Question

Uranium was used to generate electricity in a nuclear reactor of a nuclear power station. The nuclear reactor was 29% efficient and the power output was 800MW. The fuel used in this plant contained 4% of pure uranium. The plant operated 365 days per year. The average price of the fuel during the first 20 years of operation of the plant was US$12/lb, but in last 20 years of operation, the price spiked to US$65/lb. Calculate the cost of fuel for the lifetime of the plant, 40

Answer 1

Answer:

$C_{lifetime} = 2,618,017,174\,USD$

Explanation:

The energy contained per second in the fuel is:

$\dot E_{fuel} = \frac{800\times 10^{6}\,W}{0.29}$

$\dot E_{fuel} = 2.758\times 10^{9}\,W$

It is know that fission of a gram of uranium liberates $5.8\times 10^{8}\,J$. Mass flow rate is computed herein:

$\dot m_{U}= \frac{2.758\times 10^{9}\,W}{5.8\times 10^{8}\,\frac{J}{g}}$

$\dot m_{U} = 4.755\,\frac{g}{s}$

The needed quantity of fuel per second is:

$\dot m_{fuel} = \frac{4.755\,\frac{g}{s} }{0.04}$

$\dot m_{fuel} = 118.875\,\frac{g}{s}$

The annual fuel consumption is now obtained:

$\Delta m_{fuel,year} = (0.119\,\frac{kg}{s})\cdot (\frac{3600\,s}{1\,h} )\cdot (\frac{24\,h}{1\,day} )\cdot(\frac{365\,days}{1\,year} )$

$\Delta m_{fuel,year} = 3,752,784\,\frac{kg}{year}$

The cost of fuel for the lifetime of the plant is:

$C_{lifetime} = (3,752,784\,\frac{kg}{year} )\cdot (\frac{0.453\,lb}{1\,kg} )\cdot [(20\,years)\cdot(\frac{12\,USD}{1\,lb} )+(20\,years)\cdot (\frac{65\,USD}{1\,lb} )$

$C_{lifetime} = 2,618,017,174\,USD$