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Задать вопрос экспертам

Консультация № 146539

09.10.2008, 08:45

0.00 руб.

0 1 1

Образование

Привет,буду очень признателен если поможите с одной проблемкой)

. Какая часть молекул кислорода при 0 0С обладает скоростью от 100 м/с до 110 м/с?

в заранее благодарен, спасиб!

Обсуждение

Неизвестный

09.10.2008, 18:13

общий

это ответ

Здравствуйте, Масленников Александр!
Распределение молекул F(V) по скоростям, показывающее, сколько молекул ΔN обладают скоростями в диапазоне (V;V+dV) по отношению к общему числу молекул N дается распределением Максвелла:
F(V)=ΔN/N=4*exp(-U²)*U²*dU/КОРЕНЬ(pi) (1)
где u=V/V_в (2)
где V - скорость молекулы, Vв - наиболее вероятная скорость, которая находится как:
V_в=КОРЕНЬ(2*R*T/M) (3)
где M=0,016 кг/моль -молярная масса кислорода, Т=0^o C=273 К - температура газа, R=8,31 Дж/(моль*К) - универсальная газовая постоянная
V_в=КОРЕНЬ(2*8,31*373/0,016)=532,5 м/с
В общем случае, чтобы найти число молекул, скорости которых лежат в конечном диапазоне, нужно брать интеграл от выражения (1) от U₁ до U₂, но если
интервал невелик (как в данной задаче - 110-100=10 м/с), можно бесконечно малое приращение dU заменить на конечное ΔU
где ΔU=V₂-V₁/V_в=110-100/532,5=0,019
U²=(V₁/V_в)²=0,035
exp(-U²)=0,96
Подставляя полученные цифры в (1) получаем:
ΔN/N=4*0,96*0,035*0,019/КОРЕНЬ(pi)=0,0014 т.е. 0,14%

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