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Консультация № 180106
01.10.2010, 06:09
47.75 руб.
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210. Пассажирский самолет совершает полеты на высоте 8300 м. Чтобы не снабжать пассажиров кислородными масками, в кабинах при помощи компрессора поддерживается давление, соответствующее высоте 2700 м. Найти, во сколько раз плотность 2 воздуха в кабине больше плотности 1 воздуха вне ее, если тем¬пература наружного воздуха t1= -20 0С, а температура воздуха в кабине t2=+20 0С.
Обсуждение
Неизвестный
01.10.2010, 09:06
общий
это ответ
Здравствуйте, Ильчук Кирилл Юрьевич.
Исходные данные: h2=2700 м, h1=8300 м, t1=-20[$186$]C=253[$186$]K , t2=+20[$186$]C=293[$186$]K, M=2910-3 кг/моль
Воспользуемся барометрической формулой для определения давления внутри и снаружи самолета:
р = p0 exp [-Mgh/(Rt)], где p0=105 Па - нормальное атмосферное давление.
Пользуясь этой формулой надо сделать следующие допущения:
1. ускорение свободного падения g не зависит от высоты;
2. воздух - идеальный газ.
Далее запишем уравнение состояния идеального газа:
pV=mRt/M
Из него выразим плотность воздуха:
r=m/V=pM/Rt= Mp0 exp [-Mgh/(Rt)]/Rt
Значит отношение плотностей воздуха в самолете и снаружи r2/r1=[Mp0 exp [-Mgh2/(Rt2)]/Rt2]/[Mp0 exp [-Mgh1/(Rt1)]/Rt1]=exp [Mg(h1/t1-h2/t2)/R] [$149$] t1/t2 = 2,08 ≈ 2
Ответ: плотность воздуха в кабине больше плотности воздуха вне её в 2 раза.
Удачи.
Исходные данные: h2=2700 м, h1=8300 м, t1=-20[$186$]C=253[$186$]K , t2=+20[$186$]C=293[$186$]K, M=2910-3 кг/моль
Воспользуемся барометрической формулой для определения давления внутри и снаружи самолета:
р = p0 exp [-Mgh/(Rt)], где p0=105 Па - нормальное атмосферное давление.
Пользуясь этой формулой надо сделать следующие допущения:
1. ускорение свободного падения g не зависит от высоты;
2. воздух - идеальный газ.
Далее запишем уравнение состояния идеального газа:
pV=mRt/M
Из него выразим плотность воздуха:
r=m/V=pM/Rt= Mp0 exp [-Mgh/(Rt)]/Rt
Значит отношение плотностей воздуха в самолете и снаружи r2/r1=[Mp0 exp [-Mgh2/(Rt2)]/Rt2]/[Mp0 exp [-Mgh1/(Rt1)]/Rt1]=exp [Mg(h1/t1-h2/t2)/R] [$149$] t1/t2 = 2,08 ≈ 2
Ответ: плотность воздуха в кабине больше плотности воздуха вне её в 2 раза.
Удачи.
01.10.2010, 10:10
общий
Всё-таки термодинамическая температура обозначается буквой "T", а не "t", и измеряется в кельвинах (К), а не в градусах Кельвина. В выкладках произведение RT в знаменателях дробей следует заключить в скобки, чтобы правильно был задан порядок операций...
Об авторе:
Facta loquuntur.
Facta loquuntur.
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