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Консультация № 186499
05.08.2012, 13:50
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Помогите пожалуйста!1)Найти период полураспада радиактивного изотопа,если его активность за 10 суток уменьшилась на 24 процента по сравнению с первоначальной. 2)Определить КПД атомной станции мощностью 20МВт,если суточный расход ядерного горючего при работе станции состовляет 75 г урана-235.Считать,что при каждом акте деления ядра урана-235 выделяется энергия 20МэВ.
Огромное спасибо!!!!!!!!!
Помогите пожалуйста!1)Найти период полураспада радиактивного изотопа,если его активность за 10 суток уменьшилась на 24 процента по сравнению с первоначальной. 2)Определить КПД атомной станции мощностью 20МВт,если суточный расход ядерного горючего при работе станции состовляет 75 г урана-235.Считать,что при каждом акте деления ядра урана-235 выделяется энергия 20МэВ.
Огромное спасибо!!!!!!!!!
Обсуждение
05.08.2012, 16:50
общий
это ответ
Здравствуйте, lady.pch!
1)
t=10 суток
A=A0*(100%-24%)=0,76A0
Закон радиоактивного распада можно записать как
отсюда выражаем период полураспада
ln(A/A0)=-ln2*t/T1/2
T1/2=-t*ln2/ln(A/A0)=-10сут*ln2/ln0,76=25,3 суток
2)Забегая вперёд, сразу поправлю условие: при делении ядра урана-235 выделяется около 200 МэВ энергии. Иначе с имеющимеся данными у нас получится кпд больше 1
Найдём энергию, выделяющуюся при распаде массы урана-235, равной m:
Q=E*N=E*m/M*NA,
где
E - энергия, выделяющаяся при делении одного ядра
N - число ядер
m - масса урана
M - молярная масса урана
найдём выделяющуюся в реакторе мощность
P0=Q/t=E*(m/t)/M*NA
КПД равен отношению производимой мощности к выделяющейся
[$951$]=P/P0=P*M*t/(E*m*NA)=
=2*107Вт*235г/моль*24ч*3600с/ч/(2*108эВ*1,6*10-19Дж/эВ*75г*6,02*1023моль[sup]-1[/sup])=0,28=28%
1)
t=10 суток
A=A0*(100%-24%)=0,76A0
Закон радиоактивного распада можно записать как
отсюда выражаем период полураспада
ln(A/A0)=-ln2*t/T1/2
T1/2=-t*ln2/ln(A/A0)=-10сут*ln2/ln0,76=25,3 суток
2)Забегая вперёд, сразу поправлю условие: при делении ядра урана-235 выделяется около 200 МэВ энергии. Иначе с имеющимеся данными у нас получится кпд больше 1
Найдём энергию, выделяющуюся при распаде массы урана-235, равной m:
Q=E*N=E*m/M*NA,
где
E - энергия, выделяющаяся при делении одного ядра
N - число ядер
m - масса урана
M - молярная масса урана
найдём выделяющуюся в реакторе мощность
P0=Q/t=E*(m/t)/M*NA
КПД равен отношению производимой мощности к выделяющейся
[$951$]=P/P0=P*M*t/(E*m*NA)=
=2*107Вт*235г/моль*24ч*3600с/ч/(2*108эВ*1,6*10-19Дж/эВ*75г*6,02*1023моль[sup]-1[/sup])=0,28=28%
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