{"id":173,"date":"2024-10-21T00:17:14","date_gmt":"2024-10-20T21:17:14","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/caglart\/?p=173"},"modified":"2024-10-21T00:27:39","modified_gmt":"2024-10-20T21:27:39","slug":"maxwelle-boltzmanna-plancka-ve-einsteina-soralim-bakalim","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/caglart\/2024\/10\/21\/maxwelle-boltzmanna-plancka-ve-einsteina-soralim-bakalim\/","title":{"rendered":"MAXWELL\u2019e, BOLTZMANN\u2019a, PLANCK\u2019a ve E\u0130NSTE\u0130N&#8217;a SORALIM BAKALIM"},"content":{"rendered":"<p>Fizik &#8211; 5 &#8211;<\/p>\n<p>\u0130\u00e7erik: \u015eu an hava ka\u00e7 derece?<\/p>\n<p>G\u00fcnl\u00fck hayat\u0131m\u0131zda en \u00e7ok kulland\u0131\u011f\u0131m\u0131z malzeme olan suyun dondu\u011fu s\u0131cakl\u0131k 0 ve kaynad\u0131\u011f\u0131 s\u0131cakl\u0131k da 100 derece al\u0131narak Celcius (oC\udb40\uddbe) s\u0131cakl\u0131k basamaklar\u0131 tan\u0131mlan\u0131r. Termometreler (s\u0131cakl\u0131k\u00f6l\u00e7er) genellikle Celcius cinsinden g\u00f6sterir s\u0131cakl\u0131\u011f\u0131.<br \/>\nHer t\u00fcrl\u00fc devinimin, enerji aktar\u0131m\u0131n\u0131n, fiziksel etkile\u015fmelerin, atom ve molek\u00fcl sal\u0131n\u0131m ve \u0131\u015f\u0131malar\u0131n\u0131n dondu\u011fu s\u0131cakl\u0131\u011fa da mutlak s\u0131f\u0131r denir ve yakla\u015f\u0131k olarak -273.15 oC\udb40\uddbe de\u011ferindedir. Birimi de 1 oK kadard\u0131r. (*)<br \/>\nBaz\u0131 okuyucular i\u00e7in tekrarlama olmu\u015f olabilecek yukar\u0131daki bilgiye \u015fu nedenle yer verdik. Dikkatli okuyucu fark etmi\u015ftir ki, \u00f6nceki yaz\u0131lar\u0131m\u0131zda T simgesini s\u0131cakl\u0131k kar\u015f\u0131l\u0131\u011f\u0131 olarak kullanm\u0131\u015f ama tam olarak tan\u0131mlamam\u0131\u015f idik. O eksikli\u011fi burada gidermeyi deneyelim(?).<br \/>\nBoltzmann fakt\u00f6r\u00fc d\u00e2hil, Termodinamik\u2019in hemen her e\u015fitli\u011finde T simgesi mutlak s\u0131cakl\u0131k \u00f6l\u00e7\u00fct\u00fcd\u00fcr. Yani, yakla\u015f\u0131k olarak -273.15 oC\udb40\uddbe (Celcius) de\u011ferinde s\u0131f\u0131r olup birimi 1 oC\udb40\uddbe de\u011ferine e\u015fit olan ve Lord Kelvin\u2019in ad\u0131yla an\u0131lan (oK) bir birimi 1 oC\udb40\uddbe de\u011ferine e\u015fit olan bir s\u0131cakl\u0131k \u00f6l\u00e7\u00fcm sistemidir mutlak s\u0131cakl\u0131k \u00f6l\u00e7\u00fcm sistemi ve Termodinamik\u2019te yo\u011funlukla kullan\u0131l\u0131r.<br \/>\n\u00d6nemli baz\u0131 \u00f6rnekler \u015f\u00f6ylecedir:<br \/>\n1. \u00d6rnek: Maxwell-Boltzmann \u0130statisti\u011fi<\/p>\n<p><a href=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/MBstat.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-168\" src=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/MBstat-300x135.png\" alt=\"\" width=\"300\" height=\"135\" srcset=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/MBstat-300x135.png 300w, https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/MBstat.png 605w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>2. \u00d6rnek: Maxwell-Boltzmann Da\u011f\u0131l\u0131m\u0131<\/p>\n<p><a href=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/MBdagil.