The Kinetic Theory of Gases PDF

‫)‪(296‬‬ ‫ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ ‪:‬ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ‬ ‫ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫)‪(296‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version ht...

‫)‪(296‬‬ ‫ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ ‪:‬ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ‬ ‫ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫)‪(296‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(297‬‬ ‫ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ ‪:‬ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫ﻱ‬ ‫ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ‬ ‫ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫ﺍﳊﺮﻛﺔ ﺍﻟﱪﺍﻭﻧﻴﺔ‬ ‫‪Brownian Motion‬‬ ‫إن إﺣﺪى ﻣﻈﺎھﺮ اﻟﺴﻠﻮك اﻟﻤﻼﺣﻆ ﻟﻐ ﺎز‪ ،‬اﻟﺘ ﻲ ﺗ ﺰود ﺑ ﺄﻗﻮى ﻣﻌﻠﻮﻣ ﺔ ﺑﺎﻟﻨ ﺴﺒﺔ ﻟﻄﺒﯿﻌ ﺔ اﻟﻐ ﺎزات‬ ‫ھﻲ ﺗﻠﻚ اﻟﻈﺎھﺮة اﻟﻤﻌﺮوﻓﺔ ﺑﺎﻟﺤﺮﻛﺔ اﻟﺒﺮاوﻧﯿﺔ‪.‬وھﺬه اﻟﺤﺮﻛﺔ اﻟﺘﻲ ﻟﻮﺣﻈﺖ ﻷول ﻣ ﺮة ﺑﻮاﺳ ﻄﺔ‬ ‫ﻋﺎﻟﻢ اﻟﻨﺒﺎت اﻷﺳﻜﺘﻠﻨﺪي‪ ،‬روﺑﺮت ﺑﺮاون ﻓﻲ ﻋﺎم )‪ (1827‬ھﻲ ﻋﺒﺎرة ﻋﻦ ﺣﺮﻛﺔ ﻣﺘﻌﺮﺟﺔ ﻏﯿﺮ‬ ‫ﻣﻨﺘﻈﻤ ﺔ ﻟﺠ ﺴﯿﻤﺎت دﻗﯿﻘ ﺔ ﻟﻠﻐﺎﯾ ﺔ ﻋﻨ ﺪﻣﺎ ﺗﻜ ﻮن ﻣﻌﻠﻘ ﺔ ﻓ ﻲ ﺳ ﺎﺋﻞ أو ﻓ ﻲ ﻏ ﺎز‪.‬وﯾﻤﻜ ﻦ ﻣﻼﺣﻈ ﺔ‬ ‫اﻟﺤﺮﻛﺔ اﻟﺒﺮواﻧﯿ ﺔ ﺑﺘﻌ ﺪﯾﻞ ﺑ ﺆرة ﻣﯿﻜﺮوﺳ ﻜﻮب وﻓﻘ ﺎً ﻟﻤ ﺪى اﻟﻌ ﯿﻦ )‪ (focusing‬ﻋﻠ ﻰ ﺟ ﺴﯿﻤﺎت‬ ‫دﺧﺎن ﻣﻀﺎءة ﻣﻦ اﻟﺠﺎﻧﺐ‪.‬وﻻ ﯾﺮﺳﺐ اﻟﺠﺴﯿﻢ اﻟﻰ ﻗﺎع إﻧﺎﺋﮫ اﻟﺤ ﺎوي‪ ،‬وﻟﻜﻨ ﮫ ﯾﺘﺤ ﺮك ﺑﺎﺳ ﺘﻤﺮار‬ ‫ﺟﯿﺌﺔ وذھﺎﺑﺎً‪ ،‬وﻻ ﯾﺒﺪي أي إﺷﺎرة ﻟﺒﻠﻮﻏﮫ ﺣﺎﻟﺔ اﻹﺳﺘﻘﺮار‪.‬وﻛﻠﻤ ﺎ ﻛ ﺎن اﻟﺠ ﺴﯿﻢ اﻟﻤﻼﺣ ﻆ ﻣﻌﻠﻘ ﺎً‪،‬‬ ‫أﺻﻐﺮ‪ ،‬ﻛﻠﻤﺎ ﻛﺎﻧﺖ ﺗﻠﻚ اﻟﺤﺎﻟﺔ اﻟﺪاﺋﻤﺔ ﻣﻦ اﻟﺤﺮﻛﺔ ﻏﯿﺮ اﻟﻤﻨﺘﻈﻤﺔ أﻛﺜﺮ ﻋﻨﻔﺎً‪.‬وﻛﻠﻤﺎ ﻛﺎﻧﺖ درﺟ ﺔ‬ ‫ﺣﺮارة اﻟﻤﺎﺋﻊ أﻋﻠﻰ‪ ،‬ﻛﻠﻤﺎ ﻛﺎﻧﺖ ﺣﺮﻛﺔ اﻟﺠﺴﯿﻢ اﻟﻤﻌﻠﻖ أﻛﺜﺮ ﻗﻮة‪.‬‬ ‫وﯾﻨﺎﻗﺾ اﻟﺤﺮﻛﺔ اﻟﺒﺮاوﻧﯿﺔ‪ ،‬اﻟﻔﻜﺮة ﻋﻦ اﻟﻤﺎدة ﺑﺄﻧﮭﺎ ﺣﺎﻟﺔ ﺳﺎﻛﻨﺔ‪ ،‬وﺗﻘﺘﺮح أن ﺟﺰﯾﺌﺎت اﻟﻤ ﺎدة ﺗﻜ ﻮن‬ ‫اﻟ ﻰ ﺣ ﺪ ﻣ ﺎ ﻣﺘﺤﺮﻛ ﺔ ﺑﺎﺳ ﺘﻤﺮار‪.‬وﯾﺒ ﺪو أن ﺟ ﺴﯿﻢ اﻟ ﺪﺧﺎن ﯾ ﺼﻄﺪم ﺑﺠﺰﯾﺌ ﺎت اﻟﮭ ﻮاء‪ ،‬وﺑ ﺬﻟﻚ ﻓ ﺈن‬ ‫ﺣﺮﻛﺔ ﺟ ﺴﯿﻢ اﻟﮭ ﻮاء ﺗﻌﻜ ﺲ ﺑﻄﺮﯾ ﻖ ﻏﯿ ﺮ ﻣﺒﺎﺷ ﺮ اﻟﺤﺮﻛ ﺔ ﺗﺤ ﺖ اﻟﻤﯿﻜﺮوﺳ ﻜﻮﺑﯿﺔ ﻟﺠﺰﯾﺌ ﺎت اﻟﻤ ﺎدة‬ ‫ﻏﯿﺮ اﻟﻤﺮﺋﯿﺔ‪.‬وﺗﻮﺟﺪ ھﻨﺎ ﺣﯿﻨﺌﺬ دﻋﺎﻣﺔ ﻗﻮﯾﺔ ﻟﻼﻗﺘﺮاح ﺑ ﺄن اﻟﻐ ﺎزات ﺗﺘﻜ ﻮن ﻣ ﻦ أﺟ ﺰاء ﺿ ﺌﯿﻠﺔ ﻣ ﻦ‬ ‫ﻣﺎدة ‪ ،‬واﻟﺘﻲ ﺗﻜﻮن داﺋﻤﺎً ﻓﻲ ﺣﺮﻛﺔ‪.‬‬ ‫ﺷﻜﻞ ‪٩٢‬‬ ‫)‪(297‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(298‬‬ ‫ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ ‪:‬ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫‪Molecular Kinetic Theory of Gases‬‬ ‫ﺍﻟﻔﺮﻭﺽ ﻭﳕﻮﺫﺝ ﺍﻟﻐﺎﺯ ﺍﳌﺜﺎﱄ‬ ‫‪hypothesis and Ideal Gas Model‬‬ ‫ﺗﺴﺎﻋﺪ ﻗﻮاﻧﯿﻦ اﻟﻐﺎزات ﻓﻲ اﻟﺘﻨﺒﺆ ﺑﺴﻠﻮك اﻟﻐﺎزات وﻟﻜﻨﮭﺎ ﻻ ﺗﻔﺴﺮ ﻋﻠﻰ اﻟﻤﺴﺘﻮى اﻟﺠﺰﯾﺌﻲ‬ ‫اﻟﺘﻐﯿﺮات ﻓﻲ اﻟﺤﺠﻢ أو اﻟﻀﻐﻂ أو درﺟﺔ اﻟﺤﺮارة اﻟﺘﻲ ﺗﺤﺪث ﻋﻨﺪ ﺗﻐﯿﺮ اﻟﻈﺮوف‪.‬ﻓﻤﺜﻼً‪،‬‬ ‫ﻟﻤﺎذا ﯾﺘﻤﺪد ﺣﺠﻢ اﻟﻐﺎز ﻋﻨﺪ اﻟﺘﺴﺨﯿﻦ؟ ﻟﻘﺪ اﺳﺘﻄﺎع ﺑﻌﺾ اﻟﻔﯿﺰﯾﺎﺋﯿﯿﻦ ﻣﻦ أﻣﺜﺎل ﺑﻮﻟﺘﺰﻣﺎن‬ ‫)‪ (Boltzmann‬وﻣﺎﻛﺴﻮﯾﻞ )‪ (Maxwell‬أن ﯾﻔﺴﺮوا اﻟﺨﻮاص اﻟﻔﯿﺰﯾﺎﺋﯿﺔ ﻟﻠﻐﺎزات‬ ‫ﺑﻮاﺳﻄﺔ ﺣﺮﻛﺔ ﺟﺰﯾﺌﺎﺗﮭﺎ اﻟﻤﻔﺮدة‪.‬ﻟﻘﺪ وﺿﻊ ﻋﻤﻞ ﺑﻮﻟﺘﺰﻣﺎن وﻣﺎﻛﺴﻮﯾﻞ اﻷﺳﺎس ﻟﻨﻈﺮﯾﺔ‬ ‫اﻟﺤﺮﻛﺔ اﻟﺠﺰﯾﺌﯿﺔ ﻟﻐﺎزات‪.‬‬ ‫ﻟﻘﺪ ﺑﯿﻨﺖ اﻟﻘﻮاﻧﯿﻦ اﻟﺘﺠﺮﯾﺒﯿﺔ اﻟﺴﺎﺑﻘﺔ ﻟﻠﻐﺎزات ﻗﺎﺑﻠﯿﺔ اﻟﻐﺎزات ﻟﻺﻧﻀﻐﺎط‪ ،‬ﻗﺎﺑﻠﯿﺔ اﻟﻐﺎزات‬ ‫ﻟﻺﻧﺘﺸﺎر‪ ،‬ﺗﻨﺎﺳﺐ ﺣﺠﻢ اﻟﻐﺎز ﻋﻜﺴﯿﺎً ﻣﻊ ﺿﻐﻄﮫ وﻃﺮدﯾﺎً ﻣﻊ درﺟﺔ ﺣﺮارﺗﮫ اﻟﻤﻄﻠﻘﺔ‪.‬‬ ‫واﻟﻘﻮاﻧﯿﻦ اﻟﺴﺎﺑﻘﺔ ﻟﻢ ﺗﺼﻞ ﻟﺘﻔﺴﯿﺮ ﻣﻨﺎﺳﺐ ﻟﺘﻠﻚ اﻟﺨﻮاص‪ ،‬وﻟﮭﺬا ﻋﻤﻞ اﻟﻌﻠﻤﺎء ﻋﻠﻰ إﯾﺠﺎد‬ ‫ﺗﻔﺴﯿﺮ ھﺬه اﻟﺨﻮاص ﻓﻜﺎﻧﺖ ﺟﮭﻮد ھﺆﻻء اﻟﻌﻠﻤﺎء ﻓﻲ ﻧﻈﺮﯾﺔ ﺳﻤﯿﺖ ﺑﺎﻟﻨﻈﺮﯾﺔ اﻟﺤﺮﻛﯿﺔ‬ ‫اﻟﺠﺰﯾﺌﯿﺔ ﻟﻠﻐﺎزات وھﻲ ﺗﺘﺄﻟﻒ ﻣﻦ ﻓﺮوض ﺗﻔﺴﺮ ﺳﻠﻮك اﻟﻐﺎزات اﻟﻤﺜﺎﻟﯿﺔ اﻟﺘﻲ ﺗﺨﻀﻊ‬ ‫ﻟﻘﺎﻧﻮن اﻟﻐﺎز اﻟﻤﺜﺎﻟﻲ‪.‬‬ ‫وﻣﻦ اﻟﻤﻌﻠﻮم أن ﺟﺰﯾﺌﺎت اﻟﻐﺎزات ﻓﻲ ﺣﺮﻛﺔ ﻣﺴﺘﻤﺮة‪ ،‬ﻷﺟﻞ ذﻟﻚ ﻓﻼ ﺑﺪ أن ﺟﺰﯾﺌﺎت‬ ‫اﻟﻐﺎزات ﺗﻤﺘﻠﻚ ﻃﺎﻗﺔ ﺣﺮﻛﯿﺔ‪ ،‬وﺑﮭﺬا ﻓﺈن اﻟﻨﻈﺮﯾﺔ اﻟﺤﺮﻛﯿﺔ ﺗﺤﺎول أن ﺗﻮﺟﺪ ﻋﻼﻗﺔ ﺑﯿﻦ‬ ‫اﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻠﻐﺎزات ودرﺟﺔ اﻟﺤﺮارة‪.‬‬ ‫وﺗﻌﺮف اﻟﻨﻈﺮﯾﺔ اﻟﺨﺎﺻﺔ ﺑﺎﻟﺠﺰيء اﻟﻤﺘﺤﺮك‪ ،‬ﺑﻨﻈﺮﯾﺔ اﻟﺤﺮﻛﺔ ﻟﻠﻤﺎدة واﻓﺘﺮاﺿﺎھﺎ‬ ‫اﻷﺳﺎﺳﯿﺎن ھﻤﺎ أن ﺟﺰﯾﺌﺎت اﻟﻤﺎدة ﺗﻜﻮن ﻓﻲ ﺣﺮﻛﺔ‪ ،‬وأن اﻟﺤﺮارة ﻋﺒﺎرة ﻋﻦ إﻇﮭﺎر ﻟﮭﺬه‬ ‫اﻟﺤﺮﻛﺔ‪.‬وﻣﺜﻞ أي ﻧﻈﺮﯾﺔ ﻓﺈن ﻧﻈﺮﯾﺔ اﻟﺤﺮﻛﺔ ﺗﺼﻮر ﻧﻤﻮذﺟﺎً ﻣﻘﺘﺮﺣﺎً ﻟﺘﻔﺴﯿﺮ ﻣﺠﻤﻮﻋﺔ ﻣﻦ‬ ‫)‪(298‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(299‬‬ ‫اﻟﺤﻘﺎﺋﻖ اﻟﻤﺸﺎھﺪة‪.‬وﻟﻜﻲ ﯾﻜﻮن اﻟﻨﻤﻮذج ﻣﻔﯿﺪاً‪ ،‬ﻓﺈﻧﮫ ﯾﺠﺐ ﺗﻘﺪﯾﻢ ﺑﻌﻀﺎً ﻣﻦ اﻹﻓﺘﺮاﺿﺎت‬ ‫اﻟﺘﻮﺿﯿﺤﯿﺔ ﺑﺎﻟﻨﺴﺒﺔ ﻟﺨﺼﺎﺋﺼﮭﺎ‪.‬وﯾﻤﻜﻦ اﻟﺘﺤﻘﻖ ﻣﻦ ﺻﺤﺔ ﻛﻞ ﻓﺮض وإﻣﻜﺎﻧﯿﺔ اﻻﻋﺘﻤﺎد‬ ‫ﻋﻠﻰ اﻟﻨﻈﺮﯾﺔ ﻛﻜﻞ‪ ،‬ﻣﻦ ﻛﯿﻔﯿﺔ ﺗﻔﺴﯿﺮ اﻟﺤﻘﺎﺋﻖ ﺑﺸﻜﻞ ﻣﺮض‪.‬‬ ‫وﻓﻲ ﻋﺎم )‪ (1857‬ﻧﺸﺮ رودوﻟﻒ ﻛﻼوزﯾﻮس ‪(1822 – 1888) Rudolf Clausius‬‬ ‫ﻧﻈﺮﯾﺔ ﺣﺎوﻟﺖ أن ﺗﺸﺮح اﻟﻤﻼﺣﻈﺎت اﻟﺘﺠﺮﯾﺒﯿﺔ )‪ (experimental observations‬اﻟﺘﻲ‬ ‫ﻟﺨﺼﺖ ﻗﻮاﻧﯿﻦ ‪ :‬ﺑﻮﯾﻞ‪ ،‬ﺗﺸﺎرﻟﺰ‪ ،‬داﻟﺘﻮن وأﻓﻮﺟﺎدرو‪.‬‬ ‫ﺍﻓﱰﺿﺖ ﺍﻟﻨﻈﺮﻳـﺔ ﺍﳊﺮﻛﻴـﺔ ﻟﻠﻐـﺎﺯﺍﺕ ﺍﳌﺜﺎﻟﻴـﺔ ﺍﻟﻔـﺮﻭﺽ ﺍﻟﺘﺎﻟﻴـﺔ ﻟﺘﻔـﺴﲑ ﺳـﻠﻮﻙ ﺍﻟﻐـﺎﺯﺍﺕ‬ ‫ﻭﲢﺪﻳﺪ ﺻﻔﺎﺗﻬﺎ ‪:‬‬ ‫‪ (١‬ﯾﺘﺄﻟﻒ اﻟﻐﺎز ﻣﻦ ﺟﺴﯿﻤﺎت دﻗﯿﻘﺔ )دﻗﺎﺋﻖ( ﻛﺮوﯾﺔ ﺗﻌﺮف ﺑﺎﻟﺠﺰﯾﺌﺎت أو اﻟﺬرات‬ ‫) )‪ (a gas consists of small particles (atoms or molecules‬ﻟﻜﻞ ﻣﻨﮭﺎ ﻛﺘﻠﺔ‬ ‫ﻣﻌﯿﻨﺔ وﺣﺠﻢ ﻣﻌﯿﻦ ﻻ ﯾﺨﺘﻠﻔﺎن ﻟﻠﻐﺎز اﻟﻮاﺣﺪ وﻟﻜﻦ ﯾﺨﺘﻠﻔﺎن ﻣﻦ ﻏﺎز ﻵﺧﺮ‪.‬‬ ‫‪ (٢‬ﺗﺘﺒﺎﻋﺪ اﻟﺠﺰﯾﺌﺎت ﻋﻦ ﺑﻌﻀﮭﺎ ﺑﻤﺴﺎﻓﺎت ﻛﺒﯿﺮة ﺟﺪاً إذا ﻣﺎ ﻗﻮرﻧﺖ ﺑﺤﺠﻮم اﻟﺠﺰﯾﺌﺎت‬ ‫)ﺑﺤﯿﺚ أن ﺣﺠﻢ اﻟﺠﺰﯾﺌﺎت اﻟﻔﻌﻠﻲ ﯾﻜﻮن ﻛﻤﯿﺔ ﻣﮭﻤﻠﺔ ﺑﺎﻟﻤﻘﺎرﻧﺔ اﻟﻰ اﻟﻔﺮاغ اﻟﻤﻮﺟﻮد ﺑﯿﻦ‬ ‫اﻟﺠﺰﯾﺌﺎت )اﻟﺤﯿﺰ اﻟﻤﻮﺟﻮد ﺑﯿﻦ اﻟﺠﺰﯾﺌﺎت أي أن ‪ ،(V = 0‬وﻟﺬﻟﻚ ﻓﺈن أي ﺿﻐﻂ ﻋﻠﻰ اﻟﻐﺎز‬ ‫إﻧﻤﺎ ﯾﺠﻌﻞ اﻟﺠﺰﯾﺌﺎت ﺗﺘﻘﺎرب ﻣﻦ ﺑﻌﻀﮭﺎ اﻟﺒﻌﺾ أي ﯾﻘﻞ ﺣﺠﻤﮭﺎ‪.‬ﻛﻤﺎ أن اﻟﻤﺴﺎﻓﺎت ﺑﯿﻦ‬ ‫اﻟﺠﺰﯾﺌﺎت ﻓﻲ ﺣﺎﻟﺔ اﻟﻐﺎزات أﻛﺒﺮ ﺑﻜﺜﯿﺮ ﻣﻦ اﻟﻤﺴﺎﻓﺎت ﺑﯿﻦ اﻟﺠﺰﯾﺌﺎت ﻓﻲ اﻟﺤﺎﻟﺘﯿﻦ اﻟﺴﺎﺋﻠﺔ‬ ‫واﻟﺼﻠﺒﺔ )اﻟﻤﺴﺎﻓﺎت ﺑﯿﻦ اﻟﺪﻗﺎﺋﻖ أﻗﻞ ﺑﻜﺜﯿﺮ ﻓﻲ اﻟﺴﻮاﺋﻞ واﻟﻤﻮاد اﻟﺼﻠﺒﺔ(‪.