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Skli: = 0 Bowlingkule v/r Rulle: = v rull /R Skli: = 0 Bowlingkule v/r Rulle: = v rull /R B R A v 0 r Om A: L A = r m v + I 0 Ingen krefter har moment = L A = konst. = mrv 0 s v rull L start = L slutt

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Skli: = 0 Bowlingkule v/r Rulle: = v rull /R Skli: = 0 Bowlingkule v/r Rulle: = v rull /R B R A v 0 r Om A: L A = r m v + I 0 Ingen krefter har moment = L A = konst. = mrv 0 s v rull L start = L slutt = v rull = v 0 5/7 (*) -- uten å kjenne! Om B: L B =I 0 τ f = R = L B ikke konst. men I 0 d/dt = R, må kjenne R A = -ma R = Iα v 0 r sluring = μ k mg (uavhengig v) a = -μ k mg/m = -μ k g α = μ k mgr/(2/5)mr 2 = - (5/2) a/r v rull rulling, konst v = 0 t Oppgave 1 Oppgave 2 1 Oppgave 3 Oppgave 4 A18.8 If the pressure of the atmosphere is below the triple-point pressure of a certain substance, that substance can exist (depending on the temperature) A. as a liquid or as a vapor, but not as a solid. B. as a liquid or as a solid, but not as a vapor. C. as a solid or as a vapor, but not as a liquid. D. as a solid, a liquid, or a vapor. A18.5 You have a quantity of ideal gas in a cylinder with rigid walls that prevent the gas from expanding or contracting. If you double the rms speed of molecules in the gas, the gas pressure A. increases by a factor of 16. B. increases by a factor of 4. C. increases by a factor of 2. D. increases by a factor of 2 1/2. 2 A18.3 Consider two specimens of ideal gas at the same temperature. The molecules in specimen #1 have greater molar mass than the molecules in specimen #2. How do the rms speed of molecules (v rms ) and the average translational kinetic energy per molecule (KE) compare in the two specimens? v rms = v 2 A. v rms and KE are both greater in specimen #2. B. v rms is greater in specimen #2; KE is the same in both specimens. C. v rms is greater in specimen #2; KE is greater in specimen #1. D. v rms and KE are the same in both specimens. E. None of the above is correct. A19.5 An ideal gas is taken around the cycle shown in this p-v diagram, from a to b to c and back to a. Process b c is isothermal. For this complete cycle, A. Q 0, W 0, and U = 0. B. Q 0, W 0, and U 0. C. Q = 0, W 0, and U 0. D. Q = 0, W 0, and U 0. E. Q 0, W = 0, and U 0. A19.6 An ideal gas is taken around the cycle shown in this p-v diagram, from a to b to c and back to a. Process b c is isothermal. For process a b, A. Q 0 and U 0. B. Q 0 and U = 0. C. Q = 0 and U 0. D. Q = 0 and U 0. E. Q 0 and U 0. A19.9 An ideal gas begins in a thermodynamic state a. When the temperature of the gas is raised from T 1 to a higher temperature T 2 at a constant volume, a positive amount of heat Q 12 flows into the gas. If the same gas begins in state a and has its temperature raised from T 1 to T 2 at a constant pressure, the amount of heat that flows into the gas is A. greater than Q 12. B. equal to Q 12. C. less than Q 12, but greater than zero. D. zero. E. negative (heat flows out of the system). 3 A19.11 When an ideal gas is allowed to expand isothermally from volume V 1 to a larger volume V 2, the gas does an amount of work equal to W 12. If the same ideal gas is allowed to expand adiabatically from volume V 1 to a larger volume V 2, the gas does an amount of work that is A. equal to W 12. B. less than W 12. C. greater than W 12. D. either A., B., or C., depending on the ratio of V 2 to V 1. A20.4 During one cycle, an automobile engine takes in 12,000 J of heat and discards 9000 J of heat. What is the efficiency of this engine? A. 400% B. 133% C. 75% D. 33% E. 25% A20.7 A Carnot engine takes heat in from a reservoir at 400 K and discards heat to a reservoir at 300 K. If the engine does 12,000 J of work per cycle, how much heat does it take in per cycle? A. 48,000 J B. 24,000 J C. 16,000 J D J E. none of the above A20.8 You put an ice cube at 0 C inside a large metal box at 70 C. The ice melts and the entropy of the ice increases. Which statement is correct? Metal box at 70 C Metal box at 40 C Ice at 0 C Liquid water at 40 C A. Entropy of the metal box is unchanged; total entropy increases. B. Entropy of the metal box decreases; total entropy decreases. C. Entropy of the metal box decreases; total entropy is unchanged. D. Entropy of the metal box decreases; total entropy increases. E. none of the above 4 Oppgave 1 Oppgaver Løsninger uendret =0 reduserer øker F f Ytre kraft (mg sinα) endrer v gir