10 m below the surface, to what 48g:oeqvm,hlxw5y;he6/rxaj8b e8 2zllj 1 jvolume would his lungs expand if he quickly rose to the surface? Is this advisable?    L

  A space vehicle returning from the n(doajgd e9fi a9-d 49Moon 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 must be made of special materialef 4j9i(and9d9g d- oas; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)    K

  The temperature of an ideal gas is increy wuo e,f)ky.,ased 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 774c,dpee bn1v 3 5 mi)ci8wqja40m$^2$ (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 d o;t (nm:e-gratmospheric pressure at the surface of the Earth, estimate the total number of air molecules im ge-r d;no:t(n the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of rzf g *fxxj1x2iq6h,i.8wf 6o nitrogen molecules contained in a 7.6$-m^3$ volume at 4.2 atm if the total amount of nitrogen is 1800 mol?    m/s

  A standard cylinder of oxygen used in a hospital has gauge pressure = 2000+l mcn k. zx;oma1yz25s(jc 9d psi (13,800 kPa) and at T = 259K How longxa 5mkzm+jns (yz1;2c.loc 9d will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liqucc/n*ydcx f/ 1 ws1lc(*(zogaid 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 gasolineo:q t jp.dy zxbf*,b.(t6zt4f 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 the Eqtb f4t4cq2 9warth’s equator at 25$^{\circ} $C, but then was heated to 45$^{\circ} $C, how high above the Earth would the band be (assume equal everywhere)?    m

  A brass lid screws tightly onto a glass jar a31v/zdga3 uelplc od70 va) 7vt 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,3gxd pwbec-q0 v 4gh+1 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 chargfl okz -o7;oxo;stzv2m) qn ;o92e)wt ed, 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 ja2:vf x1p6ml-i 3kni 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 grav 2gjtv)qyij + w;h8mv24gxd+gkhl k+(ity by tennis balls thrown vertically upward at it. How many tennis balls p+ (v+j +8gjt;i)k 2yhqhvw24dlmgxkger 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) bubble of air* dq iq7y/m)ao from a depth of 14.0 m in a lake. Assume the te/7 qqydo )mai*mperature is constant at 298 K, and the air behaves as a perfect gas. How large is the bubble when it reaches the surface?    cm

  Calculate the total water vapouz6 u44pjiuk(clk tm-pu ,1hge)vp4 2r pressure in the air on the following two days: (pu uuml4cjhk-4gtv1e)u4i2p 6zkp,
(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 Sn+2 -bbss (yehTP, and when it is a solid deep in the Earth where t n- bbs2ey(s+hhe 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 tha elo)2ndn4fv9f8l e* st, for an ideal gas at constant pressure, the coefficient of volu*onefnfe8v ) ldl9s42me 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 dehum4:z+gvc(zgumm 9nlp*v 0 td (zidify their cellars to prevent rot and mildew. If the cellar in a h t:g0uzgc*vp9 (dn(v4 mzz+mlouse (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