‬وﺗﻔﺴﺮ ھﺬه‬ ‫اﻟﺨﺎﺻﯿﺔ اﻟﻘﺎﺑﻠﯿﺔ اﻟﻌﺎﻟﯿﺔ ﻟﻺﻧﻀﻐﺎط ﻓﻲ ﺣﺎﻟﺔ اﻟﻐﺎزات وﻟﺬﻟﻚ‪ ،‬ﻓﺈن اﻟﻐﺎزات ﺗﻜﻮن ﻗﺎﺑﻠﺔ‬ ‫ﻟﻺﻧﻀﻐﺎط أﻛﺜﺮ ﺑﻜﺜﯿﺮ ﻣﻦ اﻟﺠﺰﯾﺌﺎت ﻓﻲ اﻟﺤﺎﻟﺘﯿﻦ اﻟﺴﺎﺋﻠﺔ واﻟﺼﻠﺒﺔ‪.‬‬ ‫‪The actual volume occupied by gas molecules is extremely small compared to‬‬ ‫‪the volume that the gas occupies. The volume of the container is considered‬‬ ‫‪equal to the volume of the gas. Most of the volume of a gas is empty space,‬‬ ‫‪which allows gases to be easily compressed.‬‬ ‫‪A gas is composed of molecules whose size is much smaller than the distances‬‬ ‫‪between them. This concept accounts for the ease with which gases can be‬‬ ‫‪compressed and for the fact that gases at ordinary temperature and pressure mix‬‬ ‫‪completely with each other. These facts imply that there must be much‬‬ ‫‪unoccupied space in gases that provides substantial room for additional‬‬ ‫‪molecules in a sample of gas.‬‬ ‫)‪(299‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(300‬‬ ‫‪ (٣‬ﺑﺴﺒﺐ اﻟﻤﺴﺎﻓﺎت اﻟﻜﺒﯿﺮة ﺑﯿﻦ ﺟﺰﯾﺌﺎت اﻟﻐﺎز ﻓﺈن ﻗﯿﻤﺔ اﻟﺘﺠﺎذب ﺑﯿﻦ ﺟﺰﯾﺌﺎت اﻟﻐﺎز ﻓﻲ‬ ‫ﻏﺎﯾﺔ اﻟﺼﻐﺮ وﻟﺬﻟﻚ ﻓﮭﻲ ﻣﮭﻤﻠﺔ‪.‬‬ ‫‪The attractive forces between the particles of a gas can be neglected‬‬ ‫وﻣﻦ ھﻨﺎ ﻓﺈﻧﮫ ﻻ ﺗﻮﺟﺪ ﻗﻮى ﺗﺠﺎذب ﺑﯿﻦ اﻟﺠﺰﯾﺌﺎت أي ﻻ ﺗﻤﺎرس اﻟﺠﺴﯿﻤﺎت أي ﻗﻮة ﻋﻠﻰ‬ ‫ﺑﻌﻀﮭﺎ اﻟﺒﻌﺾ )ﻣﺎ ﻋﺪا أﺛﻨﺎء اﻟﺘﺼﺎدم(‪ ،‬ﺑﻤﻌﻨﻰ ﻻ ﺗﺘﺄﺛﺮ اﻟﺠﺰﯾﺌﺎت ﺑﺒﻌﻀﮭﺎ اﻟﺒﻌﺾ ﻛﻤﺎ ﻻ‬ ‫ﺗﻮﺟﺪ ﻗﻮى ﺗﻨﺎﻓﺮ ﺑﯿﻨﮭﺎ‪ ،‬وﺑﺎﻟﺘﺎﻟﻲ ﻓﺈن اﻟﺠﺰﯾﺌﺎت ﻣﺴﺘﻘﻠﺔ ﺗﻤﺎﻣﺎً ﻛﻞ ﻋﻦ اﻷﺧﺮى‪.‬وﺑﺬﻟﻚ‬ ‫ﻓﺈﻧﮭﺎ ﺗﺘﺤﺮك ﺑﺎﺳﺘﻘﻼﻟﯿﺔ وﺗﻤﻸ أي وﻋﺎء ﻣﮭﻤﺎ ﻛﺎن ﺣﺠﻤﮫ وﺷﻜﻠﮫ‪.‬‬ ‫‪Except when gas molecules collide, forces of attraction and repulsion between‬‬ ‫‪them are negligible. This concept is consistent with the fact that all gases‬‬ ‫‪behave in the same way, regardless of the types of noncovalent interactions‬‬ ‫‪among their molecules.‬‬ ‫‪ (٤‬ﺗﻜﻮن ﺟﺰﯾﺌﺎت اﻟﻐﺎز ﻓﻲ ﺣﺮﻛﺔ ﺳﺮﯾﻌﺔ‪ ،‬ﻋﺸﻮاﺋﯿﺔ‪ ،‬ﻓﻲ ﺧﻄﻮط ﻣﺴﺘﻘﯿﻤﺔ وﺑﺴﺮﻋﺎت‬ ‫ﻣﺨﺘﻠﻔﺔ )‪ (rapid velocities‬وﻓﻲ ﺟﻤﯿﻊ اﻹﺗﺠﺎھﺎت )‪ ، (in all directions‬وﯾﺘﻐﯿﺮ‬ ‫اﺗﺠﺎه اﻟﺠﺰيء ﻋﻨﺪﻣﺎ ﯾﺼﻄﺪم ﺑﺠﺰيء آﺧﺮ أو ﺑﺠﺪار اﻹﻧﺎء‪.‬‬ ‫ﺷﻜﻞ ‪٩٣‬‬ ‫)‪(300‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  (301) ٩٤ ‫ﺷﻜﻞ‬ Gas particles are in constant motion, moving rapidly in straight paths. When gas particles collide, they rebound and travel in new directions. When they collide with the walls of the container, they exert gas pressure. An increase in the number or force of collisions against the walls of the container cause an increase in the pressure of the gas. Gas molecules move randomly at various speeds and in every possible direction. This concept is consistent with the fact that gases quickly and completely fill any container in which they are placed. ‫( ﺗﺼﻄﺪم ھﺬه اﻟﺪﻗﺎﺋﻖ ﻣﻊ ﺑﻌﻀﮭﺎ اﻟﺒﻌﺾ أو ﻣﻊ ﺟﺪران إﻧﺎﺋﮭﺎ اﻟﺤﺎوي ﺑﺎﺻﻄﺪاﻣﺎت‬٥ ‫ ﺑﻤﻌﻨﻰ أﻧﮭﺎ ﻻ ﺗﺆدي اﻟﻰ ﻓﻘﺪان اﻟﻐﺎز ﻷي ﻣﻦ‬، (Perfectly Elastic) ‫ﺗﺎﻣﺔ اﻟﻤﺮوﻧﺔ‬ ‫ وﯾﻔﺴﺮ ھﺬا‬.‫ﻃﺎﻗﺘﮫ اﻟﺤﺮﻛﯿﺔ ﺑﺎﻟﺮﻏﻢ ﻣﻦ أﻧﮫ ﻗﺪ ﯾﻮﺟﺪ اﻧﺘﻘﺎل ﻟﻠﻄﺎﻗﺔ ﺑﯿﻦ ﺷﺮﻛﺎء اﻟﺘﺼﺎدم‬ ‫ ﻟﻜﻨﮫ ﯾﻜﺘﺴﺐ‬،‫اﻟﺘﺼﺎدم اﻟﻤﺮن ﺑﺄن اﻟﺠﺰيء ﻋﻨﺪ ﺗﺼﺎدﻣﮫ ﺑﺠﺰيء آﺧﺮ ﯾﻔﻘﺪ ﺟﺰءاً ﻣﻦ ﻃﺎﻗﺘﮫ‬ ‫ﻧﻔﺲ اﻟﻄﺎﻗﺔ ﻋﻨﺪﻣﺎ ﯾﺼﻄﺪم ﺑﮫ ﺟﺰيء آﺧﺮ وﻟﺬﻟﻚ ﻓﺈن اﻟﻄﺎﻗﺔ اﻟﻜﻠﯿﺔ ﻟﻠﺰوج ﻣﻦ اﻟﺠﺰﯾﺌﺎت‬.‫ﯾﺒﻘﻰ دون ﺗﻐﯿﯿﺮ‬ When collisions between molecules occur, they are elastic. The speeds of colliding molecules may change, but the total kinetic energy of two colliding molecules is the same after a collision as before the collision. That is the collision is elastic. This concept is consistent with the fact that a gas sample at constant temperature never " runs down" , with all molecules falling to the bottom of the container. (301) PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com  ‫)‪(302‬‬ ‫وھﺬا اﻟﻤﺒﺪأ ﯾﻔﺴﺮ اﻧﺘﺸﺎر اﻟﻐﺎز ﺑﺎﻧﺘﻈﺎم ﻓﻲ ﺟﻤﯿﻊ أﻧﺤﺎء اﻹﻧﺎء اﻟﺤﺎوي ﻟﮫ‪ ،‬أي ﯾﻜﻮن اﻟﻐﺎز‬ ‫ﻣﺘﺠﺎﻧﺴﺎً ﻓﻲ اﻹﻧﺎء‪ ،‬ﻓﮭﻮ ﻻ ﯾﻜﻮن ﻣﺤﺘﺠﺰاً ﻓﻲ ﺟﺰء ﻣﻦ اﻹﻧﺎء‪.‬وﯾﻌﺰى ﺿﻐﻂ ﻏﺎز ﻣﺎ اﻟﻰ‬ ‫اﺻﻄﺪام دﻗﺎﺋﻖ اﻟﻐﺎز ﺑﺠﺪار اﻹﻧﺎء اﻟﺤﺎوي ﻟﮭﺬا اﻟﻐﺎز‪.‬‬ ‫وﯾﻌﺮف ﻣﺘﻮﺳﻂ اﻟﻤﺴﺎﻓﺔ اﻟﺘﻲ ﯾﻘﻄﻌﮭﺎ اﻟﺠﺴﯿﻢ ﺑﯿﻦ ﺗﺼﺎدﻣﯿﻦ ﻣﺘﺘﺎﻟﯿﻦ ﺑﻤﺘﻮﺳﻂ اﻟﻤﺴﺎر‬ ‫اﻟﺤﺮ )‪ ،(Mean Free Path‬وﯾﻌﺘﺒﺮ اﻟﺰﻣﻦ اﻟﺬي ﯾﺴﺘﻐﺮﻗﮫ اﻟﺘﺼﺎدم ﺿﺌﯿﻼً ﻟﻠﻐﺎﯾﺔ‬ ‫ﺑﺎﻟﻤﻘﺎرﻧﺔ ﺑﺎﻟﺰﻣﻦ اﻟﻤﺴﺘﻐﺮق ﺑﯿﻦ اﻟﺘﺼﺎدﻣﺎت‪.‬‬ ‫ﺷﻜﻞ ‪٩٥‬‬ ‫‪ (٦‬ﯾﻌﺘﺒﺮ اﻟﺰﻣﻦ اﻟﺬي ﯾﺴﺘﻐﺮﻗﮫ اﻟﺘﺼﺎدم ﺿﺌﯿﻼً ﻟﻠﻐﺎﯾﺔ ﺑﺎﻟﻤﻘﺎرﻧﺔ ﺑﺎﻟﺰﻣﻦ اﻟﻤﺴﺘﻐﺮق ﺑﯿﻦ‬ ‫اﻟﺘﺼﺎدﻣﺎت‪.‬‬ ‫‪ (٧‬ﻋﻨﺪ ﻟﺤﻈﺔ ﻣﻌﯿﻨﺔ‪ ،‬ﻓﺈﻧﮫ ﻓﻲ أي ﺗﺠﻤﻊ ﻟﺠﺰﯾﺌﺎت ﻏﺎز‪ ،‬ﯾﻮﺟﺪ ﺟﺰﯾﺌﺎت ﻣﺨﺘﻠﻔﺔ ﻟﮭﺎ‬ ‫ﺳﺮﻋﺎت ﻣﺨﺘﻠﻔﺔ‪ ،‬وﻃﺎﻗﺎت ﺣﺮﻛﺔ ﻣﺨﺘﻠﻔﺔ وﺗﺘﻨﺎﺳﺐ ﻣﺘﻮﺳﻂ اﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻜﻞ ﺟﺰﯾﺌﺎت‬ ‫اﻟﻐﺎز ﺗﻨﺎﺳﺒﺎً ﻃﺮدﯾﺎً ﻣﻊ درﺟﺔ اﻟﺤﺮارة اﻟﻤﻄﻠﻘﺔ‪ ،‬أي أن زﯾﺎدة درﺟﺔ اﻟﺤﺮارة ﺗﺆدي اﻟﻰ‬ ‫إﻛﺴﺎب اﻟﺪﻗﺎﺋﻖ ﻃﺎﻗﺔ ﺣﺮﻛﺔ واﻟﺘﻲ ﺗﻌﺘﺒﺮ ﻣﻘﯿﺎﺳﺎً ﻟﺤﺮارة اﻟﻤﺎدة‪ ،‬ﻣﻤﺎ ﯾﺆدي اﻟﻰ زﯾﺎدة ﺳﺮﻋﺔ‬ ‫اﻟﺠﺰﯾﺌﺎت وﺑﺎﻟﺘﺎﻟﻲ ﺗﺆدي اﻟﻰ زﯾﺎدة ﻋﺪد اﻟﻀﺮﺑﺎت ﻋﻠﻰ ﺟﺪار اﻹﻧﺎء ﻓﻲ اﻟﺜﺎﻧﯿﺔ وﺑﺎﻟﺘﺎﻟﻲ‬ ‫اﻟﻰ زﯾﺎدة اﻟﻀﻐﻂ‪.