Modern Physics 5 Question 31

34. In a nuclear reactor 235U undergoes fission liberating 200MeV of energy. The reactor has a 10 efficiency and produces 1000MW power. If the reactor is to function for 10yr, find the total mass of uranium required.

(2001, 5M)

Show Answer

Solution:

  1. The reactor produces 1000MW power or 109J/s. The reactor is to function for 10yr. Therefore, total energy which the reactor will supply in 10yr is

E=( power )( time )=(109J/s)(10×365×24×3600s)=3.1536×1017J

But since the efficiency of the reactor is only 10, therefore actual energy needed is 10 times of it or 3.1536×1018J. One uranium atom liberates 200MeV of energy or 200×1.6×1013J or 3.2×1011J of energy. So, number of uranium atoms needed are

3.1536×10183.2×1011=0.9855×1029

or number of kg-moles of uranium needed are

n=0.9855×10296.02×1026=163.7

Hence, total mass of uranium required is

m=(n)M=(163.7)(235)kg or m38470kg or m=3.847×104kg



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक