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Considere um ciclo de Carnot com escoamento em regime permanente com água como fluido de trabalho. As temperaturas máxima e mínima do ciclo são 350°C e 60°C. O título da água é 0,891 no início do processo de rejeição de calor e 0,1 ao final. Determine o trabalho líquido em kJ/kg e assinale a alternativa correta:

","status","pending_classification","hasRelatedVideo","relatedVideos",[109],{"_110":111,"_129":130,"_51":145,"_163":164,"_181":182},"content",{"_43":112,"_57":113,"_114":-5,"_115":116,"_117":118,"_119":-5,"_45":120,"_123":124,"_125":124,"_126":-5,"_127":128},"162087be-594f-460e-bbdd-a339ac2f10ad","Calor Latente - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","f2b62fc2-7079-40e7-a5b5-c4a9769b205d","user_id",{"_121":122},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_131":132,"_138":139,"_140":141,"_142":143,"_28":144},"provider",{"_43":133,"_134":135,"_136":137},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","bf8aacba-3de9-4b10-961c-47ada80dfe8c","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/levels.m3u8",[146],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":155,"_127":149,"_161":162},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9","2025-04-29T03:44:27.560682+00:00",{"_156":157,"_158":64,"_159":160},"childrenCount",10,"content_count","question_count",8575,"children",[],"video",{"_43":118,"_13":113,"_114":-5,"_165":166,"_167":168,"_28":-5,"_169":-5,"_131":168,"_170":171,"_142":-5,"_172":-5,"_173":-5,"_174":-5,"_175":-5,"_45":176,"_177":64,"_178":-5,"_104":179,"_123":180,"_125":180},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_121":122},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":183,"_127":149,"_161":184},{"_156":157,"_158":64,"_159":160},[],"similarQuestions",[187,217,237],{"_40":188,"_42":41,"_43":189,"_77":190,"_101":205,"_102":206,"_51":207},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[191,194,197,200,203],{"_43":192,"_81":82,"_83":193},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":195,"_81":87,"_83":196},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":198,"_81":91,"_83":199},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":201,"_81":95,"_83":202},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":188,"_81":99,"_83":204},"y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[208],{"_43":209,"_57":210,"_59":211,"_150":151,"_152":212,"_123":213,"_125":213,"_45":214,"_127":211},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_156":215,"_158":64,"_159":216},4,12302,{"_40":218,"_42":41,"_43":219,"_77":220,"_101":232,"_102":233,"_51":234},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[221,224,227,229],{"_43":222,"_81":82,"_83":223},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":225,"_81":87,"_83":226},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":218,"_81":91,"_83":228},"