‬‬ ‫)‪(302‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  (303) The average kinetic energy of gas molecules is proportional to the Kelvin temperature. Gas particles move faster as the temperature increases. At higher temperatures, gas particles hit the walls of the container with more force, which produces higher pressures. The average kinetic energy of gas molecules is proportional to the absolute temperature. Though not part of the kinetic molecular theory, this useful concept is consistent with the fact that gas molecules escape through a tiny hole faster as the temperature increases, and with the fact that rates of chemical reactions are faster at higher temperatures. The kinetic theory helps explain some of the characteristics of gases. For example, we can quickly smell perfume from a bottle that is opened on the other side of a room, because its particles move rapidly in all directions. They move faster at higher temperatures, and more slowly at lower temperatures. Sometimes tires and gas-filled containers explode when temperatures are too high. From the kinetic theory, we know that gas particles move faster when heated, hit the walls of a container with more force, and cause a buildup of pressure inside a container. ‫ وﻟﻜﻦ‬،(‫وﻻ ﺗﺨﻀﻊ اﻟﻐﺎزات ﺧﻀﻮﻋﺎً ﺗﺎﻣﺎً ﻟﮭﺬه اﻟﻔﺮوض )ﺗﺤﯿﺪ اﻟﻐﺎزات اﻟﺤﻘﯿﻘﯿﺔ ﻋﻨﮭﺎ‬ Ideal Gas ‫اﻓﺘﺮض ﻏﺎزاً وھﻤﯿﺎً )ﻣﺜﺎﻟﯿﺎً( ﯾﺨﻀﻊ ﻟﺘﻠﻚ اﻟﻔﺮوض ﻋﺮف ﺑﺎﻟﻐﺎز اﻟﻤﺜﺎﻟﻲ‬ ‫ وﺗﺴﻠﻚ‬،(‫ أﻓﻮﺟﺎدرو‬،‫ ﺗﺸﺎرﻟﺰ‬،‫واﻟﻐﺎز اﻟﻤﺜﺎﻟﻲ ھﻮ اﻟﺬي ﯾﺨﻀﻊ ﻟﻠﻘﻮاﻧﯿﻦ اﻟﺴﺎﺑﻘﺔ )ﺑﻮﯾﻞ‬ 1 ‫اﻟﻐﺎزات اﻟﺤﻘﯿﻘﯿﺔ ﺳﻠﻮﻛﺎً ﻗﺮﯾﺒﺎً ﻣﻦ اﻟﻤﺜﺎﻟﯿﺔ ﻓﻲ اﻟﻈﺮوف اﻟﻌﺎدﯾﺔ )ﻋﻨﺪ ﺿﻐﻮط أدﻧﻰ ﻣﻦ‬ ‫ ﺳﻮف ﯾﻄﯿﻊ أي ﻏﺎز ﻗﻮاﻧﯿﻦ اﻟﻐﺎز اﻟﻤﺜﺎﻟﻲ‬273 K ‫ ودرﺟﺎت ﺣﺮارة أﻋﻠﻰ ﻣﻦ‬،atm) ‫ﻟﺪرﺟﺔ ﻣﻼﺻﻘﺔ( إﻻ أﻧﮭﺎ ﺗﻨﺤﺮف اﻧﺤﺮاﻓﺎً ﻣﻠﺤﻮﻇﺎً ﻋﻦ اﻟﺴﻠﻮك اﻟﻤﺜﺎﻟﻲ ﻋﻨﺪ درﺟﺎت‬.‫اﻟﺤﺮارة اﻟﻤﻨﺨﻔﻀﺔ واﻟﻀﻐﻮط اﻟﻌﺎﻟﯿﺔ ﻷﻧﮭﺎ ﺑﺬﻟﻚ ﺗﻘﺘﺮب ﻣﻦ اﻟﺤﺎﻟﺔ اﻟﺴﺎﺋﻠﺔ‬ (303) PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com  (304) ‫ﻣﻠﺨﺺ ﻟﻔﺮﻭﺽ ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫ وذات ﺣﺠﻢ ﺻﻐﯿﺮ ﺟﺪاً ﻟﺪرﺟﺔ‬،‫ ﺑﻌﯿﺪة ﻋﻦ ﺑﻌﻀﮭﺎ‬،‫( ﯾﺘﺄﻟﻒ اﻟﻐﺎز ﻣﻦ ﺟﺴﯿﻤﺎت )دﻗﺎﺋﻖ( ﺗﺴﻤﻰ ﺟﺰﯾﺌﺎت‬١ ‫أن اﻟﺤﺠﻢ اﻟﻔﻌﻠﻲ ﻟﻠﺠﺰﯾﺌﺎت ﯾﻜﻮن ﻣﮭﻤﻼً ﻣﻘﺎرﻧﺔ ﺑﺎﻟﺤﯿﺰ اﻟﻤﻮﺟﻮد ﺑﯿﻦ ﺟﺰﯾﺌﺎﺗﮭﺎ أو ﻣﻘﺎرﻧﺔ ﺑﺤﺠﻢ اﻹﻧﺎء‬.‫اﻟﺬي ﺗﻮﺟﺪ ﻓﯿﮫ‬ A gas is composed of molecules (discrete molecules) that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be "points"; that is, they posses mass but have negligible volume. The individual molecules are very small and are very far apart relative to their own sizes. ‫( ﻻ ﯾﻮﺟﺪ ﻗﻮى ﺗﺠﺎذب )أو ﺗﻨﺎﻓﺮ( ﺑﯿﻦ ﺟﺴﯿﻤﺎت اﻟﻐﺎز أو ﻣﻊ ﺟﺪران اﻹﻧﺎء اﻟﺬي ﺗﻮﺟﺪ ﺑﮫ وﺗﻜﻮن‬٢.‫اﻟﺠﺰﯾﺌﺎت ﻣﺴﺘﻘﻠﺔ ﺗﻤﺎﻣﺎً ﻋﻦ اﻷﺧﺮى‬ Between collisions, the molecules exert no attractive or repulsive forces on one another; instead, each molecule travels in a straight line with a constant velocity. ‫ ﻣﺴﺘﻤﺮة وﻋﺸﻮاﺋﯿﺔ ﻓﻲ ﺧﻄﻮط ﻣﺴﺘﻘﯿﻤﺔ ﻻ ﯾﺘﻐﯿﺮ اﺗﺠﺎھﮭﺎ إﻻ‬،‫( ﺗﺘﺤﺮك ﺟﺴﯿﻤﺎت اﻟﻐﺎز ﺑﺤﺮﻛﺔ ﺳﺮﯾﻌﺔ‬٣ ‫ واﺻﻄﺪام اﻟﺠﺰﯾﺌﺎت ﺑﺒﻌﻀﮭﺎ اﺻﻄﺪاﻣﺎت‬.‫ﻋﻨﺪ اﺻﻄﺪاﻣﮭﺎ ﻧﻊ ﺑﻌﻀﮭﺎ أو ﻣﻊ ﺟﺪران اﻹﻧﺎء اﻟﺤﺎوي‬ ‫ أي ﻻ ﺗﻔﻘﺪ ﻃﺎﻗﺔ ﻋﻨﺪ ﺗﺼﺎدﻣﮭﺎ ﻓﻠﯿﺲ ھﻨﺎك ﻣﺤﺼﻠﺔ ﻓﻘﺪ أو اﻛﺘﺴﺎب‬،(elastic) ‫ﻣﺮﻧﺔ‬.(there is no energy gain or loss) The gas molecules are in continuous , random, straight-line motion with varying velocities. Gas molecules are in constant (continuous) motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic. In other words, energy can be transferred from one molecule to another as a result of collision. Nevertheless, the total energy of all the molecules in a system remains the same..‫ ﯾﺘﻨﺎﺳﺐ ﻃﺮدﯾﺎً ﻣﻊ درﺟﺔ اﻟﺤﺮارة اﻟﻤﻄﻠﻘﺔ‬،‫( ﻣﺘﻮﺳﻂ ﻃﺎﻗﺔ اﻟﺤﺮﻛﺔ ﻟﺠﻤﯿﻊ اﻟﺠﺰﯾﺌﺎت‬٤ The average kinetic energy of the molecules is proportional to the (absolute) temperature of the gas in Kelvins. Any two gases at the same temperature will have the same average kinetic energy (The average kinetic energies of molecules of different gases are equal at a given temperature). For instance, in samples of H2, He, CO2 and SO2 at the same temperature, all the molecules have the same average kinetic energies. But the lighter molecules, H2 and He, have much higher average velocities than do the heavier molecules, CO2 and SO2, at the same temperature. (304) PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com  (305) The average kinetic energy of a molecule is given by : average molecular KE = KE α T or T average molecular speed = u α molecular weight 1 KE = m u 2 2 m : mass of the molecule and u is its speed. u 2 : mean square speed; it is the average of the square of the speeds of all the molecules : u12 + u 22 +..................+ u 2N u2 = , N N : the number of molecules Assumption 4 enables us to write : KE α T 1 m u 2α T 2 1 m u 2 = KT 2 According to the last equation the absolute temperature of a gas is a measure of the average kinetic energy of the molecules, the higher the temperature the more energetic the molecules. (Molecular kinetic energies of gases increase with increasing temperature and decrease with decreasing temperature). We have referred only to the average kinetic energy, in a given sample, some molecules may be moving quite rapidly while others are moving more slowly. ‫ وھ ﻮ ﯾﻌﺘﻤ ﺪ ﻋﻠ ﻰ ﺗﻜ ﺮار‬.‫( ﺿﻐﻂ اﻟﻐﺎز ھﻮ ﻧﺘﯿﺠﺔ ﻟﻠﺘﺼﺎدﻣﺎت ﺑﯿﻦ اﻟﺠﺰﯾﺌﺎت وﺟﺪران اﻟﻮﻋﺎء اﻟﺤ ﺎوي‬٥.‫اﻟﺘﺼﺎدم ﻓﻲ وﺣﺪة اﻟﻤﺴﺎﺣﺔ وﻛﺬﻟﻚ ﯾﻌﺘﻤﺪ ﻋﻠﻰ ﻣﺪى ﻗﻮة اﺻﻄﺪام اﻟﺠﺰيء ﺑﺎﻟﺠﺪار‬ According to the kinetic molecular theory, gas pressure is the result of collisions between molecules and the walls of their container. It depends on the frequency of collision per unit area and on how 'hard' the molecules strike the wall. (305) PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com  ‫)‪(306‬‬ ‫س( ﻋﻠﻞ ‪ :‬ﺗﻨﺘﺸﺮ ﺟﺰﯾﺌﺎت اﻟﻐﺎز ﻓﻲ ﺟﻤﯿﻊ أﺟﺰاء اﻹﻧﺎء ﺑﺸﻜﻞ ﻣﻨﺘﻈﻢ‪.