What is the Thermal Power PTh produced by a cylindrical reactor if the fuel volu

Question

What is the Thermal Power PTh produced by a cylindrical reactor if the fuel volume is VR = 55.5 m3 , the fission macroscopic cross section f = 11.68cm-1, and the neutron flux = 2.8 x 1011 neutron/cm2 sec.

{Hint : Use the following formula: P = VR / 3x1010 (watt) } ?

If the Utilization factor or Efficiency of the Nuclear Power plant is 1/3, What is the real Electrical Power Pe that is carried out of the plant that you calculated above, by the transmission lines, using the data from the above question ? {Hint: Efficiency= Pe/ PTh } ?

Explanation / Answer

Fuel volume , V= 55.5 cu.m

Macroscopic cross section, f = 11.68 /cm

= 1168 /m

Neutron flux, =2.8 x 1011 n/sq.cm-s

= 2.8 x 1015 n/sq.m-s

Reaction rate (RR), = x N

Atomic Number density, N = n/V

Number density, n = 2 .3 x1014 atom/cu.cm ……….. (In general)

=2 .3 x1020 atom/cu.m

Atomic Number density, N = 4.14 x1016

Reaction Rate = 1.2 x1031

Thermal Power ,P as mentioned in formula

P = VR / 3x1010

= 2.14 x 1018

For Nuclear reactor                3.12 x 1010 fission /sec is 1 watt-s of energy

Considering 1/3 efficiency

We get output power of= 2.14 x 1018 / 3.12 x 1010 x3

= 22.29 kW

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