A nuclear reactor has a rated capacity PR 1000 MW and produ

A nuclear reactor has a rated capacity PR = 1,000 MW and produces 7.9 billion kWh/year of electric power. The reactor is fueled with fuel rods that contain 2.5% U-235 by mass. The plant operates on a Rankine cycle with thermal efciency th = 0.33. The generator is 98% efcient, and 90% of the energy released in the reactor is transferred to the working uid. The heating value of U-235 is 8.2 x 1010 kJ/kg. a) What is the capacity factor (CF) of the plant? b) What mass, in kg, of fuel rods does the reactor consume in one year?

Solution

1)CAPACITYFACTOR= ACTUAL OUTPUT/MAXIMUM POSSIBLE OUTPUT

ACTUAL OUTPUT=7.9BILLION KWh/Year=7900MWh

MAXIMUM POSSIBLE OUTPUT=365DAYS*24HOURS*RATED CAPACITY=365*24*1000=8760000MW

CAPACITYFACTOR=7900/8760000=0.0901824%

2)MASS OF FUEL CONUMED IN Kg=

thermal efficiency=power output/mass flow rate of fuel consumed*calorific value

0.33=7900MWh/mass flow rate of fuel consumed*8.2*1010

mass flow rate of fuel consumed=7900/0.33*8.2*1010=2890.532 kg/year