‬‬ ‫ج( ﻷن اﻟﻐﺎزات ﺗﺘﺤﺮك ﺑﺴﺮﻋﺔ ﻓﻲ ﺧﻄﻮط ﻣﺴﺘﻘﯿﻤﺔ وﺑﻄﺮﯾﻘﺔ ﻋﺸﻮاﺋﯿﺔ ﺣﺘﻰ ﺗﺼﻄﺪم ﻓﻲ ﺟﺪار اﻹﻧﺎء‪.‬‬ ‫س( ﻋﻠﻞ ‪ :‬ﺗﺘﺴﺮب اﻟﻐﺎزات ﻣﻦ أي ﺛﻘﺐ ﻣﮭﻤﺎ ﻛﺎن ﺻﻐﯿﺮاً‪.‬‬ ‫ج( ﻷن ﺟﺰﯾﺌﺎت اﻟﻐﺎز ﺻﻐﯿﺮة ﺟﺪاً‪.‬‬ ‫س( ﻋﻠﻞ ‪ :‬ﺗﺤﺘﻞ اﻟﻐﺎزات ﺣﺠﻤﺎً أﻛﺒﺮ ﺑﻜﺜﯿﺮ ﻣﻦ اﻟﺤﺠﻢ اﻟﺬي ﺗﺸﻐﻠﮫ إذا ﺗﺤﻮﻟﺖ اﻟﻰ ﺳﺎﺋﻞ‪.‬‬ ‫ج( ﻷن ﺟﺰﯾﺌﺎت اﻟﻐﺎز ﻣﺘﺒﺎﻋﺪة ﻋﻦ ﺑﻌﻀﮭﺎ اﻟﺒﻌﺾ‪.‬‬ ‫س( ﻋﻠﻞ ‪ :‬ﯾﻘﻞ ﺣﺠﻢ اﻟﻐﺎز ﺑﺎزدﯾﺎد اﻟﻀﻐﻂ‪.‬‬ ‫ج( وذﻟﻚ ﻻﻗﺘﺮاب اﻟﺠﺰﯾﺌﺎت ﻣﻦ ﺑﻌﻀﮭﺎ اﻟﺒﻌﺾ‪.‬‬ ‫س( ﻋﻠﻞ ‪ :‬ﯾﺰداد ﺣﺠﻢ ﻓﻘﺎﻋﺔ ھﻮاء ﻋﻨﺪﻣﺎ ﺗﺼﻌﺪ ﻣﻦ ﻗﺎع ﺣﻤﺎم ﺳﺒﺎﺣﺔ اﻟﻰ ﺳﻄﺤﮫ‪.‬‬ ‫ج( ﺑﺴﺒﺐ أﻧﮫ ﻛﻠﻤﺎ ارﺗﻔﻌﺖ ﻓﻘﺎﻋﺔ اﻟﮭﻮاء ﯾﻘﻞ اﻟﻀﻐﻂ ﻋﻠﯿﮭﺎ وﺑﺬﻟﻚ ﯾﺰداد ﺣﺠﻤﮭﺎ‪.‬‬ ‫س( ﻋﻠﻞ ‪ :‬ﯾﺰداد اﻟﻀﻐﻂ إذا ﺳﺨﻦ ﻏﺎز ﻓﻲ إﻧﺎء ﻣﻐﻠﻖ‬ ‫ج( ﺑﺴﺒﺐ أن اﻟﺤﺮارة ﺗﺰﯾﺪ اﻟﻄﺎﻗ ﺔ اﻟﺤﺮﻛﯿ ﺔ ﻟﻠﺠﺰﯾﺌ ﺎت وﺑ ﺬﻟﻚ ﺗﺘﺤ ﺮك ﺑ ﺴﺮﻋﺔ أﻛﺒ ﺮ وﺗ ﺼﻄﺪم ﺑﺠ ﺪران‬ ‫اﻹﻧﺎء وﺑﺎﻟﺘﺎﻟﻲ ﯾﺰداد اﻟﻀﻐﻂ ﻷن اﻟﻀﻐﻂ ﯾﻨﺸﺄ ﻣﻦ اﺻﻄﺪام ﺟﺰﯾﺌﺎت اﻟﻐﺎز ﺑﺠﺪران اﻹﻧﺎء‪.‬‬ ‫س( ﻋﻠﻞ ‪ :‬ﯾﺰداد ﺿﻐﻂ اﻟﮭﻮاء داﺧﻞ إﻃﺎر اﻟﺴﯿﺎرة ﺑﺼﻔﺔ ﻣﻠﺤﻮﻇﺔ ﻋﻨﺪ اﻟﻘﯿﺎدة ﺑﺴﺮﻋﺔ ﻋﺎﻟﯿﺔ‪.‬‬ ‫ج( اﻟﺴﺮﻋﺔ اﻟﻌﺎﻟﯿﺔ ﺗﺰﯾﺪ ﻣﻦ ﺣﺮارة اﻹﻃﺎر وﺑﺎﻟﺘﺎﻟﻲ ﺗﺰداد اﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ ﻟﺠﺰﯾﺌﺎت اﻟﮭﻮاء داﺧﻞ اﻹﻃﺎر‬ ‫ﻓﯿﺰداد اﺻﻄﺪاﻣﮭﺎ ﺑﺠﺪران اﻹﻧﺎء ﺑﺸﻜﻞ أﻛﺒﺮ وﺑﺬﻟﻚ ﯾﺰداد اﻟﻀﻐﻂ‪.‬‬ ‫وﻗﺒﻞ ﻣﻨﺎﻗﺸﺔ ﻛﻞ ﻣﻦ ھﺬه اﻹﻓﺘﺮاﺿﺎت‪ ،‬ﻓﺈﻧﮫ ﯾﻤﻜﻨﻨ ﺎ أن ﻧ ﺴﺄل‪ ،‬ﻛﯿ ﻒ ﯾﻜ ﻮن اﻟﻨﻤ ﻮذج ﻣﺮﺗﺒﻄ ﺎً‬ ‫ﺑﺎﻟﻜﻤﯿﺎت اﻟﻤﻼﺣﻈﺔ )‪.(T, P, V‬واﻟﻨﻤﻮذج اﻟﻤﻘﺒﻮل ﺑﺎﻟﻨﺴﺒﺔ ﻟﻐﺎز‪ ،‬ھﻮ ذﻟ ﻚ اﻟ ﺬي ﯾﺘﻜ ﻮن ﻓ ﻲ‬ ‫اﻷﻏﻠ ﺐ ﻣ ﻦ ﺣﯿ ﺰ ﺧ ﺎل‪ ،‬واﻟ ﺬي ﺗﺘﺤ ﺮك ﻓﯿ ﮫ ﺑﻼﯾ ﯿﻦ ﻣ ﻦ ﻧﻘ ﺎط دﻗﯿﻘ ﺔ ﺗﻤﺜ ﻞ ﺟﺰﯾﺌ ﺎت‪ ،‬ﺑﺤﺮﻛ ﺔ‬ ‫ﻋﻨﯿﻔ ﺔ‪ ،‬ﻣﺘ ﺼﺎدﻣﺔ ﻣ ﻊ ﺑﻌ ﻀﮭﺎ اﻟ ﺒﻌﺾ‪ ،‬وﻣ ﻊ اﻟﺠ ﺪران اﻟﺨﺎﺻ ﺔ ﺑﺎﻟﻮﻋ ﺎء اﻟﺤ ﺎوي‪ ،‬إذ ﯾﻜ ﻮن‬ ‫ﺣﺠﻢ ﻏﺎز ﻓ ﻲ اﻷﻏﻠ ﺐ ﻋﺒ ﺎرة ﻋ ﻦ ﺣﯿ ﺰ ﺧ ﺎل‪ ،‬وﻟﻜﻨ ﮫ ﯾﻜ ﻮن ﻣ ﺸﻐﻮﻻً‪ ،‬ﺑﻤﻌﻨ ﻰ أن اﻟﺠ ﺴﯿﻤﺎت‬ ‫اﻟﻤﺘﺤﺮﻛﺔ ﺗﺸﻐﻞ ﻛﻞ اﻟﻤﻨﻄﻘﺔ اﻟﺘﻲ ﺗﺘﺤﺮك ﻓﯿﮭﺎ‪.‬واﻟﻀﻐﻂ‪ ،‬اﻟﻤﻌﺮف ﺑﻘﻮة ﻟﻜ ﻞ وﺣ ﺪة ﻣ ﺴﺎﺣﺔ‪،‬‬ ‫ﯾﻜﻮن ﻧﺎﺷﺌﺎً ﻋﻦ اﻟﻐ ﺎزات‪ ،‬ﻷن اﻟﺠﺰﯾﺌ ﺎت ﺗ ﺼﻄﺪم ﻣ ﻊ ﺟ ﺪران اﻟﻮﻋ ﺎء اﻟﺤ ﺎوي‪.‬وﯾﻨ ﺘﺞ ﻋ ﻦ‬ ‫)‪(306‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(307‬‬ ‫ﻛ ﻞ اﺻ ﻄﺪاﻣﺔ دﻓﻌ ﮫ ﺻ ﻐﯿﺮة ﺟ ﺪاً ‪.‬وﻣﺠﻤ ﻮع ﻛ ﻞ اﻟ ﺪﻓﻌﺎت ﻟﻜ ﻞ ﺛﺎﻧﯿ ﺔ ﻋﻠ ﻰ )‪ (1 cm2‬ﻣ ﻦ‬ ‫ﺟ ﺪار ھ ﻮ ﻋﺒ ﺎرة ﻋ ﻦ اﻟ ﻀﻐﻂ‪.‬وﺗﻌﻄ ﻲ درﺟ ﺔ اﻟﺤ ﺮارة ﻣﻘﯿﺎﺳ ﺎً ﻛﻤﯿ ﺎً ﻟﻤﺘﻮﺳ ﻂ ﺣﺮﻛ ﺔ‬ ‫اﻟﺠﺰﯾﺌﺎت‪.‬‬ ‫ﻣﻨﺎﻗﺸﺔ ﻓﺮﻭﺽ ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﺍﳉﺰﻳﺌﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫وﯾﻤﻜﻦ إدراك أن أول اﻻﻗﺘﺮاﺣﺎت اﻷرﺑﻊ ‪:‬‬ ‫‪ (١‬ﯾﺘﺄﻟﻒ اﻟﻐﺎز ﻣﻦ ﺟﺴﯿﻤﺎت )دﻗﺎﺋﻖ( ﺗﺴﻤﻰ ﺟﺰﯾﺌﺎت‪ ،‬ﺑﻌﯿﺪة ﻋﻦ ﺑﻌﻀﮭﺎ‪ ،‬وذات ﺣﺠﻢ‬ ‫ﺻﻐﯿﺮ ﺟﺪاً ﻟﺪرﺟﺔ أن اﻟﺤﺠﻢ اﻟﻔﻌﻠﻲ ﻟﻠﺠﺰﯾﺌﺎت ﯾﻜﻮن ﻣﮭﻤﻼً ﻣﻘﺎرﻧﺔ ﺑﺎﻟﺤﯿﺰ اﻟﻤﻮﺟﻮد ﺑﯿﻦ‬ ‫ﺟﺰﯾﺌﺎﺗﮭﺎ أو ﻣﻘﺎرﻧﺔ ﺑﺤﺠﻢ اﻹﻧﺎء اﻟﺬي ﺗﻮﺟﺪ ﻓﯿﮫ‪.‬‬ ‫وھﺬا اﻹﻗﺘﺮاح ﯾﻜﻮن ﻣﻌﻘﻮﻻً‪ ،‬ﻣﻦ ﺣﻘﯿﻘﺔ أن اﻧﻀﻐﺎﻃﯿﺔ اﻟﻐ ﺎزات ﺗﻜ ﻮن ﻛﺒﯿ ﺮة ﺟ ﺪاً‪.‬وﺗﻮﺿ ﺢ‬ ‫اﻟﺤﺴﺎﺑﺎت أﻧﮫ ﻓﻲ ﻏﺎز اﻷﻛﺴﺠﯿﻦ ﻣﺜﻼً‪ ،‬ﻋﻨﺪ )‪ (STP‬ﯾﻜﻮن )‪ (99.96 %‬ﻣ ﻦ اﻟﺤﺠ ﻢ اﻟﻜﻠ ﻲ‪،‬‬ ‫ﻋﺒﺎرة ﻋﻦ ﺣﯿﺰ ﺧﺎل ﻓﻲ أي ﻟﺤﻈﺔ‪.‬وﺣﯿﺚ أﻧﮫ ﯾﻮﺟ ﺪ )‪ (2.7 × 1019 molecules/ml‬ﻣ ﻦ‬ ‫ﻏﺎز اﻷﻛﺴﺠﯿﻦ ﻋﻨﺪ )‪ (STP‬ﻓﺈن اﻟﻤ ﺴﺎﻓﺔ ﺑ ﯿﻦ اﻟﺠﺰﯾﺌ ﺎت ﺗﻜ ﻮن ﺣ ﻮاﻟﻲ )‪(3.7 × 10-7 cm‬‬ ‫واﻟﺘ ﻲ ھ ﻲ ﻋﺒ ﺎرة ﻋ ﻦ )‪ (12‬ﻣ ﺮة ﻣﺜ ﻞ اﻟﻘﻄ ﺮ اﻟﺠﺰﯾﺌ ﻲ‪.‬وﻋﻨ ﺪﻣﺎ ﯾ ﻀﻐﻂ اﻷﻛ ﺴﺠﯿﻦ أو أي‬ ‫ﻏﺎز آﺧﺮ ﻓﺈن ﻣﺘﻮﺳ ﻂ اﻟﻤ ﺴﺎﻓﺔ ﺑ ﯿﻦ اﻟﺠﺰﯾﺌ ﺎت ﺳ ﻮف ﯾﺨﺘ ﺰل‪ ،‬أي ﯾ ﻨﻘﺺ اﻟﻜ ﺴﺮ ﻣ ﻦ اﻟﺤﯿ ﺰ‬ ‫اﻟﺤﺮ‪.‬‬ ‫وﺗﺘﺪﻋﻢ ﺻﺤﺔ اﻹﻓﺘﺮاض اﻟﺜﺎﻧﻲ ‪:‬‬ ‫ﻻ ﯾﻮﺟﺪ ﻗ ﻮى ﺗﺠ ﺎذب )أو ﺗﻨ ﺎﻓﺮ( ﺑ ﯿﻦ ﺟ ﺴﯿﻤﺎت اﻟﻐ ﺎز أو ﻣ ﻊ ﺟ ﺪران اﻹﻧ ﺎء اﻟ ﺬي ﺗﻮﺟ ﺪ ﺑ ﮫ‬ ‫وﺗﻜﻮن اﻟﺠﺰﯾﺌﺎت ﻣﺴﺘﻘﻠﺔ ﺗﻤﺎﻣﺎً ﻋﻦ اﻷﺧﺮى‪.‬‬ ‫ﻣﻦ ﻣﻼﺣﻈﺔ أن اﻟﻐ ﺎزات ﺗﺘﻤ ﺪد ﺗﻠﻘﺎﺋﯿ ﺎً ﻟﺘ ﺸﻐﻞ ﻛ ﻞ اﻟﺤﺠ ﻢ اﻟﻤﺘ ﺎح ﻟﮭ ﺎ‪.‬وﯾﺤ ﺪث ھ ﺬا اﻟ ﺴﻠﻮك‬ ‫ﺣﺘ ﻰ ﺑﺎﻟﻨ ﺴﺒﺔ ﻟﻠﻐ ﺎز اﻟﻤ ﻀﻐﻮط ﻟﺪرﺟ ﺔ ﻛﺒﯿ ﺮة‪ ،‬ﺣﯿ ﺚ ﺗﻜ ﻮن اﻟﺠﺰﯾﺌ ﺎت ﻣﻼﺻ ﻘﺔ ﻟﺒﻌ ﻀﮭﺎ‬ ‫اﻟ ﺒﻌﺾ اﻟ ﻰ ﺣ ﺪ ﻣ ﺎ‪ ،‬وﯾﺠ ﺐ أن ﺗﻜ ﻮن أي ﻗ ﻮى ﺑ ﯿﻦ اﻟﺠﺰﯾﺌ ﺎت ھ ﻲ اﻷﻋﻈ ﻢ‪.‬وﻣ ﻦ اﻟﺠ ﺪﯾﺮ‬ ‫ﺑﺎﻟﺬﻛﺮ أﻧﮫ ﯾﺠﺐ أن ﻻ ﯾﻮﺟﺪ ﺗﺮاﺑﻂ ﯾﻤﻜﻦ ﺗﻘﺪﯾﺮه ﺑﯿﻦ ﺟﺰيء ﻏﺎز وﺟﯿﺮاﻧﮫ‪.‬‬ ‫)‪(307‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(308‬‬ ‫اﻹﻓﺘﺮاض اﻟﺜﺎﻟﺚ‪:‬‬ ‫ﺗﺘﺤﺮك ﺟﺴﯿﻤﺎت اﻟﻐ ﺎز ﺑﺤﺮﻛ ﺔ ﺳ ﺮﯾﻌﺔ‪ ،‬ﻣ ﺴﺘﻤﺮة وﻋ ﺸﻮاﺋﯿﺔ ﻓ ﻲ ﺧﻄ ﻮط ﻣ ﺴﺘﻘﯿﻤﺔ ﻻ ﯾﺘﻐﯿ ﺮ‬ ‫اﺗﺠﺎھﮭﺎ إﻻ ﻋﻨﺪ اﺻﻄﺪاﻣﮭﺎ ﻣﻊ ﺑﻌﻀﮭﺎ أو ﻣﻊ ﺟﺪران اﻹﻧﺎء اﻟﺤﺎوي‪.‬اﺻﻄﺪاﻣﺎت اﻟﺠﺰﯾﺌ ﺎت‬ ‫ﺑﺒﻌﻀﮭﺎ اﺻﻄﺪاﻣﺎت ﻣﺮﻧﺔ‪ ،‬أي ﻻ ﺗﻔﻘﺪ ﻃﺎﻗﺔ ﻋﻨﺪ ﺗﺼﺎدﻣﮭﺎ‪.‬‬ ‫إن اﻟﻤﻼﺣﻈﺔ اﻟﺨﺎﺻﺔ ﺑﺎﻟﺤﺮﻛﺔ اﻟﺒﺮاوﻧﯿﺔ‪ ،‬ﺗﺪل ﺿﻤﻨﺎً ﻋﻠﻰ أن ﺟﺰﯾﺌ ﺎت اﻟﻐ ﺎز ﺗﺘﺤ ﺮك ﻣﺘﻔﻘ ﺔ‬ ‫ﻣﻊ اﻹﻓﺘﺮاض اﻟﺜﺎﻟﺚ‪.‬‬ ‫وﻣﺜﻞ أي ﺟﺴﯿﻢ ﻣﺘﺤ ﺮك‪ ،‬ﻓ ﺈن اﻟﺠﺰﯾﺌ ﺎت ﻟﮭ ﺎ ﻛﻤﯿ ﺔ ﻣ ﻦ ﻃﺎﻗ ﺔ اﻟﺤﺮﻛ ﺔ ﺗ ﺴﺎوي )‪،(1/2mu2‬‬ ‫ﺣﯿﺚ )‪ (m‬ﻛﺘﻠﺔ اﻟﺠﺰيء‪ ،‬و ‪ : u‬ﻋﺒﺎرة ﻋﻦ ﺳﺮﻋﺘﮫ‪.‬وذﻟﻚ أن اﻟﺠﺰﯾﺌﺎت ﺗﺘﺤﺮك ﻓﻲ ﺧﻄ ﻮط‬ ‫ﻣﺴﺘﻘﯿﻤﺔ‪ ،‬إﻧﻤﺎ ﯾﻨﺒﻊ ﻣﻦ اﻓﺘﺮاض ﻋﺪم وﺟﻮد ﻗ ﻮى ﺗﺠ ﺎذب‪.‬وﻟ ﻮ أﻧ ﮫ ﻛ ﺎن ھﻨ ﺎك ﻗ ﻮى ﺗﺠ ﺎذب‬ ‫ﺑﯿﻨﮭﺎ ﻷﻣﻜﻦ ﻟﻠﺠﺰﯾﺌﺎت أن ﺗﻨﺤﻨﻲ ﻋﻦ ﻣ ﺴﺎرات اﻟﺨ ﻂ اﻟﻤ ﺴﺘﻘﯿﻢ‪.‬وﻧﻈ ﺮاً ﻷﻧ ﮫ ﯾﻮﺟ ﺪ ﺟﺰﯾﺌ ﺎت‬ ‫ﻛﺜﯿ ﺮة اﻟ ﻰ ﺣ ﺪ ﺑﻌﯿ ﺪ‪ ،‬ﻓ ﻲ ﻋﯿﻨ ﺔ ﻏ ﺎز‪ ،‬وﺑ ﺴﺒﺐ أﻧﮭ ﺎ ﺗﺘﺤ ﺮك ﺳ ﺮﯾﻌﺎً ﺟ ﺪاً )ﻋﻨ ﺪ ‪ 0 °C‬ﺗﻜ ﻮن‬ ‫اﻟ ﺴﺮﻋﺔ اﻟﻤﺘﻮﺳ ﻄﺔ ﻟﺠﺰﯾﺌ ﺎت اﻷﻛ ﺴﺠﯿﻦ ﺣ ﻮاﻟﻲ ‪ (1000 mph‬ﻓﺈﻧ ﮫ ﯾﻮﺟ ﺪ ﺗ ﺼﺎدﻣﺎت‬ ‫ﻣﺘﻜﺮرة اﻟﺤﺪوث‪.‬وﻣﻦ اﻟﻀﺮوري اﻋﺘﺒﺎر أن اﻟﺘﺼﺎدﻣﺎت ﺗﻜﻮن ﺗﺎﻣﺔ اﻟﻤﺮوﻧ ﺔ‪ ،‬وذﻟ ﻚ ﺣﯿ ﺚ‬ ‫أﻧﮭﺎ ﻻ ﺗﻔﻘﺪ ﻃﺎﻗﺔ ﺣﺮﻛﺔ ﻋﻦ ﻃﺮﯾﻖ اﻟﺘﺤﻮل اﻟﻰ ﻃﺎﻗ ﺔ وﺿ ﻊ )ﻣ ﺜﻼً ﻋﻨ ﺪ ﺗ ﺸﻮﯾﮫ اﻟﺠﺰﯾﺌ ﺎت(‪.‬‬ ‫وإذا ﻟﻢ ﯾﻜﻦ ذﻟﻚ ﺣﻘﯿﻘﯿﺎً ﻓﺈن ﺣﺮﻛﺔ اﻟﺠﺰﯾﺌﺎت ﺳﻮف ﺗﻘﻒ ﻓﻲ آﺧ ﺮ اﻷﻣ ﺮ‪ ،‬ﻛﻤ ﺎ أن اﻟﺠﺰﯾﺌ ﺎت‬ ‫ﺳﻮف ﺗﺮﺳﺐ اﻟﻰ ﻗﺎع اﻹﻧﺎء اﻟﺤﺎوي‪.