Announcements 1. Exam 4 starts Friday! a. Available in esting Center from Friday, Dec 7 (opening time), up to Monday, Dec 10 at 4:00 pm. i. Late fee if you start your exam after 4 pm b. Covers C. 9-1 (up troug HW 0) c. Sample Exam 4 is posted on te website and Sample Exam 4 Solutions also. d. Exam 4 formulas posted on website: wic ones you need to memorize, and wic ones will be given i. Also in today s notes e. ere s still a 3 our time limit. Late submissions for HWs 17 troug 0 are due Friday evening 3. Online course evaluations, do before Dec 13 ttp://studentratings.byu.edu 4. Final exam info a. ake in esting Center any time during Finals week b. No time limit, but approx. same lengt as oter exams c. Approx 40-45 problems (answer blanks) i. Approx. 10-1 on new stuff (Cap 13 & 14), te rest is cumulative ii. Not as many of te ardest problems Exam 4 formulas (te new ones) o be given on exam New for exam 4 Constants ρ water = 1000 kg/m 3 k B = 1.381 10-3 J/K N A = 6.0 10 3 R = k B N A = 8.314 J/mol K = 0.0806 liter atm/mol K σ = 5.67 10-8 W/m K 4 Conversion factors: 1 atm = 1.013 10 5 Pa = 14.7 psi 9 F = C + 3 5 K = C + 73.15 1 cal = 4.186 J 1 m 3 = 1000 L stress = F/A; strain = L/L P = P 0 + ρg A 1 v 1 = A v P1 + ρ v1 + ρgy1 = P + ρv + ρgy L = α L 0 0 V = 3α V KE ave 1 3 = mv ave = k B Colton Exam 4 Review, urs 1/6/07 - pg 1 Colton Exam 4 Review, urs 1/6/07 - pg Q = ka 1 L 4 P = eσ A W on gas = P V (constant pressure) 3 3 U = nr = Nk B (monatomic ideal gas) Wnet Qc Definition: e = = 1 Qadded Q c Carnot eorem: emax =1 o be memorized New for exam 4 m Definition: ρ = V Definition: F P = A Arcimedes Principle: F B = w displaced fluid = m displaced fluid g = ρ fluid V object g Ideal Gas Law PV = nr = NkB Calorimetry: Q = mc ; Q = ml First Law of ermodynamics: U = Q added + W on system Definition: isotermal = no temperature cange Definition: adiabatic = no eat excanged Cycles: U = 0; W net = Q added Q exausted = Q Q c Exam 4 - Review of important concepts Bold = someting tat must be memorized 1. Pressure a. Definition: P = F/A b. Stress & strain of solids c. Increase wit dept in a liquid: P = P surface + ρg d. Pascal s principle: pressure in fluid te same at same e. Arcimedes Principle: F B = weigt of displaced fluid (= ). Fluid dynamics a. Viscosity b. Equation of continuity: A 1 v 1 = A v i. Wy/wen true c. Bernoulli effect: motion of fluid causes P to decrease i. wings: air deflection elps, Bernoulli elps d. Bernoulli eqn: P1 + ρ v1 + ρgy1 = P + ρv + ρgy 3. emperature effects a. ermal expansion of solids: L = α L o b. Ideal gas law: PV = Nk B ; PV = nr Colton Exam 4 Review, urs 1/6/07 - pg 3 Colton Exam 4 Review, urs 1/6/07 - pg 4
3 = c. Average kinetic energy of gas: mvave k B i. Relationsip to internal energy, U = 3/ nr for monatomic ideal gas 4. Heat a. Calorimetry: Q = mc ; Q = ml b. Radiation: P = eσa 4 (bot eat absorbed & emitted) Q c. Conduction: = ka 1 L d. Convection: qualitative only 5. ermodynamics a. P-V diagrams i. Isotermal contours ii. ypes of state canges: constant P, constant V, constant ( U=0), adiabatic (Q=0), cycle ( U=0) b. Work done on/by a gas: area under curve on P-V i. Positive vs. negative c. First Law: U = Q added + W on system d. Engines: general picture i. Q = W net + Q c Wnet Q e = = 1 ii. Efficiency: Q Q added c e ; max =1 c HW 17, Problem (87 correct) A container is filled to a dept of 0.0 cm wit water. On top of te water floats a 44.1-cm-tick layer of oil wit specific gravity 0.700. Wat is te absolute pressure at te bottom of te container? Assume tat te atmosperic pressure is 1.00 Atm. Answer: 10685 Pa Colton Exam 4 Review, urs 1/6/07 - pg 5 Colton Exam 4 Review, urs 1/6/07 - pg 6 HW 18, Problem 4 (197 correct) e inside diameters of te large portions of te orizontal pipe in te figure are.50 cm. Water flows to te rigt at a rate of 1.83E-04 m 3 /s. Determine te inside diameter of te constriction. HW 19, Problem (8 correct) A pair of eyeglass frames are made of epoxy plastic (coefficient of linear expansion =134 10 6 C 1 ). At room temperature (1.9 C) te frames ave circular lens oles.3 cm in radius. o wat temperature must te frames be eated in order to insert lenses.5 cm in radius? Answer: 0.0148 m Answer: 88.8 C Colton Exam 4 Review, urs 1/6/07 - pg 7 Colton Exam 4 Review, urs 1/6/07 - pg 8