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-169\" src=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/MBdagil-300x231.png\" alt=\"\" width=\"300\" height=\"231\" srcset=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/MBdagil-300x231.png 300w, https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/MBdagil.png 585w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>3. \u00d6rnek: Planck Karacisim I\u015f\u0131ma \u0130zgesi (\u2018spectrum\u2019)<\/p>\n<p><a href=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/spectrum.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-172\" src=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/spectrum.png\" alt=\"\" width=\"188\" height=\"72\" \/><\/a><\/p>\n<p>T\u00fcm simgeler \u00f6nceki gibi.<br \/>\n4. \u00d6rnek: Einstein Is\u0131 S\u0131\u011fas\u0131<\/p>\n<p><a href=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/Esolid.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-170\" src=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/Esolid.png\" alt=\"\" width=\"279\" height=\"80\" \/><\/a><\/p>\n<p>\u00dcstteki \u00f6rneklerde ve Termodinamik\u2019in pek\u00e7ok denkleminde g\u00f6r\u00fclebilece\u011fi gibi enerji b\u00f6l\u00fc s\u0131cakl\u0131\u011f\u0131n Boltzmann sabitiyle \u00e7arp\u0131m\u0131 olan kBT (kT) ifadesi boyutsuzdur yani salt say\u0131d\u0131r ve dolay\u0131s\u0131 ile birimsizdir.<br \/>\nBuraya dek her \u015fey iyi ho\u015f da (enerji\/ k_BT) ifadesi son derece ciddi baz\u0131 sorunlar i\u00e7ermekte (ama bunlardan derslerde ve ders kitaplar\u0131nda hemen hi\u00e7 s\u00f6z edilmemektedir).<br \/>\nBak\u0131n\u0131z, enerji terimi \u00f6rne\u011fin \u00d6rnek 2\u2019de k\u00fctle ve h\u0131z cinsinden \u00d6rnek 3\u2019te de frekans cinsinden gayet hassal\u0131kl\u0131 (\u2018precise, accurate\u2019) olarak tan\u0131mlanabilir. Ama T\u2019yi, \u00f6rne\u011fin bir karacisim olan bir f\u0131r\u0131n\u0131n veya bir bardak suyun hatta bizzat bu sat\u0131rlar\u0131 okumakta olan sizin s\u0131cakl\u0131\u011f\u0131n\u0131z\u0131 \u00f6l\u00e7mek m\u00fcmk\u00fcn m\u00fcd\u00fcr acaba?<br \/>\n\u201cA sistemi ile B sistemi ve A sistemi ile C sistemi ayn\u0131 s\u0131cakl\u0131kta ise, B sistemi ile C sistemi de ayn\u0131 s\u0131cakl\u0131ktad\u0131r.\u201d denir ya hani. Ama herhangi bir s\u0131cakl\u0131\u011f\u0131n nas\u0131l \u00f6l\u00e7\u00fcle_B\u0130LE_ce\u011fi s\u00f6ylenmez, bir t\u00fcrl\u00fc!<br \/>\nEn basitinden alttaki gibi bir bardak suyunuz ve bir tane de s\u0131cakl\u0131k\u00f6l\u00e7eriniz olsun.