‬‬ ‫واﻻﻓﺘﺮاض اﻟﺮاﺑﻊ ‪:‬‬ ‫ﻋﻨﺪ ﻟﺤﻈ ﺔ ﻣﻌﯿﻨ ﺔ‪ ،‬ﻓﺈﻧ ﮫ ﻓ ﻲ أي ﺗﺠﻤ ﻊ ﻟﺠﺰﯾﺌ ﺎت ﻏ ﺎز‪ ،‬ﯾﻮﺟ ﺪ ﺟﺰﯾﺌ ﺎت ﻣﺨﺘﻠﻔ ﺔ ﻟﮭ ﺎ ﺳ ﺮﻋﺎت‬ ‫ﻣﺨﺘﻠﻔﺔ‪ ،‬وﻃﺎﻗﺎت ﺣﺮﻛﺔ ﻣﺨﺘﻠﻔﺔ وﺗﺘﻨﺎﺳﺐ ﻣﺘﻮﺳﻂ اﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻜﻞ ﺟﺰﯾﺌﺎت اﻟﻐ ﺎز ﺗﻨﺎﺳ ﺒﺎً‬ ‫ﻃﺮدﯾﺎً ﻣﻊ درﺟﺔ اﻟﺤﺮارة اﻟﻤﻄﻠﻘﺔ‬ ‫وھﺬا اﻹﻓﺘﺮاض ﻟﮫ ﺷﻘﺎن ‪:‬‬ ‫‪ (١‬أﻧﮫ ﯾﻮﺟﺪ ﺗﻮزﯾﻊ ﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﺔ‪.‬‬ ‫)‪(308‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(309‬‬ ‫‪ (٢‬ﻃﺎﻗﺔ اﻟﺤﺮﻛﺔ اﻟﻤﺘﻮﺳﻄﺔ ﺗﺘﻨﺎﺳﺐ ﻣﻊ درﺟﺔ اﻟﺤﺮارة اﻟﻤﻄﻠﻘﺔ‪.‬وﯾﺤﺪث اﻟﺘﻮزﯾﻊ‪ ،‬أو اﻟﻤﺪى‬ ‫ﻟﻠﻄﺎﻗﺎت ﻧﺘﯿﺠﺔ ﻟﻠﺘﺼﺎدﻣﺎت اﻟﺠﺰﯾﺌﯿﺔ‪ ،‬اﻟﺘﻲ ﺗﻐﯿ ﺮ ﺑﺎﺳ ﺘﻤﺮار ﻣ ﻦ ﺳ ﺮﻋﺔ ﺟ ﺰيء ﻣﻔ ﺮد‪.‬إذ أن‬ ‫ﺟﺰﯾﺌﺎً ﻣﻌﯿﻨﺎً‪ ،‬ﯾﻤﻜﻨﮫ أن ﯾﺘﺤﺮك اﻟﻰ اﻷﻣﺎم ﺑ ﺴﺮﻋﺔ ﻣﺤ ﺪدة‪ ،‬إﻟ ﻰ أن ﯾ ﺮﺗﻄﻢ ﺑ ﺂﺧﺮ‪ ،‬اﻟ ﺬي ﯾﻔﻘ ﺪ‬ ‫إﻟﯿ ﮫ ﺑﻌ ﻀﺎً ﻣ ﻦ ﻃﺎﻗ ﺔ ﺣﺮﻛﺘ ﮫ‪ ،‬ورﺑﻤ ﺎ ﻓﯿﻤ ﺎ ﺑﻌ ﺪ‪ ،‬ﯾﻠﻘ ﻰ ارﺗﻄﺎﻣ ﺎً ﻣ ﻦ ﺛﺎﻟ ﺚ‪ ،‬وﯾﻜﺘ ﺴﺐ ﻃﺎﻗ ﺔ‬ ‫ﺣﺮﻛﺔ‪.‬وھﺬا اﻟﺘﺒﺎدل ﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﺔ ﺑﯿﻦ اﻟﺠﯿﺮان ﯾﺤ ﺪث ﺑﺎﺳ ﺘﻤﺮار‪ ،‬ﺑﺤﯿ ﺚ أن ﻃﺎﻗ ﺔ اﻟﺤﺮﻛ ﺔ‬ ‫اﻟﻜﻠﯿﺔ ﻟﻌﯿﻨﺔ ﻏﺎز ھﻲ اﻟﺘﻲ ﺗﺒﻘﻰ ﻛﻤﺎ ھﻲ‪ ،‬ﺑ ﺸﺮط أﻧ ﮫ ﻃﺒﻌ ﺎً ﻻ ﺗ ﻀﺎف ﻃﺎﻗ ﺔ ﻟﻌﯿﻨ ﺔ اﻟﻐ ﺎز ﻣ ﻦ‬ ‫اﻟﺨﺎرج‪ ،‬ﻣﺜﻼً ﺑﺎﻟﺘﺴﺨﯿﻦ )أو ﺗﺴﺤﺐ ﻣﺜﻼً ﺑﺎﻟﺘﺒﺮﯾ ﺪ(‪.‬وﺗﺘﺮﻛ ﺐ ﻃﺎﻗ ﺔ اﻟﺤﺮﻛ ﺔ اﻟﻜﻠﯿ ﺔ ﻟﻐ ﺎز ﻣ ﻦ‬ ‫ﻃﺎﻗﺎت اﻟﺤﺮﻛﺔ ﻟﺠﻤﯿﻊ اﻟﺠﺰﯾﺌﺎت‪ ،‬اﻟﺘﻲ ﯾﻤﻜ ﻦ أن ﯾﻜ ﻮن ﻛ ﻞ ﻣﻨﮭﻤ ﺎ ﻣﺘﺤﺮﻛ ﺎً ﺑ ﺴﺮﻋﺔ ﻣﺨﺘﻠﻔ ﺔ‪.‬‬ ‫وﻋﻨﺪ ﻟﺤﻈﺔ ﻣﻌﯿﻨﺔ‪ ،‬ﯾﻤﻜﻦ ﻟﻘﻠﯿﻞ ﻣﻦ اﻟﺠﺰﯾﺌﺎت‪ ،‬أن ﺗﻘﻒ ﺳﺎﻛﻨﺔ ﺑﺪون ﻃﺎﻗﺔ ﺣﺮﻛﺔ‪ ،‬وﻗ ﺪ ﯾﻜ ﻮن‬ ‫ﻟﻘﻠﯿ ﻞ ﻃﺎﻗ ﺔ ﺣﺮﻛ ﺔ ﻋﺎﻟﯿ ﺔ‪ ،‬وﯾﻜ ﻮن ﻟﻤﻌﻈﻤﮭ ﺎ ﻃﺎﻗ ﺔ ﺣﺮﻛ ﺔ ﻗﺮﯾﺒ ﺔ ﻣ ﻦ اﻟﻤﺘﻮﺳ ﻂ‪.‬وﯾ ﺘﻠﺨﺺ‬ ‫اﻟﻮﺿﻊ ﻓﻲ اﻟﺸﻜﻞ )‪.(٩٦‬‬ ‫ﺷﻜﻞ ‪ : ٩٦‬ﺗﻮزﯾﻊ اﻟﻄﺎﻗﺔ ﻓﻲ ﻏﺎز‬ ‫)‪(309‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(310‬‬ ‫اﻟﺬي ﯾﻮﺿﺢ اﻟﺘﻮزﯾﻊ اﻟﻌﺎدي ﻟﻄﺎﻗﺎت اﻟﺤﺮﻛﺔ ﻓﻲ ﻋﯿﻨﺔ ﻏﺎز‪.‬وﺗﻌﺒﺮ ﻛﻞ ﻧﻘﻄ ﺔ ﻋﻠ ﻰ اﻟﻤﻨﺤﻨ ﻰ‬ ‫ﻋﻦ أي ﻛﺴﺮ ﻣﻦ اﻟﺠﺰﯾﺌﺎت ﺗﻜﻮن ﻟﮫ ﻗﯿﻤﺔ ﻣﻌﯿﻨﺔ ﻣﻦ ﻃﺎﻗﺔ اﻟﺤﺮﻛﺔ‪.‬‬ ‫وﯾﻤﻜﻦ أن ﺗﺮﺗﻔﻊ درﺟﺔ ﺣ ﺮارة ﻏ ﺎز ﺑﺈﺿ ﺎﻓﺔ ﺣ ﺮارة‪.‬وﻣ ﺎذا ﯾﺤ ﺪث ﻟﻠﺠﺰﯾﺌ ﺎت ﻋﻨ ﺪﻣﺎ ﺗﺮﻓ ﻊ‬ ‫درﺟﺔ اﻟﺤﺮارة؟ ﻓ ﺎﻟﺤﺮارة اﻟﺘ ﻲ ﺗ ﻀﺎف ﻋﺒ ﺎرة ﻋ ﻦ ﺻ ﻮرة ﻟﻠﻄﺎﻗ ﺔ‪ ،‬وﺑ ﺬﻟﻚ ﻓﺈﻧﮭ ﺎ ﯾﻤﻜ ﻦ أن‬ ‫ﺗ ﺴﺘﺨﺪم ﻓ ﻲ زﯾ ﺎدة ﺳ ﺮﻋﺔ اﻟﺠﺰﯾﺌ ﺎت‪ ،‬وﺑﺎﻟﺘ ﺎﻟﻲ ﻣﺘﻮﺳ ﻂ ﻃﺎﻗ ﺔ اﻟﺤﺮﻛ ﺔ‪.‬وﯾﻮﺿ ﺢ ذﻟ ﻚ ﻓ ﻲ‬ ‫اﻟﺸﻜﻞ )‪(٩٧‬‬ ‫ﺷﻜﻞ ‪ : ٩٧‬ﺗﻮزﯾﻊ اﻟﻄﺎﻗﺔ ﻓﻲ ﻏﺎز ﻋﻨﺪ درﺟﺔ ﺣﺮارة‬ ‫ﺣﯿﺚ ﯾﺼﻒ اﻟﺨﻂ اﻟﻤﺘﻘﻄﻊ اﻟﻮﺿﻊ ﻋﻨ ﺪ درﺟ ﺔ ﺣ ﺮارة أﻋﻠ ﻰ‪.‬ﻓﻌﻨ ﺪ درﺟ ﺔ اﻟﺤ ﺮارة اﻷﻋﻠ ﻰ‬ ‫ﯾﻜﻮن ﻟﻠﺠﺰﯾﺌﺎت ﻣﺘﻮﺳﻂ ﻃﺎﻗﺔ ﺣﺮﻛﺔ أﻋﻠﻰ ﻣﻨﮭﺎ ﻋﻨﺪ درﺟﺔ ﺣﺮارة أدﻧ ﻰ‪.‬وﺑ ﺬﻟﻚ ﻓ ﺈن درﺟ ﺔ‬ ‫اﻟﺤﺮارة ﺗﺼﻠﺢ ﻛﻤﻘﯿﺎس ﻟﻤﺘﻮﺳﻂ ﻃﺎﻗﺔ اﻟﺤﺮﻛﺔ‪.‬‬ ‫)‪(310‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(311‬‬ ‫ﺍﳌﻌﺎﺩﻟﺔ ﺍﻷﺳﺎﺳﻴﺔ ﻟﻠﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫اﻟﺼﯿﻐﺔ اﻟﺮﯾﺎﺿﯿﺔ ﻟﻠﻤﻌﺎدﻟﺔ اﻷﺳﺎﺳﯿﺔ ﻟﻠﻨﻈﺮﯾﺔ اﻟﺤﺮﻛﯿﺔ ‪:‬‬ ‫‪1‬‬ ‫= ‪PV‬‬ ‫‪m N u2‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪PV = m ( nN A ) u 2‬‬ ‫‪3‬‬ ‫ﺣﯿﺚ ‪:‬‬ ‫‪ : P‬اﻟﻀﻐﻂ ﺑﻮﺣ ﺪة ‪ : V ،Pa‬اﻟﺤﺠ ﻢ ﺑﻮﺣ ﺪة ‪ : N ،m3‬ﻋ ﺪد اﻟﺠﺰﯾﺌ ﺎت‪ : m ،‬ﻛﺘﻠ ﺔ اﻟﺠ ﺰيء‬ ‫اﻟﻮاﺣﺪ ﺑﻮﺣﺪة اﻟﻜﯿﻠﻮﺟﺮام‪ : u 2 ،.‬ﻣﺘﻮﺳﻂ ﻣﺮﺑﻊ ﺳﺮﻋﺔ اﻟﺠﺰيء )‪(m2/s2‬‬ ‫ﻣﺜﺎﻝ )‪(١٦١‬‬ ‫اﺣﺴﺐ اﻟ ﻀﻐﻂ ﺑﻮﺣ ﺪة ‪ kPa‬اﻟﻤﺒ ﺬول ﺑﻮاﺳ ﻄﺔ )‪ (2 × 1021 molecule‬ﻣ ﻦ ﻏ ﺎز ‪ N2‬ﻓ ﻲ‬ ‫‪ (1‬ﻋﻠﻤ ﺎً ﺑ ﺄن ﻣﺘﻮﺳ ﻂ ﻣﺮﺑ ﻊ اﻟ ﺴﺮﻋﺔ ﻟﮭ ﺬه اﻟﺠﺰﯾﺌ ﺎت ھ ﻮ‬ ‫وﻋ ﺎء ﺣﺠﻤ ﮫ )‪L‬‬ ‫)‪).(244036 m2/s2‬اﻟﻜﺘﻠﺔ اﻟﺬرﯾﺔ ﻟـ ‪(14 = N‬‬ ‫ﺍﳊﻞ‬ ‫ﻧﺤﺴﺐ أوﻻً ﻛﺘﻠﺔ ا ﻟﺠﺰيء اﻟﻮاﺣﺪ ﻣﻦ ﻏﺎز اﻟﻨﯿﺘﺮوﺟﯿﻦ ﺑﻮﺣﺪة ‪: Kg‬‬ ‫‪Mw N2 = 2 × 14 = 28 g mol-1‬‬ ‫‪Mw N2 = 0.028 kg mol-1‬‬ ‫‪Mw N2‬‬ ‫‪0.028 kg mol-1‬‬ ‫= ‪m‬‬ ‫=‬ ‫‪NA‬‬ ‫‪6.023 × 1023 molecules mol -1‬‬ ‫‪m = 4.65 × 10-26 kg molecule‬‬ ‫)‪(311‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  (312) : ‫وﺑﺘﻄﺒﯿﻖ اﻟﻤﻌﺎدﻟﺔ اﻷﺳﺎﺳﯿﺔ ﻟﻠﻨﻈﺮﯾﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻠﻐﺎزات‬ 1 m N u2 1 PV = m N u 2 ⇒ P = 3 3 V × ( 4.65 × 10-26 kg molecule-1 ) × ( 2 × 1021 molecule) × ( 244036 m s ) 1 2 -2 P= 3  1L   -3   1000 L m  P = 7565.116 Kg / m s 2 P = 7565.116 Pa P = 7.565 kP (where 1 Pa = 1 Nm-2 = (kg m s-2 ) × (m-2 ) = kg /m s2 (312) PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com  ‫)‪(313‬‬ ‫ﺍﺷﺘﻘﺎﻕ ﺍﳌﻌﺎﺩﻟﺔ ﺍﻷﺳﺎﺳﻴﺔ ﻟﻠﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ‬ ‫‪Fundamental Equation of the Kinetic Theory‬‬ ‫ﺍﳌﻌﺎﺩﻟﺔ ﺍﳊﺮﻛﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫‪Kinetic Equation of Gases‬‬ ‫ﻣﻦ اﻟﻤﻤﻜﻦ ﺑﻨﺎءً ﻋﻠﻰ اﻟﻔﺮوض اﻟﺴﺎﺑﻘﺔ )ﻓﺮوض اﻟﻨﻈﺮﯾﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻠﻐﺎزات( إﯾﺠﺎد ﻋﻼﻗﺔ‬ ‫ﺗﺮﺑﻂ ﺑﯿﻦ ﺿﻐﻂ اﻟﻐﺎز اﻟﻤﺜﺎﻟﻲ )‪ (P‬وﻛﺘﻠﺔ اﻟﻐﺎز)‪ (m‬وﺳﺮﻋﺔ اﻟﺠﺰﯾﺌﺎت )‪.(u‬‬ ‫ ﻧﻔﺘﺮض أن ﻟﺪﯾﻨﺎ ﻏﺎز ﻣﺤﺒﻮس ﻓﻲ إﻧﺎء ﻣﻜﻌﺐ اﻟﺸﻜﻞ ﻃﻮل ﺿﻠﻌﮫ )‪ (L‬وﺣﺠﻤﮫ )‪(L3‬‬ ‫وﻣﺴﺎﺣﺔ ﻛﻞ ﺟﺪار ﻟﮫ )‪(L2‬‬ ‫ﺷﻜﻞ ‪ : ٩٨‬ﺗﺤﻠﯿﻞ اﻟﺴﺮﻋﺔ ﺑﺎﺗﺠﺎه ﻣﺤﺎور )‪(X, Y, Z‬‬ ‫)‪(313‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(314‬‬ ‫ ﯾﺤﺘﻮي اﻟﻤﻜﻌﺐ ﻋﻠﻰ ﻋﺪد )‪ (N‬ﻣﻦ اﻟﺠﺰﯾﺌﺎت‪ ،‬ﻛﺘﻠﺔ اﻟﺠﺰيء اﻟﻮاﺣﺪ ﻣﻨﮭﺎ )‪(m‬‬ ‫وﺳﺮﻋﺘﮫ )‪ (u‬ﻋﻨﺪ درﺟﺔ ﺣﺮارة ﺛﺎﺑﺘﺔ‪.‬‬ ‫ ووﻓﻘﺎً ﻟﻠﻨﻈﺮﯾﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻠﻐﺎز ﻓﺈن اﻟﺠﺰﯾﺌﺎت ﺗﺘﺤﺮك ﻋﺸﻮاﺋﯿﺔ ﻓﻲ ﺟﻤﯿﻊ اﻹﺗﺠﺎھﺎت‬ ‫)ﺗﺘﺤﺮك ﻓﻲ ﻛﻞ اﺗﺠﺎه(‬ ‫ وﻟﺘﺒﺴﯿﻂ اﻻﺷﺘﻘﺎق ﻓﺈﻧﮫ ﯾﻤﻜﻦ ﺗﺤﻠﯿﻞ اﻟﺴﺮﻋﺔ )‪ (u‬ﻟﻠﺠﺰﯾﺌﺎت ﻓﻲ أي ﻟﺤﻈﺔ ﻓﻲ ﺛﻼث‬ ‫اﺗﺠﺎھﺎت ﻣﺤﻮرﯾﺔ )‪ (x, y, z‬ﻣﺘﻌﺎﻣﺪة ﻋﻠﻰ ﺑﻌﻀﮭﺎ ﻛﻤﺎ ھﻮ ﻣﺒﯿﻦ ﺑﺎﻟﺸﻜﻞ )‪(٩٨‬‬ ‫وﺑﺎﻟﺘﺎﻟﻲ ﻓـ )‪ (1/3‬اﻟﺠﺰﯾﺌﺎت أي )‪ (1/3)N‬ﯾﺘﺤﺮك ﻓﻲ اﺗﺠﺎه اﻹﺣ ﺪاﺛﻲ ‪ ،X‬وﻣﺜﻠ ﮫ ﻓ ﻲ اﺗﺠ ﺎه‬ ‫اﻹﺣﺪاﺛﻲ ‪ Y‬وآﺧﺮ ﻓ ﻲ اﺗﺠ ﺎه ‪.Z‬وھ ﺬا اﻟﺘﺒ ﺴﯿﻂ ﻻ ﻏﺒ ﺎر ﻋﻠﯿ ﮫ ﺣﯿ ﺚ أن ﺳ ﺮﻋﺔ ﻛ ﻞ ﺟ ﺰيء‬ ‫ﯾﻤﻜﻦ ﺗﺤﻠﯿﻠﮭﺎ اﻟﻰ ﻣﻜﻮﻧﺎﺗﮭﺎ ﻓﻲ اﺗﺠﺎه ﺛﻼﺛﺔ ﻣﺤﺎور ﻋﻤﻮدﯾﺔ ھﻲ ‪.