   Chapter 28, Problem 67PE

Chapter
Section
Textbook Problem

(a) A nuclear power plant converts energy from nuclear fission into electricity with an efficiency of 35.0%. How much mass is destroyed in one year to produce a continuous 1000 MW of electric power? (b) Do you think it would be possible to observe this mass loss if the total mass of the fuel is 104 kg?

To determine

(a)

The mass to produce a continuous 1000MWof electric power in one year.

Explanation

Given:

Mass of electron, P=1000MW

Speed of light, c=3×108m/s

Formula used:

Formula to calculate the mass in one year is,

P=Et    ...... (I)

Calculation:

Electric power is defined as the rate of electrical energy consumption.

Simplify equation (I) to calculate the energy consumed in one year.

P=EtE=Pt

Substitute 1000MWfor Pand 1yearfor tto calculate the energy consumed in the above equation.

E=1000MW×1year

Convert MWinto J/s.

1000MW=1000×106J/s=108J/s

Convert year into seconds.

1year=1×(365.24days1year)×(24hours1day)×(3600seconds1hour)=31.556×106s

Solve the above equation to calculate energy consumed.

E=(1000×106J/s)×(31.556×106s)=3

To determine

(b)

Whether 1kgmass loss is observable or not if the total mass of the fuel is 104kg.

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