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Уважаемые эксперты, помогите решить задачу! Температура водорода 300 К. Определить, какую часть от общего числа молекул составляют молекулы, модули скоростей которых отличаются от наиболее вероятной не более чем на 5 м/с. http://s004.radikal.ru/i206/1002/9b/52f9175659af.jpg
наиболее вероятная скорость vp=[$8730$](2RT/M)=1579,3 м/с≈1580 м/с Распределение Максвелла 4п*(M/2пRT)1,5*v2*e-Mv²/2RT Требуется проинтегрировать его от 1575 до 1585 м/с Так как аналитического интеграла выражения подобного типа не имеют, придётся делать приближения. Экспоненциальная часть при малом изменении аргумента практически не меняется (в данном случае на концах интервала разница чуть больше 1%), поэтому рассматриваем её как постоянную. Более того, подставив в выражение в показателе v=vp, получаем там -1. 15751585[$8747$]4п*(M/2пRT)1,5*v2*e-Mv²/2RT dv≈15751585[$8747$]4п*(M/2пRT)1,5*v2*e-1 dv= =4п*(M/2пRT)1,5*(15853-15753)/3*e-1= =4п*(0,002кг/моль/(2п*8,314Дж/(моль*К)*300К))1,5*(15853-15753(м/с)[sup]3[/sup])/3*e-1=0,00526=0,526%
Примечание: результат практически не отличается, если просто умножить значение функции распределения Максвелла при vp на [$916$]v=10 м/с
Неизвестный
26.02.2010, 15:07
общий
А что происходит с v2 , откуда 3 степень у 1585-1575, что такое e и чему оно равно, и п - это 3,14 ? , скажите пожалуйста.
Химик CH: Да , но вы думаете я бы к вам обратился, если бы с такой лёгкостью владел и решал интегралы и дифференцирование! А так как у вас платное решение задач то на пару вопросов могли бы ответить, тем более что, я смотрю вы такие задачки как орешки...
Проинтегрировали (потому и спрашивал, вдруг не проходили): v[size=1]1[/size]v[size=1]2[/size][$8747$]v2dv=v3/3 |v[size=1]1[/size]v[size=1]2[/size]=(v23-v13)/3
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