(X, Y, Z) :‬‬ ‫ ﯾﻨﺘﺞ ﺿﻐﻂ اﻟﻐﺎز ﻋﻠﻰ أي ﺟﺪار ﻣ ﻦ ﺟ ﺪران اﻹﻧ ﺎء ﻧﺘﯿﺠ ﺔ اﻹﺻ ﻄﺪاﻣﺎت اﻟﺘ ﻲ ﺗﻘ ﻮم ﺑﮭ ﺎ‬ ‫اﻟﺠﺰﯾﺌﺎت ﻋﻠﻰ ھﺬا اﻟﺠﺪار‪ ،‬وﻣﻦ اﻟﻤﻌﺮوف أن اﻟﻘ ﻮة اﻟﻨﺎﺗﺠ ﺔ ﻋ ﻦ ﻛ ﻞ اﺻ ﻄﺪاﻣﺔ ﯾﻤﻜ ﻦ‬ ‫ﺣﺴﺎﺑﮭﺎ ﻣﻦ ﻣﻌﺮﻓﺘﻨﺎ أن اﻟﻘ ﻮة ﻋﺒ ﺎرة ﻋ ﻦ ﻣﻌ ﺪل ﺗﻐﯿ ﺮ ﻛﻤﯿ ﺔ اﻟﺤﺮﻛ ﺔ ﻣ ﻊ اﻟ ﺰﻣﻦ‪ ،‬وﻣ ﻦ‬ ‫ﻣﻌﺮﻓﺘﻨﺎ ﻟﮭﺬه اﻟﻤﺒﺎديء ﯾﻤﻜﻦ أن ﻧﺸﺘﻖ اﻟﻤﻌﺎدﻟﺔ اﻟﻌﺎﻣﺔ ﻟﻠﻐﺎز اﻟﻤﺜﺎﻟﻲ‪.‬‬ ‫ وﻟﻨﺮﻣﺰ اﻟﻰ اﻟﺴﺮﻋﺎت ﻓﻲ اﻹﺗﺠﺎھﺎت اﻟﺜﻼث ﺑﺎﻟﺮﻣﻮز )‪ (ux, uy, uz‬وﻣﺘﻮﺳﻂ اﻟﺠﺬر‬ ‫اﻟﺘﺮﺑﯿﻌﻲ ﻟﻠﺴﺮﻋﺔ ) ‪( Root Mean Square Velocity u‬‬ ‫‪2‬‬ ‫‪u 2 = u x2 + u 2y + u z2‬‬ ‫ وإذا ﺗﺼﻮرﻧﺎ ﺟﺰﯾﺌﺎً واﺣﺪاً ﯾﺼﻄﺪم ﺑﺠﺪار اﻟﻤﻜﻌﺐ )‪ (A‬أي ﻓﻲ اﺗﺠﺎه اﻟﻤﺤﻮر‬ ‫)اﻹﺣﺪاﺛﻲ( )‪ (x‬وﺑﺴﺮﻋﺔ ﻗﺪرھﺎ )‪.(u m/s‬ھﺬا اﻟﺠﺰيء اﻟﻤﺘﺤﺮك ﻓﻲ ھﺬا اﻹﺗﺠﺎه‬ ‫ﺳﯿﺼﻄﺪم ﺑﺎﻟﺠﺪار اﻟﻤﻈﻠﻞ ﻛﻠﻤﺎ ﻗﻄﻊ ﻣﺴﺎﻓﺔ ‪ 2 L cm‬ﺧﻼل ﻣﺴﺎره وذﻟﻚ ﻷﻧﮫ ﺑﻌﺪ‬ ‫اﻻﺻﻄﺪام ﻻ ﺑﺪ أن ﯾﻘﻄﻊ ﻣﺴﺎﻓﺔ )‪ (L‬ﻟﯿﺼﻞ اﻟﻰ اﻟﺠﺪار اﻟﻤﻘﺎﺑﻞ ﺛﻢ ﯾﻌﻮد ﻣﺴﺎﻓﺔ )‪(L‬‬ ‫)‪(314‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(315‬‬ ‫ﻟﯿﺼﻄﺪم ﻣﺮة أﺧﺮى ﺑﺎﻟﺠﺪار اﻟﻤﻈﻠﻞ أي ﯾﻘﻄﻊ ﻣﺴﺎﻓﺔ ‪ 2 L‬ﻟﯿﺼﻄﺪم ﻣﺮة أﺧﺮى ﺑﻨﻔﺲ‬ ‫اﻟﺠﺪار‪.‬‬ ‫ ﻓﺈذا ﻛﺎن اﻟﺠﺰيء ﯾﺘﺤﺮك ﺑﺴﺮﻋﺔ ‪ u m/s‬ﻓﻤﻌﻨﻰ ذﻟﻚ أﻧﮫ ﺧﻼل ﺛﺎﻧﯿﺔ واﺣﺪة ﯾﻜﻮن ﻗﺪ‬ ‫ﻗﻄﻊ ﻣﺴﺎﻓﺔ ‪u cm‬‬ ‫وﺑﺎﻟﺘﺎﻟﻲ ﻓﺎﻟﺰﻣﻦ اﻟﺬي ﯾﻤﺮ ﻗﺒﻞ أن ﯾﻘﻮم اﻟﺠﺰيء ﺑﻌﻤﻞ اﺻﻄﺪاﻣﺔ ﺛﺎﻧﯿﺔ ﻣﻊ ﻧﻔﺲ وﺟﮫ‬ ‫اﻟﺼﻨﺪوق ﺗﺤﺪده اﻟﻌﻼﻗﺔ ‪:‬‬ ‫اﻟﻤﺴ ﺎﻓﺔ اﻟﻜﻠﯿ ﺔ اﻟﻤﻘﻄﻮﻋ ﺔ‬ ‫‪2L‬‬ ‫= اﻟ ﺰﻣﻦ اﻟﻤﺴ ﺘﻐﺮق‬ ‫=‬ ‫ﺳ ﺮﻋﺔ اﻟﺠﺴ ﯿﻢ‬ ‫‪ux‬‬ ‫ وﺑﺎﻟﺘﺎﻟﻲ ﻓﺈن ﻋﺪد اﻹﺻﻄﺪاﻣﺎت اﻟﺘﻲ ﺳﯿﺤﺪﺛﮭﺎ ﻋﻠﻰ اﻟﺠﺪار اﻟﻤﻈﻠﻞ ﻓﻲ اﻟﺜﺎﻧﯿﺔ اﻟﻮاﺣﺪة‬ ‫)ﻓﻲ وﺣﺪة اﻟﺰﻣﻦ( ﯾﻜﻮن ﻣﺴﺎوﯾﺎً ﻟﻠﻤﺴﺎﻓﺔ اﻟﺘﻲ ﻗﻄﻌﮭﺎ ﻓﻲ اﻟﺜﺎﻧﯿﺔ اﻟﻮاﺣﺪة ﻣﻘﺴﻮﻣﺎً‬ ‫ﻋﻠﻰ اﻟﻤﺴﺎﻓﺔ اﻟﺘﻲ ﯾﻘﻄﻌﮭﺎ ﻟﯿﺤﺪث اﻹﺻﻄﺪاﻣﺔ )ﻣﻘﻠﻮب اﻟﺘﻌﺒﯿﺮ اﻟﺴﺎﺑﻖ(‬ ‫‪ u ‬‬ ‫ﻋﺪد اﻹﺻﻄﺪاﻣﺎت ﻓﻲ اﻟﺜﺎﻧﯿﺔ اﻟﻮاﺣﺪة ‪   collisions/second‬اﺻﻄﺪاﻣﺔ‪/‬ﺛﺎﻧﯿﺔ‬ ‫‪ 2L ‬‬ ‫وﺑﻔﺮض أن ﻋﻤﻠﯿﺔ اﻹﺻﻄﺪام ﻣﺮﻧﺔ ﻓﺈن اﻟﺠﺰيء ﺳﻮف ﯾﺮﺗﺪ ﻓﻲ اﻹﺗﺠﺎه اﻟﻤﻌﺎﻛﺲ ﺑﻨﻔﺲ‬ ‫اﻟﺴﺮﻋﺔ اﻟﺴﺎﺑﻘﺔ )ﻷن اﻻﺻﻄﺪام ﻣﺮن( ﻣﻊ ﻋﻜﺲ اﻹﺷﺎرة )‪ ، (- u‬وﺑﺎﻟﺘﺎﻟﻲ ﻓﺈن ﻛﻤﯿﺔ‬ ‫ﺗﺤﺮك اﻟﺠﺰيء )ﻛﻤﯿﺔ اﻟﺤﺮﻛﺔ ﻟﻠﺠﺰيء( ﻗﺒﻞ اﺻﻄﺪاﻣﮫ ﺑﺎﻟﺴﻄﺢ )اﻟﺠﺪار ‪ (A‬ﻓﻲ اﺗﺠﺎه‬ ‫اﻟﻤﺤﻮر‪ x‬ﺗﺴﺎوي ‪:‬‬ ‫اﻟﻜﺘﻠﺔ × اﻟﺴﺮﻋﺔ‬ ‫‪mu‬‬ ‫وﻛﻤﯿﺔ اﻟﺤﺮﻛﺔ ﺑﻌﺪ اﻻﺻﻄﺪام ﺑﺎﻟﺠﺪار = ‪- mu‬‬ ‫ إذاً اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك ﻟﻠﺠﺰيء ﻓﻲ ﻛﻞ اﺻﻄﺪاﻣﺔ ﻋﻠﻰ اﻟﺴﻄﺢ )‪) (A‬اﻟﺘﻐﯿﺮ ﻓﻲ‬ ‫ﻛﻤﯿﺔ اﻟﺤﺮﻛﺔ ﻟﻺﺻﻄﺪام اﻟﻮاﺣﺪ( ‪:‬‬ ‫‪ = mu - ( - mu) = 2 mu Kg m s-1‬اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺤﺮﻛﺔ ﻓﻲ اﻹﺻﻄﺪاﻣﺔ اﻟﻮاﺣﺪة‬ ‫)‪(315‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(316‬‬ ‫واﻵن ﻓﺈن اﻟﻘﻮة اﻟﺘﻲ ﯾﺆﺛﺮ ﺑﮭﺎ ﺟﺴﯿﻢ وﺣﯿﺪ ﻋﻠﻰ ذﻟﻚ اﻟﻮﺟﮫ ﻣﻦ اﻟﺼﻨﺪوق ﯾﺤﺪدھﺎ ﻣﻌﺪل‬ ‫اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك اﻟﺬي ﯾﻤﺎرﺳﮫ اﻟﺠﺴﯿﻢ )اﻟﻘﺎﻧﻮن اﻟﺜﺎﻧﻲ ﻟﻨﯿﻮﺗﻦ(‪:‬‬ ‫اﻟﻘﻮة = ﻣﻌﺪل اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك‬ ‫وﻟﮭﺬا ﺳﯿﻜﻮن اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك ﻟﻜﻞ ﺛﺎﻧﯿﺔ ﺑﺎﻟﻨﺴﺒﺔ ﻟﺠﺰيء واﺣﺪ ﻟﻠﺴﻄﺢ اﻟﻮاﺣﺪ ﻓﻲ‬ ‫اﻟﺬھﺎب ﯾﺴﺎوي‬ ‫اﻟﻘﻮة اﻟﻨﺎﺗﺠﺔ ﻋﻦ اﺻﻄﺪام ﺟﺰيء واﺣﺪ ﺑﺎﻟﺠﺪار اﻟﻤﻈﻠﻞ =‬ ‫‪ u ‬‬ ‫× اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺤﺮﻛﺔ ﻓﻲ اﻹﺻﻄﺪاﻣﺔ‬ ‫‪‬‬ ‫‪‬‬ ‫ﻋﺪد اﻹﺻﻄﺪاﻣﺎت ﻓﻲ اﻟﺜﺎﻧﯿﺔ اﻟﻮاﺣﺪة‬ ‫‪ 2L ‬‬ ‫اﻟﻮاﺣﺪة )‪(2mu‬‬ ‫‪ u   mu ‬‬ ‫‪2‬‬ ‫‪Force = ( 2 mu )   = ‬‬ ‫‪ kg m s‬‬ ‫‪-1‬‬ ‫‪ 2L   L ‬‬ ‫ وﻋﻨﺪ اﻹﯾﺎب ﺳﻮف ﯾﺘﻌﺮض اﻟﺴﻄﺢ )‪ (B‬اﻟﻤﻘﺎﺑﻞ ﺑﺤﯿﺚ ﯾﺼﺒﺢ اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك‬ ‫ﻟﻜﻞ ﺛﺎﻧﯿﺔ ﻟﻨﻔﺲ اﻟﺠﺰيء ھﻮ ‪:‬‬ ‫‪ mu 2 ‬‬ ‫‪−‬‬ ‫‪‬‬ ‫‪ L ‬‬ ‫ وﺑﺎﻟﺘﺎﻟﻲ ﻓﺈن ﻣﻌﺪل اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك ﻟﻜﻞ ﺛﺎﻧﯿﺔ ﻟﻠﺠﺰيء ﻋﻠﻰ اﻟﺴﻄﺤﯿﻦ اﻟﻤﺘﻘﺎﺑﻠﯿﻦ‬ ‫)‪ (A. B‬ﻋﻠﻰ ﻃﻮل اﻟﻤﺤﻮر ‪ X‬ﯾﺴﺎوي ‪:‬‬ ‫‪mu 2 mu 2 2mu 2x‬‬ ‫‪+‬‬ ‫=‬ ‫‪L‬‬ ‫‪L‬‬ ‫‪L‬‬ ‫ وﺑﺎﻟﻤﺜﻞ ﯾﻤﻜﻦ ﺣﺴﺎب اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك ﻟﻨﻔﺲ اﻟﺠﺰيء ﻓﻲ اﺗﺠﺎه اﻟﻤﺤﻮرﯾﻦ‬ ‫)‪ (y, z‬ﯾﺴﺎوي ‪:‬‬ ‫اﻵﺧﺮﯾﻦ‬ ‫‪2mu 2y 2mu 2z‬‬ ‫‪,‬‬ ‫‪L‬‬ ‫‪L‬‬ ‫)‪(316‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(317‬‬ ‫ﻋﻠﻰ اﻟﺘﻮاﻟﻲ‪.‬‬ ‫ وﯾﺼﺒﺢ اﻟﺘﻐﯿﺮ اﻟﻜﻠﻲ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك ﺑﺎﻟﻨﺴﺒﺔ ﻟﻸوﺟﮫ اﻟﺴﺘﺔ ﻟﻠﻤﻜﻌﺐ ھﻮ ‪:‬‬ ‫‪2‬‬ ‫‪2mu 2x 2mu y 2mu 2z 2m 2‬‬ ‫‪2mu 2‬‬ ‫‪L‬‬ ‫‪+‬‬ ‫‪L‬‬ ‫‪+‬‬ ‫‪L‬‬ ‫=‬ ‫‪L‬‬ ‫‪( u x + u y + uz ) = L Newtons‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫ وﻃﺒﻘﺎً ﻟﻘﺎﻧﻮن ﻧﯿﻮﺗﻦ ﻟﻠﺤﺮﻛﺔ ﻓﺈن ﻣﻌﺪل اﻟﺘﻐﯿﺮ ﻓﻲ ﻛﻤﯿﺔ اﻟﺘﺤﺮك ﯾﻜﻮن ﻣﺴﺎوﯾﺎً ﻟﻠﻘﻮة‬ ‫اﻟﻤﺆﺛﺮة‪ ،‬واﻟﻘﻮة اﻟﻨﺎﺗﺠﺔ ﻋﻦ ﺿﺮﺑﺎت اﻟﺠﺰيء اﻟﻮاﺣﺪ ھﻲ ‪:‬‬ ‫‪2m u 2‬‬ ‫‪Newtons‬‬ ‫‪L‬‬ ‫ واﻟﻘﻮة اﻟﻜﻠﯿﺔ اﻟﻨﺎﺗﺠﺔ ﻋﻦ ﻋﺪد ‪ N‬ﻣﻦ اﻟﺠﺰﯾﺌﺎت ھﻲ ‪:‬‬ ‫‪2 m N u2‬‬ ‫‪L‬‬ ‫ وﺣﯿﺚ أن اﻟﻀﻐﻂ ﯾﻌﺮف ﺑﺄﻧﮫ اﻟﻘﻮة اﻟﺪاﻓﻌﺔ ﻋﻠﻰ وﺣﺪة اﻟﻤﺴﺎﺣﺎت‪:‬‬ ‫‪F 2 m N u2‬‬ ‫= =‪P‬‬ ‫‪A‬‬ ‫‪AL‬‬ ‫ﺣﯿﺚ أن ‪ P‬اﻟﻀﻐﻂ ‪ A ،‬ﻣﺴﺎﺣﺔ ﺳﻄﺢ اﻟﻮﺟﮫ اﻟﻮاﺣﺪ ﻣﻦ اﻟﻤﻜﻌﺐ‪ ،‬وﺣﯿﺚ أن ﻣﺴﺎﺣﺔ أوﺟﮫ‬ ‫اﻟﻤﻜﻌﺐ اﻟﺴﺖ ھﻲ ‪:‬‬ ‫‪A = 6 L2‬‬ ‫وﺑﺎﻟﺘﺎﻟﻲ ‪:‬‬ ‫‪2 m N u2‬‬ ‫‪1‬‬ ‫‪m N u2‬‬ ‫=‪P‬‬ ‫=‬ ‫×‬ ‫‪6 L2 × L‬‬ ‫‪3‬‬ ‫‪L3‬‬ ‫‪L3 = V‬‬ ‫‪1‬‬ ‫‪m N u2‬‬ ‫=‪P‬‬ ‫×‬ ‫‪3‬‬ ‫‪V‬‬ ‫)‪(317‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(318‬‬ ‫أو‬ ‫‪1‬‬ ‫= ‪PV‬‬ ‫‪m N u2‬‬ ‫‪3‬‬ ‫وﺗﻌﺮف ھﺬه اﻟﻤﻌﺎدﻟﺔ ﺑﺎﻟﻤﻌﺎدﻟﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻠﻐﺎزات اﻟﻤﺜﺎﻟﯿﺔ‪.