Verdadeiro, falso, verdadeiro

",{"_43":230,"_81":95,"_83":231},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[258],{"_43":209,"_57":210,"_59":211,"_150":151,"_152":212,"_123":213,"_125":213,"_45":259,"_127":211},{"_156":215,"_158":64,"_159":216},[261,263,270,280,287,294,296,304,310,315,321,328],{"_43":209,"_57":210,"_59":211,"_150":151,"_152":212,"_123":213,"_125":213,"_45":262,"_127":211},{"_156":215,"_158":64,"_159":216},{"_43":264,"_57":58,"_59":60,"_150":151,"_152":265,"_123":154,"_125":154,"_45":266,"_127":269},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_156":267,"_158":64,"_159":268},2,11846,"termodinamica-3",{"_43":271,"_57":272,"_59":273,"_150":151,"_152":274,"_123":275,"_125":275,"_45":276,"_127":279},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_156":277,"_158":64,"_159":278},5,30614,"engenharia-mecatronica-1",{"_43":281,"_57":282,"_59":283,"_150":151,"_152":271,"_123":213,"_125":213,"_45":284,"_127":286},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_156":277,"_158":64,"_159":285},25741,"mecanica-3",{"_43":265,"_57":288,"_59":289,"_150":151,"_152":274,"_123":275,"_125":275,"_45":290,"_127":293},"Engenharia Mecânica","engenharia-mecanica",{"_156":291,"_158":64,"_159":292},11,36318,"engenharia-mecanica-2",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":295,"_127":149},{"_156":157,"_158":64,"_159":160},{"_43":297,"_57":298,"_59":299,"_150":151,"_152":-5,"_123":300,"_125":300,"_45":301,"_127":299},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_156":302,"_158":64,"_159":303},18,135489,{"_43":305,"_57":58,"_59":60,"_150":151,"_152":209,"_123":306,"_125":306,"_45":307,"_127":309},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_156":64,"_158":64,"_159":308},8597,"termodinamica-5",{"_43":212,"_57":311,"_59":312,"_150":151,"_152":274,"_123":275,"_125":275,"_45":313,"_127":314},"Engenharia de Petróleo","engenharia-de-petroleo",{"_156":277,"_158":64,"_159":216},"engenharia-de-petroleo-1",{"_43":153,"_57":316,"_59":317,"_150":151,"_152":297,"_123":275,"_125":275,"_45":318,"_127":320},"Física","fisica",{"_156":291,"_158":64,"_159":319},13777,"fisica-4",{"_43":274,"_57":322,"_59":323,"_150":151,"_152":-5,"_123":324,"_125":324,"_45":325,"_127":323},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_156":326,"_158":64,"_159":327},29,351586,{"_43":329,"_57":58,"_59":60,"_150":151,"_152":281,"_123":330,"_125":330,"_45":331,"_127":332},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_156":64,"_158":64,"_159":308},"termodinamica-4","tagsTree",[335,344],{"_43":297,"_57":298,"_59":299,"_150":151,"_152":-5,"_123":300,"_125":300,"_45":336,"_127":299,"_161":337},{"_156":302,"_158":64,"_159":303},[338],{"_43":153,"_57":316,"_59":317,"_150":151,"_152":297,"_123":275,"_125":275,"_45":339,"_127":320,"_161":340},{"_156":291,"_158":64,"_159":319},[341],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":342,"_127":149,"_161":343},{"_156":157,"_158":64,"_159":160},[],{"_43":274,"_57":322,"_59":323,"_150":151,"_152":-5,"_123":324,"_125":324,"_45":345,"_127":323,"_161":346},{"_156":326,"_158":64,"_159":327},[347,356,362],{"_43":271,"_57":272,"_59":273,"_150":151,"_152":274,"_123":275,"_125":275,"_45":348,"_127":279,"_161":349},{"_156":277,"_158":64,"_159":278},[350],{"_43":281,"_57":282,"_59":283,"_150":151,"_152":271,"_123":213,"_125":213,"_45":351,"_127":286,"_161":352},{"_156":277,"_158":64,"_159":285},[353],{"_43":329,"_57":58,"_59":60,"_150":151,"_152":281,"_123":330,"_125":330,"_45":354,"_127":332,"_161":355},{"_156":64,"_158":64,"_159":308},[],{"_43":265,"_57":288,"_59":289,"_150":151,"_152":274,"_123":275,"_125":275,"_45":357,"_127":293,"_161":358},{"_156":291,"_158":64,"_159":292},[359],{"_43":264,"_57":58,"_59":60,"_150":151,"_152":265,"_123":154,"_125":154,"_45":360,"_127":269,"_161":361},{"_156":267,"_158":64,"_159":268},[],{"_43":212,"_57":311,"_59":312,"_150":151,"_152":274,"_123":275,"_125":275,"_45":363,"_127":314,"_161":364},{"_156":277,"_158":64,"_159":216},[365],{"_43":209,"_57":210,"_59":211,"_150":151,"_152":212,"_123":213,"_125":213,"_45":366,"_127":211,"_161":367},{"_156":215,"_158":64,"_159":216},[368],{"_43":305,"_57":58,"_59":60,"_150":151,"_152":209,"_123":306,"_125":306,"_45":369,"_127":309,"_161":370},{"_156":64,"_158":64,"_159":308},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários