PHYS 1101 Practice problem set 5, Chapter 18: 4, 9, 15, 23, 27, 32, 40, 43, 55, 56, 59 1 = = = Nk T Nk T Nk T B 1 B 2 B 1

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1 PHYS 0 Practice roble set, Chater 8: 4, 9,,, 7,, 40, 4,, 6, Sole: (a he ean free ath of a olecule in a gas at teerature, olue V, and ressure is λ 00 n. We also know that λ λ V 4 π ( N V r Although, constant olue (V V eans that λ λ 00 n. (b For and, the ideal gas equation gies ecause λ V, λ λ (00 n 600 n. V V V V V Nk Nk Nk ( 8.9. Sole: (a he atoic ass nuber of argon is 40. his eans the ass of an argon ato is he ressure of the gas is N V rs u 40(.66 0 kg kg (.0 0 ( kg( 4 /s Pa (b he teerature of the gas in the container can be obtained fro the ideal-gas equation in the for V Nk : 4 V Pa K (.0 0 (.8 0 J/K Nk 8.. Sole: ecause the neon and argon atos in the ixture are in theral equilibriu, the teerature of each gas in the ixture ust be the sae. hat is, using quation 8.6, Ar rs Ar Ne rs Ne Ne rs Ar rs Ne ( 400 /s Ar 0 u 8 /s 40 u 8.. Sole: (a he aerage kinetic energy of a roton at the center of the sun is (b he root-ean-square seed of the roton is ε k 7 6 ag ( (.8 0 J/K 0 K 4 0 J 7 ( ( k.8 0 J/K 0 K.67 0 kg rs /s

2 8.7. Sole: (a For a onatoic gas, th ncv.0 J.0 ol. J/ol K C or K (b For a diatoic gas,.0 J (.0 ol(0.8 J/ol K C or K (c For a solid,.0 J (.0 ol(.0 J/ol K C or K 8.. Sole: he equilibriu condition is hus the final theral energies are Af f tot (ε A ag (ε ag (ε tot ag n n n + n n 4.0 ols A A ( 9000 J 000 J A Af tot + na + n 4.0 ols +.0 ols n.0 ols ( 4,000 J 6000 J f tot na + n 7.0 ols 8000 J ecause Ai 9000 J and Af 8000 J, 000 J of heat energy is transferred fro gas A to gas Visualize: Please refer to Figure P8.40 in the textbook. Sole: (a he ost robable seed is 4 /s. (b he aerage seed is ag (c he root-ean-square seed is rs /s /s + 6 /s + 8 /s 4.6 /s ( ( ( ( /s /s + 6 /s + 8 /s 4.94 /s

3 8.4. Sole: (a he nuber of olecules of heliu is he initial internal energy of heliu is he nuber of olecules of argon is he initial theral energy of argon is N N 6 ( Pa ( 00 0 V.96 0 heliu k (.8 0 J/K( 7 K.96 0 nheliu ol heliu i Nheliuk 0.4 J ol 6 ( Pa ( 00 0 V argon k (.8 0 J/K( 67 K nargon ol (b he equilibriu condition for onatoic gases is heliu argon tot argon i Nargonk.6 J ol (ε heliu f ag (ε argon f ag (ε total ag ( + heliu f argon f J tot 78 J/ol n n n ol heliu f ( + ( nheliu 78 J/ol 78 J/ol ol 47. J argon f (c he aount of heat transferred is ( nargon 78 J/ol 78 J/ol ol 04.7 J heliu f heliu i 47. J 0.4 J 6.9 J argon f argon i 04.7 J.6 J 6.9 J he heliu gains 6.9 J of heat energy and the argon loses 6.9 J. hus 6.9 J are transferred fro the argon to the heliu. (d he equilibriu condition for onatoic gases is Substituting the aboe alues, ( ε heliu ( εargon ag ag 47. J 04.7 J (e he final ressure of the heliu and argon are N k heliu f argon f kf Nheliu Nargon (.8 0 J/K (.96 0 (.8 0 J/K( 80 K heliu heliu f 6 Vheliu 00 0 N k ( (.8 0 J/K( 80 K argon argon f 6 Vargon 00 0 f 80 K F. 0 Pa. at.49 0 Pa.4 at

4 8.. Sole: he theral energy of a onatoic gas of n oles is n. he theral energy of a diatoic gas of n oles is n. he total theral energy of the ixture is Coaring this exression with we get + ( + ( th n n th n + n ( n C n + n C th total V V ( ( n + n n + n CV he requireent that the ratio of secific heats is.0 eans he aboe equation is then C C + γ + P V.0 CV CV CV CV ( n + n n n n n n n n n hus, onatoic and diatoic olecules need to be ixed in the ratio :. Or the fraction of the olecules that are onatoic needs to be Sole: (a he theral energy of a onatoic gas of n oles is n. he theral energy of a diatoic gas of n oles is n. he total theral energy of the ixture is Coaring this exression with we get ( + ( th n n th n + n ( n C n + n C th total V V C V ( n + n ( n + n (b For a diatoic gas, n 0, and C. For a onotoic gas, n 0, and C. V V 4

5 8.9. Sole: (a We are gien that i f ( ( ( rs i k rs f his eans that f 4 i. Using the ideal-gas law, it also eans that f V f 4 i V i. Since the ressure is directly roortional to the olue during the rocess, we hae i /V i f /V f. Cobining these two equations gies f i and V f V i. k rs i (b he change in theral energy for any ideal gas rocess is related to the olar secific heat at constant olue nc. he work done on the gas is by ( th V f i W dv (area under the -ersus-v grah V i i he first law of therodynaics th Q + W can be written ( ( Q W nc + V nc + V th V f i i i V i i i n + V V + V 9 V i i i i i i i i i

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