‬‬ ‫وﯾﻤﻜﻦ ﻛﺘﺎﺑﺔ اﻟﺘﻌﺒﯿﺮ اﻷﺧﯿﺮ ﻟﻀﻐﻂ اﻟﻐﺎز ﺑﺼﻮرة ﺑﺪﯾﻠﺔ‪ ،‬ﺣﯿﺚ )‪ (mN‬ھﻲ اﻟﻜﺘﻠﺔ اﻟﻜﻠﯿﺔ‬ ‫ﻟﻠﻐﺎز‪ (V) ،‬ھﻲ اﻟﺤﺠﻢ اﻟﻜﻠﻲ‪ ،‬وﺑﺬﻟﻚ ﻓﺈن اﻟﻜﺜﺎﻓﺔ )‪ (d‬ﺗﺴﺎوي )‪ (mN/V‬وﺗﺼﺒﺢ اﻟﻤﻌﺎدﻟﺔ‬ ‫ﻛﻤﺎ ﯾﻠﻲ ‪:‬‬ ‫‪1‬‬ ‫=‪P‬‬ ‫‪d u2‬‬ ‫‪3‬‬ ‫ﻣﻌﺎﺩﻟﺔ ﺍﻟﻄﺎﻗﺔ ﺍﳊﺮﻛﻴﺔ ﻟﻠﺠﺰﻳﺌﺎﺕ‬ ‫اﻟﺼﯿﻐﺔ اﻟﺮﯾﺎﺿﯿﺔ ‪:‬‬ ‫‪1‬‬ ‫= ‪ke‬‬ ‫‪m u2‬‬ ‫‪2‬‬ ‫ﺣﯿﺚ ‪:‬‬ ‫‪ : ke‬اﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ ﺑﻮﺣﺪة )‪ (J‬ﻟﺠﺰيء واﺣﺪ ﻣﻦ اﻟﻐﺎز‬ ‫‪ : m‬ﻛﺘﻠﺔ اﻟﺠﺰيء اﻟﻮاﺣﺪ ﺑﻮﺣﺪة اﻟﻜﯿﻠﻮﺟﺮام )‪(kg‬‬ ‫‪ : u 2‬ﻣﺘﻮﺳﻂ ﻣﺮﺑﻊ ﺳﺮﻋﺔ اﻟﺠﺰيء ﺑﻮﺣﺪة )‪(m2/s2‬‬ ‫واﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻌﺪد )‪ (N‬ﻣﻦ اﻟﺠﺰﯾﺌﺎت ھﻲ ‪:‬‬ ‫‪1‬‬ ‫= ‪KE‬‬ ‫‪m N u2‬‬ ‫‪2‬‬ ‫)‪(318‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(319‬‬ ‫ﺍﺷﺘﻘﺎﻕ ﻗﻮﺍﻧﲔ ﺍﻟﻐﺎﺯ ﺍﳌﺜﺎﱄ ﻣﻦ ﺍﳌﻌﺎﺩﻟﺔ ﺍﳊﺮﻛﻴﺔ‬ ‫‪Derivation of the Ideal Gas Laws from the Kinetic Equation‬‬ ‫ﺗﻔﺴﲑ ﻧﻈﺮﻳﺔ ﺍﳊﺮﻛﺔ ﻟﻘﺎﻧﻮﻥ ﺑﻮﻳﻞ ﻣﻦ ﺧﻼﻝ ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ‬ ‫إن أھﻢ ﺧﺎﺻﯿﺔ ﻣﻠﻔﺘﺔ ﻟﻠﻨﻈ ﺮ ھ ﻲ ﻗﺎﺑﻠﯿ ﺔ اﻟﻐ ﺎز ﻟﻺﻧ ﻀﻐﺎط‪.‬ﻟ ﺬﻟﻚ‪ ،‬ﯾﺠ ﺐ أن ﺗﻜ ﻮن اﻟﺠﺰﯾﺌ ﺎت‬ ‫اﻟﺘﻲ ﺗﻢ ﺗﺼﻮرھﺎ ﻓﻲ اﻟﻨﻈﺮﯾﺔ اﻟﺠﺰﯾﺌﯿﺔ اﻟﺤﺮﻛﯿﺔ دﻗﯿﻘﺔ ﺟ ﺪاً وﻣﺘﺒﺎﻋ ﺪة ﻋ ﻦ ﺑﻌ ﻀﮭﺎ ﻓ ﻲ اﻟﻐ ﺎز‬ ‫ﺑﺤﯿ ﺚ ﯾﻮﺟ ﺪ ھﻨﺎﻟ ﻚ وﻓ ﺮة ﻓ ﻲ اﻟﺤﯿ ﺰ اﻟﻔ ﺎرغ ﺑﯿﻨﮭ ﺎ‪.‬ﻓﺒﮭ ﺬه اﻟﻄﺮﯾﻘ ﺔ ﻓﻘ ﻂ ﯾﻤﻜ ﻦ أن ﺗﺤ ﺸﺮ‬ ‫اﻟﺠﺰﯾﺌﺎت ﻣﻊ ﺑﻌﻀﮭﺎ ﺑﻌﻀﺎً ﺑﮭﺬه اﻟﺴﮭﻮﻟﺔ‪.‬ﻓﺄﺛﻨﺎء ﺗﻄﺎﯾﺮ ھﺬه اﻟﺠﺴﯿﻤﺎت اﻟﺪﻗﯿﻘﺔ‪ ،‬ﺗﺼﻄﺪم ﻣ ﻊ‬ ‫ﺑﻌﻀﮭﺎ وﺑﺠ ﺪران اﻟﻮﻋ ﺎء‪.‬وﻛ ﻞ ﺗ ﺼﺎدم ﻣ ﻊ اﻟﺠ ﺪار ﯾﻤ ﺎرس دﻓﻌ ﺔ ﺿ ﺌﯿﻠﺔ ﺟ ﺪاً‪.‬واﻟﺘ ﺄﺛﯿﺮات‬ ‫اﻟﻤﺘﺮاﻛﻤﺔ ﻟﻸﻋﺪاد اﻟﻀﺨﻤﺔ ﻓﻲ ﻣﺜﻞ ھﺬه اﻟﺘﺼﺎدﻣﺎت ﻛﻞ ﺛﺎﻧﯿ ﺔ ﻋﻠ ﻰ ﻛ ﻞ ﺳ ﻨﺘﯿﻤﺘﺮ ﻣﺮﺑ ﻊ ﻓ ﻲ‬ ‫اﻟﺠﺪار ﺗﺆدي اﻟﻰ ﺿﻐﻂ اﻟﻐﺎز‪.‬‬ ‫ﯾﻌﺘﻤﺪ اﻟﻀﻐﻂ ﻋﻠﻰ ﻋﺎﻣﻠﯿﻦ ‪(pressure depends on two factors) :‬‬ ‫‪ (١‬ﻋﺪد اﻟﺠﺰﯾﺌﺎت اﻟﺘﻲ ﺗﺮﺗﻄﻢ ﺑﺎﻟﺠﺪران ﻓﻲ وﺣﺪة اﻟﺰﻣﻦ‬ ‫‪The number of molecules striking the walls per unit time‬‬ ‫‪ (٢‬ﻣﺪى ﻗﻮة اﺻﻄﺪام اﻟﺠﺰﯾﺌﺎت ﺑﺎﻟﺠﺪران‬ ‫‪how vigorously the molecules strike the walls‬‬ ‫وﻋﻨﺪ درﺟﺔ ﺣﺮارة ﺛﺎﺑﺘ ﺔ ‪ ،‬ﻓ ﺈن ﻣﺘﻮﺳ ﻂ اﻟ ﺴﺮﻋﺔ )‪ (average speed‬وﻗ ﻮة اﻹﺻ ﻄﺪاﻣﺎت‬ ‫)‪ (force of the collisions‬ﺗﺒﻘﻰ ﻧﻔﺴﮭﺎ )‪.(remain the same‬‬ ‫وﯾﻌﺘﻤﺪ ﺿﻐﻂ اﻟﻐﺎز ﻓﻘﻂ ﻋﻠ ﻰ ﻋ ﺪد اﻟ ﺼﺪﻣﺎت اﻟﺠﺰﯾﺌﯿ ﺔ )‪ (molecular collisions‬ﻟﻜ ﻞ‬ ‫وﺣﺪة ﻣﺴﺎﺣﺔ‬ ‫ﻣﻦ اﻟﺠﺪار ﻟﻜﻞ ﺛﺎﻧﯿﺔ )‪ ،(with the walls per second‬إذا أﺑﻘﯿ ﺖ درﺟ ﺔ اﻟﺤ ﺮارة ﺛﺎﺑﺘ ﺔ‬ ‫ﻟﻜﻲ ﺗﺘﺤﺮك اﻟﺠﺰﯾﺌﺎت ﺑﻨﻔﺲ اﻟﺴﺮﻋﺔ اﻟﻤﺘﻮﺳﻄﺔ‪.‬وﻋﺪد اﻟﺼﺪﻣﺎت ﯾﻌﺘﻤ ﺪ ﻋﻠ ﻰ اﻟﻜﺜﺎﻓ ﺔ )ﻋ ﺪد‬ ‫اﻟﺠﺰﯾﺌ ﺎت ﻓ ﻲ وﺣ ﺪة اﻟﺤﺠ ﻢ ‪.(number of molecules per unit volume‬وﻋﻨ ﺪ‬ ‫)‪(319‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(320‬‬ ‫ﺧﻔﺾ ﺣﺠﻢ اﻟﻐﺎز ﻓﺈن ﻛﺜﺎﻓﺘﮫ ﺗﺰﯾﺪ وﺑﺎﻟﺘﺎﻟﻲ ﯾﺰداد ﻣﻌﺪل اﻟﺘ ﺼﺎدم ﻓﯿ ﺰداد اﻟ ﻀﻐﻂ‪.‬وﻣ ﻦ ھﻨ ﺎ‬ ‫ﻧﺸﺄت اﻟﻌﻼﻗﺔ اﻟﻌﻜﺴﯿﺔ ﺑﯿﻦ اﻟﻀﻐﻂ واﻟﺤﺠﻢ‬ ‫)‪(as volume decreases, pressure increases and vice versa‬‬ ‫وﺑﻤﺜﻞ ھﺬا اﻟﻨﻤﻮذج ﻟﻠﻐﺎز ﻓﻲ ذھﻨﻨﺎ‪ ،‬ﻧﺴﺘﻄﯿﻊ ﺗﻔﺴﯿﺮ ﻗ ﺎﻧﻮن ﺑﻮﯾ ﻞ‪.‬ﻓﻌﻨ ﺪﻣﺎ ﻧ ﺸﻄﺮ ﺣﺠ ﻢ اﻟﻐ ﺎز‬ ‫اﻟ ﻰ ﻧ ﺼﻔﯿﻦ‪ ،‬ﻓ ﻨﺤﻦ ﻧ ﺮص ﺿ ﻌﻒ ﻋ ﺪد اﻟﺠﺰﯾﺌ ﺎت ﻓ ﻲ ﻛ ﻞ ﺳ ﻨﺘﯿﻤﺘﺮ ﻣﻜﻌ ﺐ )ﻋﻨ ﺪﻣﺎ ﯾ ﻨﻘﺺ‬ ‫اﻟﺤﺠ ﻢ ﻻ ﯾﻜ ﻮن ﻟﻠﺠﺰﯾﺌ ﺎت ﻗ ﺪر ﻛﺒﯿ ﺮ ﻣ ﻦ ﺣﺠ ﻢ ﺗﺘﺤ ﺮك ﻓﯿ ﮫ(‪.‬ﻛﻤ ﺎ أن ھﻨ ﺎك اﻵن ﻋﻠ ﻰ ﻛ ﻞ‬ ‫ﺳﻨﺘﯿﻤﺘﺮ ﻣﺮﺑﻊ ﻓﻲ اﻟﺠﺪار ﺟﺰﯾﺌﺎت ﺿﻌﻒ ﻣﺎ ﻛﺎن ﻓﻲ اﻟﺴﺎﺑﻖ‪ ،‬وﻟﺬﻟﻚ ﯾﺠﺐ أن ﯾﻜﻮن ﺿ ﻌﻒ‬ ‫ﻋﺪد ﺗﺼﺎدﻣﺎت اﻟﺠﺰﯾﺌﺎت ﻣﻊ اﻟﺠﺪار ﻓﻲ ﻛﻞ ﺛﺎﻧﯿﺔ )ﺗﺼﻄﺪم اﻟﺠﺰﯾﺌ ﺎت ﻣ ﻊ اﻟﺠ ﺪران ﺑﺘﻜ ﺮار‬ ‫أﻛﺜ ﺮ‪ ،‬وﺑ ﺬﻟﻚ ﻓ ﺈن اﻟﺠ ﺪران ﺗ ﺴﺘﻘﺒﻞ ﺻ ﺪﻣﺎت أﻛﺜ ﺮ ﻟﻜ ﻞ ﺛﺎﻧﯿ ﺔ(‪.‬وھ ﺬا ﯾﻌﻨ ﻲ أن اﻟ ﻀﻐﻂ‬ ‫ﯾﺘﻀﺎﻋﻒ )اﻟﻀﻐﻂ ﯾﻜﻮن أﻛﺒﺮ ﻓﻲ ﺣﺠﻢ أﺻﻐﺮ( ﻛﻤﺎ ھﻮ ﻣﻮﺿﺢ ﺑﺎﻟﺸﻜﻞ )‪.(٩٩‬‬ ‫ﺷﻜﻞ ‪٩٩‬‬ ‫)‪(320‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(321‬‬ ‫ﺷﻜﻞ ‪ : ١٠٠‬ﺗﻮزﯾﻊ اﻟﻄﺎﻗﺔ ﻓﻲ ﻏﺎز ﻋﻨﺪ درﺟﺔ ﺣﺮارة‬ ‫إذا ﻛ ﺎن ﺗﻨ ﺼﯿﻒ اﻟﺤﺠ ﻢ ﯾ ﻀﺎﻋﻒ اﻟ ﻀﻐﻂ‪ ،‬ﻋﻨﺪﺋ ﺬ اﻟ ﻀﻐﻂ واﻟﺤﺠ ﻢ ﯾﺘﻨﺎﺳ ﺒﺎن ﻋﻜ ﺴﯿﺎً ﻣ ﻊ‬ ‫ﺑﻌﻀﮭﻤﺎ ﺑﻌﻀﺎً‪ ،‬وھﺬه اﻟﻌﺒﺎرة ھﻲ ﻗﺎﻧﻮن ﺑﻮﯾﻞ‪.‬‬ ‫إن اﻟﻐﺎز اﻟﻤﺜﺎﻟﻲ‪ ،‬ﻛﻤﺎ ﺗﺬﻛﺮ‪ ،‬ﯾﺨﻀﻊ ﻟﻘﺎﻧﻮن ﺑﻮﯾﻞ ﺗﻤﺎﻣﺎً ﺗﺤﺖ ﻛﺎﻓﺔ اﻟﻈﺮوف‪.‬وھﺬا ﯾﻌﻨ ﻲ أﻧ ﮫ‬ ‫ﻣﮭﻤ ﺎ ﻛﺎﻧ ﺖ اﻟﺠﺰﯾﺌ ﺎت ﻣﺮﺻﻮﺻ ﺔ ﺑﺈﺣﻜ ﺎم‪ ،‬ﺳ ﯿﻜﻮن داﺋﻤ ﺎً ﻣ ﻦ اﻟﻤﻤﻜ ﻦ ﺗﻨ ﺼﯿﻒ ﺣﺠﻤﮭ ﺎ‬ ‫ﺑﻤ ﻀﺎﻋﻔﺔ اﻟ ﻀﻐﻂ‪.‬واﻟﻄﺮﯾﻘ ﺔ اﻟﻮﺣﯿ ﺪة اﻟﺘ ﻲ ﯾﻤﻜ ﻦ ﺑﮭ ﺎ ﺣ ﺪوث ذﻟ ﻚ ﻣ ﺮة ﺑﻌ ﺪ أﺧ ﺮى‪ ،‬ھ ﻲ‬ ‫ﺑﺎﻟﻄﺒﻊ إذا ﻛﺎن اﻟﻐﺎز ﻣﻜﻮﻧﺎً ﻣﻦ ﺟ ﺴﯿﻤﺎت ﻟ ﯿﺲ ﻟﮭ ﺎ ﺣﺠ ﻢ‪ ،‬ﺑﺤﯿ ﺚ أن اﻟﺤﺠ ﻢ ﻛﻠ ﮫ ﻋﺒ ﺎرة ﻋ ﻦ‬ ‫ﺣﯿﺰ ﻓﺮاغ‪.‬وﻟﻜﻦ اﻟﺠﺰﯾﺌﺎت اﻟﺤﻘﯿﻘﯿﺔ ﻟﮭﺎ أﺣﺠﺎم ﻣﺤﺪدة‪ ،‬وھﻜﺬا ﻻ ﯾﻤﻜﻦ ﻷي ﻏ ﺎز ﺣﻘﯿﻘ ﻲ أن‬ ‫ﯾﺨﻀﻊ ﻟﻘﺎﻧﻮن ﺑﻮﯾﻞ ﺗﻤﺎﻣﺎً‪ ،‬ﺧﺎﺻﺔ ﺗﺤﺖ ﺿﻐﻂ ﻋﺎل‪.‬‬ ‫ً‬ ‫ﺇﺛﺒﺎﺕ ﻗﺎﻧﻮﻥ ﺑﻮﻳﻞ ﺭﻳﺎﺿﻴﺎ ‪:‬‬ ‫ﻃﺒﻘﺎً ﻟﻠﻨﻈﺮﯾﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻠﺠﺰﯾﺌﺎت ﺗﺘﻨﺎﺳﺐ اﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻠﺠﺰﯾﺌﺎت ﻃﺮدﯾﺎً ﻣﻊ درﺟﺔ‬ ‫اﻟﺤﺮارة اﻟﻤﻄﻠﻘﺔ ﻟﻠﻐﺎز أي أن ‪:‬‬ ‫)‪(321‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  (322) 1 m u 2 α T (Kelvin) 2 1 m N u 2 α NT 2 1 m N u 2 = KT N..................( × 2/3) 2 21 2 2  m N u = K T N 32  3 21 2 2 PV =  m N u  = KT N 32  3 2 PV = K T N 3 at constant T, N ⇒ PV= constant : ‫ﻃﺮﻳﻖ ﺇﺛﺒﺎﺕ ﺃﺧﺮﻯ‬ 1 T(Kelvin) α mc2 2 1 ⇒ PV = Nmc 2 3 2N  1 2  PV =  mc  3 2  1 ⇒ T α mc 2 2 PV α NT PV = const (for fixed N and T) ⇒ PV = nRT (322) PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com  ‫)‪(323‬‬ ‫‪ -٢‬ﺗﻔﺴﲑ ﻧﻈﺮﻳﺔ ﺍﳊﺮﻛﺔ ﻟﻘﺎﻧﻮﻥ ﺗﺸﺎﺭﻟﺰ ﻣﻦ ﺧﻼﻝ ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ ‪:‬‬ ‫ﯾ ﻨﺺ ھ ﺬا اﻟﻘ ﺎﻧﻮن ﺑ ﺄن اﻟﺤﺠ ﻢ ﯾ ﺰداد ﻋﻨ ﺪ رﻓ ﻊ درﺟ ﺔ اﻟﺤ ﺮارة ﺑ ﺸﺮط إﺑﻘ ﺎء اﻟ ﻀﻐﻂ ﺛﺎﺑﺘ ﺎً‪.‬‬ ‫وﻟﻘﺪ رأﯾﻨﺎ ﻟﻠﺘﻮ أن رﻓﻊ درﺟ ﺔ اﻟﺤ ﺮارة ﯾﺘ ﺴﺒﺐ ﻓ ﻲ ﺟﻌ ﻞ ﻋ ﺪد أﻛﺜ ﺮ ﻣ ﻦ اﻟﺠﺰﯾﺌ ﺎت ﯾ ﺼﻄﺪم‬ ‫ﺑﺎﻟﺠﺪار ﻓﻲ ﻛﻞ ﺛﺎﻧﯿﺔ )اﻟﺘﺄﺛﯿﺮ اﻟﻨﺎﺗﺞ ﻋﻦ رﻓﻊ درﺟﺔ اﻟﺤﺮارة ﺑﺎﻟﻨﺴﺒﺔ ﻟﻐﺎز ھ ﻮ زﯾ ﺎدة ﻣﺘﻮﺳ ﻂ‬ ‫ﻃﺎﻗﺔ اﻟﺤﺮﻛﺔ ﻟﻠﺠﺰﯾﺌﺎت(‪،‬‬ ‫‪the average kinetic energy is directly proportional to the absolute temperature.‬‬ ‫وﯾﺘﺴﺒﺐ أﯾﻀﺎً ﻓﻲ ﺟﻌﻞ ﻗﻮة ﺻﺪﻣﺔ اﻟﺠﺰﯾﺌﺎت ﻣﻊ اﻟﺠﺪران ﺗﺰداد ﺑ ﺴﺒﺐ اﻟﺰﯾ ﺎدة ﻓ ﻲ ﻣﺘﻮﺳ ﻂ‬ ‫اﻟﻄﺎﻗ ﺔ اﻟﺤﺮﻛﯿ ﺔ ﻟﻠﺠﺰﯾﺌ ﺎت‪ ،‬ﺑﺤﯿ ﺚ ﯾ ﺆدي اﻟ ﻰ ﻣﻌ ﺪل أﻛﺒ ﺮ ﻓ ﻲ ﺗﻐﯿ ﺮ ﻛﻤﯿ ﺔ اﻟﺘﺤ ﺮك )ﻋﻨ ﺪﻣﺎ‬ ‫ﺗﺘﺤﺮك اﻟﺠﺰﯾﺌﺎت وھﻲ ﻣﺰودة ﺑﻄﺎﻗﺔ أﻛﺒﺮ ﻓﺈﻧﮭﺎ ﺗﺮﺗﻄﻢ ﺑﺠﺪران اﻹﻧﺎء اﻟﺤﺎوي ﺑﺘﻜ ﺮار أﻛﺜ ﺮ‬ ‫وﺑﻨﺸﺎط أﻛﺜﺮ ﻣﺤﺪﺛﺔ ﺑﺬﻟﻚ ﺿﻐﻄﺎً أﻛﺒﺮ‪ ،‬ﻣﻤﺎ ﯾﻨﺘﺞ ﻋﻨﮫ زﯾﺎدة ﻓﻲ اﻟﻀﻐﻂ(‪.