moment til rotasjonen Oppgave 2 Oppgave 3 5 Oppgave 4 A18.8 If the pressure of the atmosphere is below the triple-point pressure of a certain substance, that substance can exist (depending on the temperature) A. as a liquid or as a vapor, but not as a solid. B. as a liquid or as a solid, but not as a vapor. C. as a solid or as a vapor, but not as a liquid. D. as a solid, a liquid, or a vapor. p atm A18.5 You have a quantity of ideal gas in a cylinder with rigid walls that prevent the gas from expanding or contracting. If you double the rms speed of molecules in the gas, the gas pressure Kinetisk gassteori E k = ½ m v 2 = 3/2 k B T A. increases by a factor of 16. B. increases by a factor of 4. C. increases by a factor of 2. D. increases by a factor of 2 1/2. A18.3 Consider two specimens of ideal gas at the same temperature. The molecules in specimen #1 have greater molar mass than the molecules in specimen #2. How do the rms speed of molecules (v rms ) and the average translational kinetic energy per molecule (KE) compare in the two specimens? v rms = v 2 A. v rms and KE are both greater in specimen #2. B. v rms is greater in specimen #2; KE is the same in both specimens. C. v rms is greater in specimen #2; KE is greater in specimen #1. D. v rms and KE are the same in both specimens. E. None of the above is correct. Kinetisk gassteori pv = N/V k B T = N/V 2/3 E k (formelark) E k = ½ m v 2 = 3/2 k B T lik for begge = minst m (#2) har høyest v 2 6 A19.5 An ideal gas is taken around the cycle shown in this p-v diagram, from a to b to c and back to a. Process b c is isothermal. For this complete cycle, A19.6 An ideal gas is taken around the cycle shown in this p-v diagram, from a to b to c and back to a. Process b c is isothermal. For process a b, A. Q 0, W 0, and U = 0. B. Q 0, W 0, and U 0. C. Q = 0, W 0, and U 0. D. Q = 0, W 0, and U 0. E. Q 0, W = 0, and U 0. A. Q 0 and U 0. B. Q 0 and U = 0. C. Q = 0 and U 0. D. Q = 0 and U 0. E. Q 0 and U 0. a- b isokor = W=0 1. hovedsetning kretsprosess ΔU = Q W = 0 W = areal inni kurve 0 1.H = ΔU = Q Temp øker = ΔU og Q er positive A19.9 An ideal gas begins in a thermodynamic state a. When the temperature of the gas is raised from T 1 to a higher temperature T 2 at a constant volume, a positive amount of heat Q 12 flows into the gas. If the same gas begins in state a and has its temperature raised from T 1 to T 2 at a constant pressure, the amount of heat that flows into the gas is 1. Hovedsetning: Q = ΔU + W A. greater than Q 12. Temp øker likt = ΔU 0 og lik begge Konstant volum: W = 0 B. equal to Q 12. Konstant trykk: W 0 C. less than Q 12, but greater than zero. D. zero. E. negative (heat flows out of the system). A19.11 When an ideal gas is allowed to expand isothermally from volume V 1 to a larger volume V 2, the gas does an amount of work equal to W 12. If the same ideal gas is allowed to expand adiabatically from volume V 1 to a larger volume V 2, the gas does an amount of work that is Ved adiabatisk ekspansjon A. equal to W 12. faller temperaturen fordi ΔU = W 0 B. less than W 12. Areal under pv-kurve og dermed arbeidet er mindre enn for isoterm. C. greater than W 12. D. either A., B., or C., depending on the ratio of V 2 to V 1. 7 A20.4 During one cycle, an automobile engine takes in 12,000 J of heat and discards 9000 J of heat. What is the efficiency of this engine? A. 400% B. 133% C. 75% D. 33% E. 25% η = W/Q inn = (Q inn- Q ut )/Q inn = ( )/12000 = 1/4 A20.7 A Carnot engine takes heat in from a reservoir at 400 K and discards heat to a reservoir at 300 K. If the engine does 12,000 J of work per cycle, how much heat does it take in per cycle? A. 48,000 J η = 1 T L /T H = 1 300/400 = 1/4 B. 24,000 J η = W/Q inn C. 16,000 J = Q inn = W / η = J 4 = J D J E. none of the above A20.8 You put an ice cube at 0 C inside a large metal box at 70 C. The ice melts and the entropy of the ice increases. Which statement is correct? Metal box at 70 C Metal box at 40 C Ice at 0 C Liquid water at 40 C A. Entropy of the metal box is unchanged; total entropy increases. B. Entropy of the metal box decreases; total entropy decreases. C. Entropy of the metal box decreases; total entropy is unchanged. D. Entropy of the metal box decreases; total entropy increases. E. none of the above Boksen avgir varme og entropi. Lykke til med eksamen og videre studier! Siden noe av prosessen er irreversibel, øker total S 8

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