<\/p>\n<p><a href=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/Resim-Thermo-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-171\" src=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/Resim-Thermo-1-300x174.png\" alt=\"\" width=\"300\" height=\"174\" srcset=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/Resim-Thermo-1-300x174.png 300w, https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/Resim-Thermo-1-768x445.png 768w, https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/Resim-Thermo-1-624x361.png 624w, https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/10\/Resim-Thermo-1.png 843w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>\u00d6nce X okuyan s\u0131cakl\u0131k\u00f6l\u00e7eri suyun i\u00e7ine soktuk ve bir s\u00fcre bekledikten sonra bakt\u0131k ki, Y okuyor.<br \/>\n\u015eimdi de Maxwell\u2019e, Boltzmann\u2019a, Planck\u2019a ve Einstein soral\u0131m; suyun s\u0131cakl\u0131\u011f\u0131 Y mi idi \u00f6nce ve hatta Y midir sonras\u0131nda?<br \/>\nYine soral\u0131m; Is\u0131\u00f6l\u00e7eri i\u00e7ine sokmazdan evvelki s\u0131cakl\u0131\u011f\u0131 ne idi acep ayn\u0131 suyun?<br \/>\nBenzer ba\u015fka sorular\u0131m\u0131z da var da onlar\u0131 sona saklay\u0131p Maxwell, Boltzmann, Planck ve Einstein yerine yan\u0131tlayal\u0131m:<br \/>\n\u0130lkin; \u0131s\u0131\u00f6l\u00e7eri i\u00e7ine sokmazdan evvelki s\u0131cakl\u0131\u011f\u0131n\u0131 asla bilemeyiz suyun! Totoloji kadar yal\u0131n ve a\u00e7\u0131k bir yan\u0131t, de\u011fil mi? \u00d6l\u00e7meden nas\u0131l bilebiliriz ki?<br \/>\n\u201cEn \u00e7o\u011fu; bilebilece\u011fimiz, \u0131s\u0131\u00f6l\u00e7eri i\u00e7ine soktuktan sonraki s\u0131cakl\u0131\u011f\u0131d\u0131r suyun.\u201d Bu s\u00f6ylem hakk\u0131nda da emin olamay\u0131z; \u00e7\u00fcnk\u00fc \u0131s\u0131\u00f6l\u00e7er bize bizatihi (arac\u0131s\u0131z, kendisi olarak) kendi s\u0131cakl\u0131\u011f\u0131n\u0131 s\u00f6ylemektedir ister su d\u0131\u015f\u0131nda olsun ister su i\u00e7inde. Oysa suyun s\u0131cakl\u0131\u011f\u0131n\u0131 bizatihi de\u011fil, \u0131s\u0131\u00f6l\u00e7er arac\u0131l\u0131\u011f\u0131 ile ve dolayl\u0131 olarak saptamaya \u00e7al\u0131\u015fmaktay\u0131z. Bunun m\u00fcmk\u00fcn olup olmayaca\u011f\u0131n\u0131 anlamaya \u00e7al\u0131\u015fmaktay\u0131z.<br \/>\n\u0130kincileyin, d\u0131\u015far\u0131daki ve s\u0131cakl\u0131\u011f\u0131 o an X olan \u0131s\u0131\u00f6l\u00e7erin demek ki bir de \u0131s\u0131s\u0131 var (\u0131s\u0131 s\u0131\u011fas\u0131 ile k\u00fctle ve s\u0131cakl\u0131\u011f\u0131 cinsinden tan\u0131mlanan) ve bu s\u0131cakl\u0131k\u00f6l\u00e7er suya sokuldu\u011fu zaman \u0131s\u0131lar toplan\u0131r ve yeniden su ve \u0131s\u0131\u00f6l\u00e7erin k\u00fctleleri ve \u0131s\u0131 s\u0131\u011falar\u0131na ba\u011fl\u0131 olarak ve ayn\u0131 s\u0131cakl\u0131kta olacak \u015fekilde payla\u015f\u0131l\u0131r, \u00fcle\u015filir. Bu demektir ki, s\u0131cakl\u0131k i\u00e7ine sokulduktan sonra suyun s\u0131cakl\u0131\u011f\u0131 de\u011fi\u015fir.