‬‬ ‫‪Doubling the absolute temperature of a sample of gas doubles the average‬‬ ‫‪kinetic energy of the gaseous molecules, and the increasing force of the‬‬ ‫‪collisions of molecules with the walls doubles the volume at constant‬‬ ‫‪pressure.‬‬ ‫واﻟﻄﺮﯾﻘﺔ اﻟﻮﺣﯿﺪة ﻟﻠﻤﺤﺎﻓﻈﺔ ﻋﻠﻰ ﺛﺒﺎت اﻟﻀﻐﻂ ھ ﻮ ﺗﺨﻔ ﯿﺾ ﻋ ﺪد اﻹﺻ ﻄﺪاﻣﺎت ﻓ ﻲ اﻟﺜﺎﻧﯿ ﺔ‬ ‫اﻟﻮاﺣ ﺪة ﻣ ﻊ ﻛ ﻞ ﺳ ﻨﺘﯿﻤﺘﺮ ﻣﺮﺑ ﻊ ﻣ ﻦ اﻟﺠ ﺪار‪.‬وﺑﺎﻹﻣﻜ ﺎن ﺗﺤﻘﯿ ﻖ ھ ﺬا ﺑﺎﻟ ﺴﻤﺎح ﻟﻠﻐ ﺎز ﺑﺎﻟﺘﻤ ﺪد‬ ‫ﻓﯿﺘﻮاﺟ ﺪ ﻋ ﺪد أﻗ ﻞ ﻣ ﻦ اﻟﺠﺰﯾﺌ ﺎت ﻋﻠ ﻰ ﻛ ﻞ ﺳ ﻨﺘﯿﻤﺘﺮ ﻣﺮﺑ ﻊ ﻣ ﻦ اﻟﺠ ﺪار‪.‬وﺑﺘﻌﺒﯿ ﺮ آﺧ ﺮ‪،‬‬ ‫ﻓﻠﻠﻤﺤﺎﻓﻈﺔ ﻋﻠﻰ ﺿﻐﻂ اﻟﻐﺎز ﺛﺎﺑﺘﺎً ﻋﻨﺪﻣﺎ ﻧﺮﻓﻊ درﺟ ﺔ ﺣﺮارﺗ ﮫ‪ ،‬ﻋﻠﯿﻨ ﺎ أن ﻧ ﺴﻤﺢ ﻟ ﮫ ﺑﺎﻟﺘﻤ ﺪد‬ ‫وإﺷﻐﺎل ﺣﺠﻢ أﻛﺒﺮ )وھﺬا اﻟﺘﻤﺪد ﯾﻜ ﻮن ﻓ ﻲ اﻟﺠ ﺪران اﻟﻤﺮﻧ ﺔ ﺣﯿ ﺚ ﯾﺘﻤ ﺪد اﻟﻐ ﺎز ﻟﻜ ﻲ ﯾ ﺸﻐﻞ‬ ‫ﺣﺠﻤﺎً أﻛﺒﺮ‪ ،‬وﺑﺬﻟﻚ ﯾﺤﺘﻔﻆ اﻟﻐﺎز ﺑﺎﻟﻀﻐﻂ اﻹﺑﺘﺪاﺋﻲ وﯾ ﺴﺘﻤﺮ اﻟﺘﻤ ﺪد ﻓ ﻲ ﺣﺠ ﻢ اﻟﻮﻋ ﺎء ﺣﺘ ﻰ‬ ‫ﯾﻌﺎدل ﺿﻐﻂ اﻟﻐﺎز ﻣﻊ اﻟﻀﻐﻂ اﻟﺜﺎﺑﺖ اﻟﺨﺎرﺟﻲ‬ ‫‪The volume of gas will expand until the gas pressure is balanced by the‬‬ ‫‪constant external pressure.‬‬ ‫)‪(323‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(324‬‬ ‫واﻟ ﺸﻜﻞ )‪ (١٠١‬ﯾﻮﺿ ﺢ أﻧ ﮫ إذا ﻛ ﺎن اﻟ ﻀﻐﻂ ﻋﻠ ﻰ اﻟﺒ ﺎﻟﻮن ﺛﺎﺑﺘ ﺎً‪ ،‬ﻓ ﻲ ﺣ ﯿﻦ ﺗﺮﻓ ﻊ درﺟ ﺔ‬ ‫اﻟﺤﺮارة‪ ،‬ﻓﺈن اﻟﻐﺎز ﯾﻤﺪد اﻟﺒﺎﻟﻮن إﻟﻰ ﺣﺠﻢ أﻛﺒﺮ‪ ،‬وﯾﺤﺪث ﻓﯿﮫ ﺗﻌﻮﯾﺾ ﻣﻦ اﻟﺤﺮﻛ ﺔ اﻟﺠﺰﯾﺌﯿ ﺔ‬ ‫اﻷﻛﺜﺮ ﻧﺸﺎﻃﺎً‪.‬‬ ‫ﺷﻜﻞ ‪ : ١٠١‬ﺗﻔﺴﯿﺮ ﻧﻈﺮﯾﺔ اﻟﺤﺮﻛﺔ ﻟﻘﺎﻧﻮن ﺗﺸﺎرﻟﺰ‬ ‫واﻵن‪ ،‬دﻋﻨﺎ ﻧﺘﺄﻣﻞ ﻓﯿﻤﺎ ﯾﺤﺪث ﻋﻨ ﺪ ﺗﺒﺮﯾ ﺪ ﻏ ﺎز ﻣ ﺎ‪.‬ﻓ ﺈذا اﺗﺒﻌﻨ ﺎ اﻟﺘﻌﻠﯿ ﻞ ﻧﻔ ﺴﮫ ﻛﻤ ﺎ ﻓ ﻲ اﻟﻔﻘ ﺮة‬ ‫اﻟﺴﺎﺑﻘﺔ‪ ،‬ﻓﺈﻧﻨﺎ ﻧﺠﺪ أﻧﮫ ﺣﺘﻰ ﻧﺤ ﺎﻓﻆ ﻋﻠ ﻰ ﺛﺒ ﺎت اﻟ ﻀﻐﻂ ﻋﻨ ﺪﻣﺎ ﯾﺒ ﺮد اﻟﻐ ﺎز‪ ،‬ﻓﺈﻧ ﮫ ﯾﺠ ﺐ ﻋﻠﯿﻨ ﺎ‬ ‫إﻧﻘﺎص اﻟﺤﺠﻢ‪.‬ﻓﺎﻟﺠﺰﯾﺌﺎت ﺗﺘﺤﺮك ﺑﺒﻂء أﻛﺜﺮ ﻓﺄﻛﺜﺮ‪ ،‬واﻟﺤﯿﺰ ﺑﯿﻨﮭﺎ ﯾﺼﺒﺢ أﻗﻞ ﺗﺪرﯾﺠﯿﺎً‪.‬‬ ‫‪Halving the absolute temperature decreases kinetic energy to half its original‬‬ ‫‪value, at constant pressure, the volume decreases by half because of the‬‬ ‫‪reduced vigor of the collision of gaseous molecules with the container walls.‬‬ ‫وﻓ ﻲ آﺧ ﺮ اﻷﻣ ﺮ‪ ،‬ﺗﺘﻜﺜ ﻒ ﺟﻤﯿ ﻊ اﻟﻐ ﺎزات اﻟﺤﻘﯿﻘﯿ ﺔ ﻟﺘﻜ ﻮن ﺳ ﺎﺋﻼً‪ ،‬ﻋﻨ ﺪﻣﺎ ﯾ ﺘﻢ ﺗﺒﺮﯾ ﺪھﺎ ‪ ،‬ﻷن‬ ‫ﻗ ﻮى اﻟﺘﺠ ﺎذب ﺑ ﯿﻦ اﻟﺠﺰﯾﺌ ﺎت ﺗ ﺴﺒﺐ ﻓ ﻲ ﻧﮭﺎﯾ ﺔ اﻷﻣ ﺮ اﺻ ﻄﺪاﻣﺎت "ﻟﺰﺟ ﺔ" ‪.‬إﻻ أن اﻟﻐ ﺎز‬ ‫)‪(324‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(325‬‬ ‫اﻟﻤﺜﺎﻟﻲ ﻻ ﯾﺘﻜﺜﻒ ﺑﻐﺾ اﻟﻨﻈﺮ ﻋﻦ ﻛﻤﯿﺔ اﻟﺘﺒﺮﯾﺪ اﻟﺘﻲ ﻧﻘﻮم ﺑﮭﺎ‪ ،‬وﻣﻦ ھﻨﺎ ﻓﺈن ﺧﺎﺻ ﯿﺔ أﺧ ﺮى‬ ‫" ﻟﺠﺰﯾﺌﺎت" اﻟﻐﺎز اﻟﻤﺜﺎﻟﻲ ھﻲ أﻧﮫ ﻟﯿﺲ ﻟﺪﯾﮭﺎ ﻗ ﻮى ﺗﺠ ﺎذب ﺑ ﯿﻦ ﺟﺰﯾﺌﯿ ﺔ‪.‬ﻓﺎﻟﻐ ﺎز اﻟﻤﺜ ﺎﻟﻲ إذاً‬ ‫ﻣﺎدة اﻓﺘﺮاﺿﯿﺔ ﻟﯿﺲ ﻟﺠﺰﯾﺌﺎﺗﮭﺎ ﺣﺠﻢ وﻻ ﻗﻮى ﺗﺠﺎذب "ﺑﯿﻦ ﺟﺰﯾﺌﯿﺔ"‪.‬‬ ‫ﺷﻜﻞ ‪١٠٢‬‬ ‫ً‬ ‫ﺇﺛﺒﺎﺕ ﻗﺎﻧﻮﻥ ﺗﺸﺎﺭﻟﺰ ﺭﻳﺎﺿﻴﺎ ‪:‬‬ ‫‪2‬‬ ‫= ‪PV‬‬ ‫‪KTN‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪KTN‬‬ ‫=‪V‬‬ ‫×‬ ‫‪3‬‬ ‫‪P‬‬ ‫‪V‬‬ ‫‪2‬‬ ‫‪KN‬‬ ‫=‬ ‫×‬ ‫‪T‬‬ ‫‪3‬‬ ‫‪P‬‬ ‫‪at constant P, N‬‬ ‫‪V‬‬ ‫‪= constant‬‬ ‫‪T‬‬ ‫)‪(325‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(326‬‬ ‫)ﻗﺎﻧﻮﻥ ﺍﻟﻀﻐﻂ(‬ ‫‪ -٣‬ﺇﺛﺒﺎﺕ ﻗﺎﻧﻮﻥ ﻏﺎﻱ ﻟﻮﺳﺎﻙ )ﺃﻭ ﺁﻣﻮﻧﺘﻮﻧﺰ( ‪:‬‬ ‫‪P‬‬ ‫‪= constant‬‬ ‫‪T‬‬ ‫ﯾﻨﺺ ھ ﺬا اﻟﻘ ﺎﻧﻮن أﻧ ﮫ إذا أﺑﻘﯿﻨ ﺎ اﻟﺤﺠ ﻢ ﺛﺎﺑﺘ ﺎً‪ ،‬ﯾﺘﻨﺎﺳ ﺐ اﻟ ﻀﻐﻂ ﻣﺒﺎﺷ ﺮة ﻣ ﻊ درﺟ ﺔ اﻟﺤ ﺮارة‬ ‫اﻟﻤﻄﻠﻘ ﺔ‪.‬وﺑﻌﺒ ﺎرة أﺧ ﺮى‪ ،‬ﻋﻨ ﺪﻣﺎ ﺗ ﺰداد درﺟ ﺔ اﻟﺤ ﺮارة‪ ،‬ﯾ ﺰداد اﻟ ﻀﻐﻂ أﯾ ﻀﺎً‪.‬ﻓﻜﯿ ﻒ‬ ‫ﺑﻤﻘﺪورﻧﺎ ﺗﻔ ﺴﯿﺮ ھ ﺬا؟ ﺑﻤﻮﺟ ﺐ اﻟﻨﻈﺮﯾ ﺔ اﻟﺤﺮﻛﯿ ﺔ‪ ،‬ﯾ ﺆدي رﻓ ﻊ درﺟ ﺔ اﻟﺤ ﺮارة اﻟ ﻰ ازدﯾ ﺎد‬ ‫ﻣﺘﻮﺳﻂ اﻟﻄﺎﻗ ﺔ اﻟﺤﺮﻛﯿ ﺔ ﻟﻠﺠﺰﯾﺌ ﺎت وھﻜ ﺬا ﺗﺘﺤ ﺮك اﻟﺠﺰﯾﺌ ﺎت ﺑ ﺴﺮﻋﺔ أﻋﻠ ﻰ )ﺑﺰﯾ ﺎدة درﺟ ﺔ‬ ‫اﻟﺤﺮارة ﺳﻮف ﯾﺰداد ﻣﺘﻮﺳﻂ اﻟﻄﺎﻗﺔ اﻟﺤﺮﻛﯿﺔ ﻟﻠﺠﺰﯾﺌﺎت ﻣﻤﺎ ﯾﺆدي اﻟﻰ زﯾﺎدة ﻓﻲ اﻟﺘﻐﯿ ﺮ ﻓ ﻲ‬ ‫ﻛﻤﯿﺔ اﻟﺘﺤﺮك ﻋﻨﺪ ﺟﺪران اﻟﻮﻋﺎء اﻟﺤ ﺎوي ﺛﺎﺑ ﺖ اﻟﺤﺠ ﻢ‪ ،‬واﻟﻨﺘﯿﺠ ﺔ ھ ﻲ زﯾ ﺎدة ﻓ ﻲ اﻟ ﻀﻐﻂ(‪.‬‬ ‫وھﺬا ﯾﻌﻨﻲ أﻧﮭ ﺎ ﺳﺘ ﺼﻄﺪم ﺑﺎﻟﺠ ﺪار ﻋ ﺪداً أﻛﺜ ﺮ ﻣ ﻦ اﻟﻤ ﺮات وأﻧ ﮫ ﻋﻨ ﺪ اﺻ ﻄﺪاﻣﮭﺎ ﺑﺎﻟﺠ ﺪار‬ ‫ﺳ ﯿﻜﻮن ﻣﺘﻮﺳ ﻂ ﻗ ﻮة اﻟ ﺼﺪﻣﺔ أﻛﺒ ﺮ‪.‬ﻓﺘ ﺆدي ھ ﺬه اﻟﻌﻮاﻣ ﻞ اﻟ ﻰ ازدﯾ ﺎد اﻟ ﻀﻐﻂ‪.‬وﻋ ﺎدة ﻣ ﺎ‬ ‫ﯾﻼﺣﻆ ھﺬا اﻟﺘﺄﺛﯿﺮ ﺑﺎﻟﻨﺴﺒﺔ ﻹﻃﺎر اﻟﺴﯿﺎرة ﺣﯿﺚ ﯾﻜﻮن اﻟﻐﺎز ﻣﺤﺼﻮراً ﻓﻲ ﺣﺠﻢ ﺛﺎﺑﺖ ﺗﻘﺮﯾﺒ ﺎً‪.‬‬ ‫وﻧﺘﯿﺠﺔ ﻟﻈﺮوف اﻹﺣﺘﻜﺎك واﻧﺜﻨﺎﺋﯿﺔ اﻟﻤﻄﺎط‪ ،‬ﻓﺈن اﻟﮭ ﻮاء داﺧ ﻞ اﻹﻃ ﺎر ﺳ ﻮف ﺗ ﺰداد درﺟ ﺔ‬ ‫ﺣﺮارﺗﮫ وﯾﺘﻌﺎﻇﻢ اﻟﻀﻐﻂ‪.‬‬ ‫‪ -٤‬ﺇﺛﺒﺎﺕ ﻗﺎﻧﻮﻥ ﺃﻓﻮﺟﺎﺩﺭﻭ ﻣﻦ ﺧﻼﻝ ﺍﻟﻨﻈﺮﻳﺔ ﺍﳊﺮﻛﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ ‪::‬‬ ‫إن اﻷﺣﺠﺎم اﻟﻤﺘﺴﺎوﯾﺔ ﻟﻠﻐﺎز‪ ،‬ﺗﺤﺖ ﻧﻔﺲ درﺟﺔ اﻟﺤ ﺮارة واﻟ ﻀﻐﻂ‪ ،‬ﺗﺤﺘ ﻮي أﻋ ﺪاداً ﻣﺘ ﺴﺎوﯾﺔ‬ ‫ﻣﻦ اﻟﺠﺰﯾﺌﺎت‪.‬وھﺬا ھﻮ ﻣﺒ ﺪأ أﻓﻮﺟ ﺎدرو اﻟ ﺬي ﯾﻤﻜ ﻦ أن ﻧﻌﺮﺿ ﮫ ﺑﻄﺮﯾﻘ ﺔ أﺧ ﺮى ﻛﻤ ﺎ ﯾﻠ ﻲ ‪:‬‬ ‫اﻷﻋﺪاد اﻟﻤﺘﺴﺎوﯾﺔ ﻣﻦ ﺟﺰﯾﺌﺎت اﻟﻐﺎز اﻟﺘﻲ ﺗﺸﻐﻞ اﻟﺤﺠ ﻢ ﻧﻔ ﺴﮫ ﻋﻨ ﺪ درﺟ ﺔ اﻟﺤ ﺮارة ﻧﻔ ﺴﮭﺎ‬ ‫ﺗﻤﺎرس اﻟﻀﻐﻂ ﻧﻔﺴﮫ‪.‬وﯾﻤﻜﻦ ﺗﻔﺴﯿﺮ ھﺬا ﺑﺎﻹﺷ ﺎرة اﻟ ﻰ أن ﻣﺘﻮﺳ ﻂ ﻗ ﻮة اﻟ ﺼﺪﻣﺔ ﻟﻠﺠﺰﯾﺌ ﺎت‬ ‫اﻟﺘﻲ ﺗﺼﻄﺪم ﻣﻊ ﻣ ﺴﺎﺣﺔ ﻣﻌﯿﻨ ﺔ ﻣ ﻦ اﻟﺠ ﺪار ﺗﻌﺘﻤ ﺪ ﻋﻠ ﻰ ﻣﺘﻮﺳ ﻂ ﻃﺎﻗﺘﮭ ﺎ اﻟﺤﺮﻛﯿ ﺔ‪ ،‬وﺑﺎﻟﺘ ﺎﻟﻲ‬ ‫ﻋﻠ ﻰ درﺟ ﺔ ﺣﺮارﺗﮭ ﺎ‪.‬ﻓ ﺈذا ﻛﺎﻧ ﺖ درﺟﺘ ﺎ ﺣ ﺮارة ﻋﯿﻨﺘ ﻲ ﻏ ﺎز ﻣﺘﻤ ﺎﺛﻠﺘﯿﻦ‪ ،‬ﻋﻨﺪﺋ ﺬ ﯾﺠ ﺐ أن‬ ‫ﯾﺘ ﺴﺎوى ﻣﺘﻮﺳ ﻂ اﻟﻄﺎﻗ ﺔ اﻟﺤﺮﻛﯿ ﺔ ﻟﺠﺰﯾﺌﺎﺗﮭ ﺎ‪ ،‬وإذا ﻛ ﺎن ﻋ ﺪد اﻟﺠﺰﯾﺌ ﺎت ﻓ ﻲ وﺣ ﺪة اﻟﺤﺠ ﻢ‬ ‫ﻣﺘﻤﺎﺛﻼً‪ ،‬ﻓﻌﻨﺪﺋﺬ‪ ،‬ﯾﺘﺒﻊ ذﻟﻚ أن ﺿﻐﻄﯿﮭﻤﺎ ﯾﺠﺐ أﯾﻀﺎً أن ﯾﻜﻮﻧﺎ ﻣﺘﻤﺎﺛﻠﯿﻦ‪.‬‬ ‫)‪(326‬‬ ‫‪PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com‬‬  ‫)‪(327‬‬ ‫ً‬ ‫ﺇﺛﺒﺎﺕ ﻗﺎﻧﻮﻥ ﺃﻓﻮﺟﺎﺩﺭﻭ ﺭﻳﺎﺿﻴﺎ ‪:‬‬ ‫ﻧﻔﺘﺮض أن ﻟﺪﯾﻨﺎ ﻏﺎزﯾﻦ )‪ (1, 2‬ﻣﺘﺴﺎوﯾﯿﻦ ﻓﻲ اﻟﺤﺠﻢ واﻟﻀﻐﻂ وﻃﺒﻘﺎً ﻟﻔﺮض أﻓﻮﺟﺎدرو‬ ‫ﻓﺈﻧﮭﻤﺎ ﯾﺤﺘﻮﯾﺎن ﻋﻠﻰ ﻧﻔﺲ اﻟﻌﺪد ﻣﻦ اﻟﺠﺰﯾﺌﺎت وﻹﺛﺒﺎت ذﻟﻚ ﻓﺈن‪:‬‬ ‫‪1‬‬ ‫‪P1V1 = m1 N1u12‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪P2 V2 = m 2 N 2 u 22‬‬ ‫‪3‬‬ ‫وﺑﻔﺮض ﺗﺴﺎوي اﻟﻐﺎزﯾﻦ ﻓﻲ اﻟﻀﻐﻂ واﻟﺤﺠﻢ ﻓﺈن ‪:‬‬ ‫‪P1V1 = P2V2‬‬ ‫أي أن ‪:‬‬ ‫‪1‬‬ ‫‪1‬‬ ‫)‪m1N1u12 = m 2 N 2 u 22.............( × 3‬‬ ‫‪3‬‬