Physics 140. Assignment 4 (Mechanics & Heat)

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Oliver Cummings
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1 Physis 14 Assignen 4 (Mehanis & Hea) This assignen us be handed in by 1 nn n Thursday 11h May. Yu an hand i in a he beginning f he leure n ha day r yu ay hand i yur labrary densrar befrehand if yu ish. Yu shuld rie yur ansers in he spae prvided n hese shees. Spae is als prvided fr yu sh he seps in yur alulains. Yu shuld indiae any physial las ha yu have used and any assupins ha yu have ade. Suden nuber Yur nae Day f he eek fr yur lab lass Nae f yur labrary densrar SOUTIONS 1. A beaker ade f Pyrex is filled he very bri ih 1. 3 f aer a 1 C. H uh ill verfl hen i is raised 65 C? (Ceffiiens f vlueri expansin: Pyrex 9. x 1-6 K -1, aer 7 x 1-6 K -1 ) A 1 C vlue f aer vlue f Pyrex nainer V Vlue f verfl Vaer VPyrex β V T β V T aer Pyrex ( βaer βpyrex ) V T 6 ( 7 9. ) 1 1. ( 65 1) Vlue ha ill verfl is If he densiy f nirgen in a haber a a pressure f 1. a is fund be 1.45 kg/ 3, ha is he eperaure f he gas? Assue ha nirgen is far fr liquefain (i.e a a eperaure uh greaer han 77 K - he biling pin f nirgen a 1 a). Then N behaves as ideal gas. Ideal gas la gives PV nrt PV PVNA PV PV P S T nr NR Nk Mk ρk here Nis al nuber f as in gas, kis Blzann' s nsan, is he ass f ne leule f gas, and ρis he densiy f he gas. Ne ha nirgen gas is diai herefre ai ass f nirgen Therefre T K Ne ha his is ell abve liquefain pin hus jusifying iniial assupin Teperaure f gas is 74 K

2 3. Waer a C fls hrugh a 5.-kW heaer a a rae f 1.5 lier/in. Assuing n lsses, a ha eperaure ill i eerge? Elerial energy ransfred hea energy Per f heaer ie Teperaure rise f aer T here is hea added aer f ass, is he speifi hea f aer P T K Tep f eerging aer C Waer ill eerge a a eperaure f 7 C ( sig figs) 4. Suppse e have.3 kg f unknn aerial. I is heaed K and plaed in.6 kg f r eperaure (93. K) aer. The aer is in a pper up f ass.14 kg surrunded by insulaing aerial. The final eperaure f he aer a equilibriu is 95. K. Calulae he speifi hea f he unknn aerial. Hea ls by saple Hea gained by aer + Hea gained by pper up s s Ts T+ T T+ T S s s Ts ( ) J kg K Speifi hea f unknn aerial is.5 x 1 K kg -1 K Wha is he rai f he rs-speeds f nirgen in he air a C and 1 C? A C nirgen gas is far fr liquefain pin s behaves as ideal gas rs - speed f leules in ideal gas here is ass f a leule. Rai f rs - speeds f nirgen in air a C and 1 C is given by 3kT1 Rai 3kT v 3kT T T 373. Rai f rs-speeds is.856

3 6. A pisn ih a rss-seinal area f.5 seals a gas ihin a ylinder a a pressure f.3 MPa. Hea is very gradually added he ylinder and he pisn rises 6.5 as he gas expands isbarially. H uh rk is dne by he gas? Wrk is dne by gas n pisn Wrk dne Fre applied disane ved in direin f applied fre pressure area f pisn disane ved by pisn J Ne ha fre applied by gas n pisn is nral pisn surfae Wrk dne by gas is 9.8 kj 7. Yu are designing an eleri refrigerar reve 36 J f hea per inue fr a ld haber a -4. C and exhaus ha energy in a r a 7.5 C. A he very bes, h uh elerial per ill i require? The Send a f Therdynais ells us ha ax effiieny f hea engine given by W T e 1 1 (Carn) here H is he hea inpu fr he h reservir a H H TH eperaure TH and is he hea exhaused he ld reservir a eperaure T and Wis he rk dne by he engine. A refrigerar is a hea engine in reverse. In his ase, Wis he rk dne n he refrigerar reve hea fr he ld reservir and exhaus hea H + Win he h reservir. S, assuing ax pssible effiieny, per required given by P W H T H T T H T W 6 Elerial per required ill be a leas.7 W

4 8. A -kg saple f pure aer a 4. C is ixed ih a -kg saple f pure aer a 3. C. Using he average eperaures f eah saple, deerine he apprxiae ne hange in enrpy f he al quaniy f aer. S T Change in enrpy f ar aer S T T T average Change in enrpy f l aer T T T Ne hange in enrpy S average T T + S + T T average average 4186 ( ) ( ) ( ) J/K Ne enrpy hange ill be 14 J/K 9. A 1.-g lead bulle a 3. C slas in a sne all and, squashing, es res. Assuing very lile energy lss he envirnen, h fas us he bulle be ravelling if i is ally el? (aen hea f fusin fr lead,.9 kj/kg, eling pin f lead is 37.4 C, and speifi hea f lead is.13 kj kg -1 K -1 ) During llisin, nearly all kinei energy is nvered hea energy in he bulle (assuing very lile energy lss envirnen). 1 v Fr bulle pleely el, us be enugh raise he ep f he bulle 37.4 C and el i i.e. T + lf 1 v T + l f S v ( T + l f) ( T + lf) 3 3 ( ( ) ) /s Speed f bulle us be 35 /s ( sig figs)

5 1. The huan brain peraes ih an average per nsupin f abu W. Wha is ha in kilalries per hur? 1 alrie J Jules Jules alrie 6 sends kilal Brain per send send Jules hur 1 alries kilalries hur. 86 kilal per hur Per nsupin f brain is.3 kilalries per hur NB: 1 glass f dry red ine nains apprx 75 kal herefre shuld help keep yur brain ging fr abu 75/.3 5 hurs 1 days!

Lecture 3: Resistive forces, and Energy

Lecture 3: Resistive forces, and Energy Lecure 3: Resisive frces, and Energy Las ie we fund he velciy f a prjecile ving wih air resisance: g g vx ( ) = vx, e vy ( ) = + v + e One re inegrain gives us he psiin as a funcin f ie: dx dy g g = vx,