More Sample Exam Problems (answers at end) Problem 1. You are at te bottom of a lake in a submarine. e air pressure at te surface of te lake is 1 atm. e absolute pressure at te bottom is 6 atmosperes. e dept of te lake is [1] m. e force of te water on a submarine portole of radius 4 cm is [] N. Problem. An ideal (Carnot) eat engine takes eat from water always at 100 C in a natural ot spring under te ground (geotermal energy), and generates useful work (electricity). It exausts te waste eat to te air above te ground. e engine will be te most efficient in [3?]. 1) Summer ) Winter 3) neiter; always te same. If te outside temperature is 30 C, and 000 J is taken from te ot water, te eat exausted to te air must be [4] J Colton Exam 4 Review, urs 1/6/07 - pg 9 Colton Exam 4 Review, urs 1/6/07 - pg 10 Problem 3. A solid iron spere of volume 8 m3 is totally submerged in water at te bottom of a pond. e density of iron is 8000 kg/m3. e bouyant force on te spere is [5] N. e weigt of te spere is [6] N. o lift te spere wit a cable will require a minimum cable force of [7] N. Problem 4. Wen a spinning "curve" ball is trown, it will tend to curve because of [8?] 1) te Bernoulli effect ) conservation of angular momentum 3) Newton's 3rd law 4) te torque applied Colton Exam 4 Review, urs 1/6/07 - pg 11 Colton Exam 4 Review, urs 1/6/07 - pg 1
Problem 5. Cooled elium gas in a closed tank of volume 1 m3 is at -100 C, at one atm pressure. If te tank is cooled furter to -00 C, te pressure in te tank will be [9] atmosperes. e number of molecules in te gas is [10] molecules. e average kinetic energy of a molecule at -100 C is [11] J. Problem 6. A contraption allows you to narrow a region of a ose as water is flowing troug it. e water is initially flowing troug at a speed of 1.5 m/s. If te ose is narrowed in a region from a diameter of.5 cm to a diameter of.0 cm, wat will be te speed of te water in te narrowed region? [1] m/s. e pressure in te narrowed region will be [13?] 1) te same as ) less tan 3) greater tan te pressure in te region of ose just before te narrowing. Colton Exam 4 Review, urs 1/6/07 - pg 13 Colton Exam 4 Review, urs 1/6/07 - pg 14 Problem 7. A 5 kg book falls onto te floor from a self 3 m above te floor. e entropy cange in te universe was [14] 1) positive ) negative 3) zero. Problem 8. One mole of a monatomic ideal gas is taken around te cycle sown. In te process B C, te cange in te internal energy was [15] J, and it was [16?] 1) positive ) negative 3) zero In te process B C, te eat excanged was [17] J, and it was going [18?] 1) into ) out of 3) neiter te gas. For te wole cycle, te net work done on te gas was [19] J, and was [0?] 1) positive ) negative 3) zero. e eat excanged for te cycle was [1] J, and it was going [?] 1) into ) out of 3) neiter te gas. Colton Exam 4 Review, urs 1/6/07 - pg 15 Colton Exam 4 Review, urs 1/6/07 - pg 16
Problem 9. You ave a pool of ot lava at 500 C in your backyard. You decide to stir it wit a steel rod, wic as a diameter of cm. You need to coose te lengt of te rod to be long enoug so tat you don't burn your and, wic is at 30 C. If you want te eat flow rate from te rod into your skin to be only 0 Watts, you sould coose a rod of lengt [3] m. (e termal conductivity of steel is 80 W/m C.) (Note: actual exam will be ~3 answer blanks) Answers to More Sample Exam Problems Not guaranteed (I didn t double-ceck my work) Bonus points for te first people to find errors 1) 1 (51.68 m) ) 0 (3055 N) 3) (Winter) 4) 6 (165 J) 5) 8 (78400 N) 6) (6700 N) 7) 4 (548800 N) 8) 1 (Bernoulli effect) 9) (0.4 atm) 10) 0 (5.087E6) 11) 5 (3.584E-1 J) 1) 3 (.344 m/s) 13) (less tan) 14) 1 (positive) 15) 7 (3750 J) 16) 1 (positive) 17) (650 J) 18) 1 (into) 19) 5 (-750 J) 0) (negative) 1) 5 (750 J) ) 1 (into) 3) 1 (3.179 m) Colton Exam 4 Review, urs 1/6/07 - pg 17 Colton Exam 4 Review, urs 1/6/07 - pg 18