<br \/>\nFizik deyimiyle s\u00f6yleyecek olursak; her \u00f6l\u00e7\u00fcm, \u00fcst\u00fcnde \u00f6l\u00e7\u00fcm yap\u0131lan sistemde de\u011fi\u015fikli\u011fe yol a\u00e7ar. W. Heisenberg\u2019den beridir bu ilke, Belirsizlik \u0130lkesi olarak bilinir. \u00d6rne\u011fin, bir elektronun yerini saptamak, konumunu \u00f6l\u00e7mek i\u00e7in \u00fcst\u00fcne \u0131\u015f\u0131k fotonu yollad\u0131\u011f\u0131m\u0131zda, foton elektronu etkileyip konum de\u011fi\u015fikli\u011fine sebep olur. Bu etkilemeyi en aza indirmek i\u00e7in fotonun enerjisini ve momentumunu azaltmak amac\u0131yla d\u00fc\u015f\u00fck frekansl\u0131 uzun dalga boylu foton yollasak da, bu kez konum \u00f6l\u00e7\u00fcm\u00fcndeki belirsizlik hayli artm\u0131\u015f olur \u00e7\u00fcnk\u00fc konumdaki belirsizlik dalgan\u0131n dalga boyu ile do\u011fru orant\u0131l\u0131d\u0131r. Elektron, o fotonun dalga boyu uzunlu\u011fu kadar bir uzay par\u00e7as\u0131n\u0131n herhangi bir yerinde bulunmu\u015f olabilir. Yok e\u011fer, konum \u00f6l\u00e7\u00fcm\u00fcndeki hassal\u0131\u011f\u0131 art\u0131rmak i\u00e7in k\u0131sa dalga boylu foton kullansak, bu kez de enerji ve momentum artm\u0131\u015f olaca\u011f\u0131 i\u00e7in elektron h\u0131zla konum de\u011fi\u015ftirecektir. Yani, \u00f6l\u00e7\u00fclm\u00fc\u015f olan ilk konumundan uzakla\u015fm\u0131\u015f olacakt\u0131r.<br \/>\nBelirsizlik hayat\u0131n ba\u015fka alanlar\u0131nda da mevcut. Bu s\u00f6ze inanmayan, bu gece nas\u0131l uyuyakald\u0131\u011f\u0131n\u0131 g\u00f6zlemeye, anlamaya \u00e7al\u0131\u015fs\u0131n bakal\u0131m.<br \/>\nB\u00fct\u00fcn bunlar yetmezmi\u015f gibi \u015f\u00f6yle de bir \u00f6zelli\u011fi var s\u0131cakl\u0131k \u00f6l\u00e7\u00fcmlerinin. Bundan sonra, s\u00f6z\u00fcm ona anlam\u0131nda s\u0131cakl\u0131k \u00f6l\u00e7\u00fcmleri s\u00f6zc\u00fckleri t\u0131rnak (\u2018\u2026\u2019) i\u00e7ine al\u0131nm\u0131\u015f olsa yanl\u0131\u015f olmaz.<br \/>\nIs\u0131\u00f6l\u00e7erin \u00f6l\u00e7t\u00fc\u011f\u00fc s\u0131cakl\u0131\u011f\u0131n (X ve Y) kendi s\u0131cakl\u0131\u011f\u0131 oldu\u011fundan s\u00f6z etmi\u015f idik. Bu s\u0131cakl\u0131klar\u0131n, \u0131s\u0131\u00f6l\u00e7ere o an dokunmakta olan hava ve su miktar\u0131n\u0131n da s\u0131cakl\u0131\u011f\u0131 oldu\u011fu a\u00e7\u0131kt\u0131r.<br \/>\nPeki ama, bardak i\u00e7indeki suyun di\u011fer taraflar\u0131ndaki suyun veya karacisim f\u0131r\u0131n\u0131n di\u011fer taraflar\u0131ndaki f\u0131r\u0131n s\u0131cakl\u0131\u011f\u0131n\u0131 \u00f6l\u00e7mek i\u00e7in \u0131s\u0131 \u00f6l\u00e7erimizi de dola\u015ft\u0131rmak gerekli de\u011fil midir? Ayn\u0131 \u015fekilde, bir insan\u0131n\u0131n s\u0131cakl\u0131\u011f\u0131 nas\u0131l tan\u0131mlan\u0131r ve nas\u0131l \u00f6l\u00e7\u00fcl\u00fcr? Ayr\u0131ca, bu dola\u015ft\u0131rmalar s\u0131ras\u0131nda suyun veya f\u0131r\u0131n\u0131n s\u0131cakl\u0131\u011f\u0131 s\u00fcrekli olarak de\u011fi\u015fmeyecek midir? Dahas\u0131, kat\u0131 i\u00e7indeki minik hacimler i\u00e7indeki yerel s\u0131cakl\u0131\u011f\u0131 nas\u0131l \u00f6l\u00e7ece\u011fiz de Planck\u2019\u0131n Karacisim I\u015f\u0131ma izgesi\u2019nden ve Einstein\u2019\u0131n Is\u0131 S\u0131\u011fas\u0131\u2019ndan emin yani bilimsel kesinli\u011fe sahip olaca\u011f\u0131z?<br \/>\nMaxwell\u2019e, Boltzmann\u2019a, Planck\u2019a ve Einstein&#8217;a soral\u0131m bakal\u0131m ne derler?<br \/>\nS\u0131cakl\u0131\u011f\u0131 tan\u0131mlamayan, s\u0131cakl\u0131\u011f\u0131 nas\u0131l \u00f6l\u00e7e_B\u0130LE_ce\u011fimizi a\u00e7\u0131klamayan Maxwell, Boltzmann, Planck ve Einstein zaten bir de evrende var olmayan \u2018sonsuz\u2019 b\u00fcy\u00fck enerji kullanmam\u0131\u015flar m\u0131yd\u0131 form\u00fcllerinde?<br \/>\nS\u0131cakl\u0131\u011f\u0131 tan\u0131mlamayan, s\u0131cakl\u0131\u011f\u0131 nas\u0131l \u00f6l\u00e7e_B\u0130LE_ce\u011fimizi a\u00e7\u0131klamayan fizik kitab\u0131 yazarlar\u0131na, internetteki sitelerinde yaz\u0131 yaz\u0131veren bilgi\u00e7lere de soral\u0131m bakal\u0131m bir \u015fey diyecekler mi?<br \/>\nBir de \u015funu soral\u0131m:<br \/>\nS\u0131cakl\u0131\u011f\u0131 tan\u0131mlamayan, s\u0131cakl\u0131\u011f\u0131 nas\u0131l \u00f6l\u00e7e_B\u0130LE_ce\u011fimizi a\u00e7\u0131klamayan \u00f6\u011fretmenlerin de hocalar\u0131n da s\u0131navda s\u0131cakl\u0131k ile ilgili bir soruyu tam yan\u0131tla_YA_mad\u0131\u011f\u0131 i\u00e7in \u00f6\u011frencisinden not k\u0131rmas\u0131 reva m\u0131d\u0131r?<br \/>\nNe dersiniz?<\/p>\n<p>(*) Mutlak s\u0131cakl\u0131\u011f\u0131n ne kadar da yak\u0131nda ya\u015f\u0131yoruz, de\u011fil mi? Bu sat\u0131rlar\u0131n yazan\u0131, arada bir bo\u015f kald\u0131\u011f\u0131nda falan, daha y\u00fcksek, \u00e7ok daha y\u00fcksek s\u0131cakl\u0131klarda nas\u0131l canl\u0131lar\u0131n olu\u015fabilece\u011fini, dolay\u0131s\u0131 ile de G\u00fcne\u015f ve di\u011fer y\u0131ld\u0131zlar i\u00e7inde canl\u0131lar olabilece\u011fini hayal eder baz\u0131 baz\u0131.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fizik &#8211; 5 &#8211; \u0130\u00e7erik: \u015eu an hava ka\u00e7 derece? G\u00fcnl\u00fck hayat\u0131m\u0131zda en \u00e7ok kulland\u0131\u011f\u0131m\u0131z malzeme olan suyun dondu\u011fu s\u0131cakl\u0131k 0 ve kaynad\u0131\u011f\u0131 s\u0131cakl\u0131k da 100 derece al\u0131narak Celcius (oC\udb40\uddbe) s\u0131cakl\u0131k basamaklar\u0131 tan\u0131mlan\u0131r. Termometreler (s\u0131cakl\u0131k\u00f6l\u00e7er) genellikle Celcius cinsinden g\u00f6sterir s\u0131cakl\u0131\u011f\u0131. Her t\u00fcrl\u00fc devinimin, enerji aktar\u0131m\u0131n\u0131n, fiziksel etkile\u015fmelerin, atom ve molek\u00fcl sal\u0131n\u0131m ve \u0131\u015f\u0131malar\u0131n\u0131n dondu\u011fu s\u0131cakl\u0131\u011fa [&hellip;]<\/p>\n","protected":false},"author":1425,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1],"tags":[],"class_list":["post-173","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/173","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/users\/1425"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/comments?post=173"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/173\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}