Question 2.1: A Car Powered by Nuclear Fuel An average car consumes about ...

A car powered by nuclear energy comes equipped with nuclear fuel. It is to be determined if this car will ever need refueling.
Assumptions 1 Gasoline is an incompressible substance with an average density of 0.75 kg/L. 2 Nuclear fuel is completely converted to thermal energy.
Analysis The mass of gasoline used per day by the car is

m_{\text {gasoline }}=(\rho V)_{\text {gasoline }}=(0.75 kg / L )(5 L / \text { day })=3.75 kg / \text { day }

Noting that the heating value of gasoline is 44,000 kJ/kg, the energy supplied to the car per day is

\begin{aligned}E &=\left(m_{\text {gasoline }}\right)(\text { Heating value }) \\&=(3.75 kg / \text { day })(44,000 kJ / kg )=165,000 kJ / \text { day }\end{aligned}

The complete fission of 0.1 kg of uranium-235 releases

\left(6.73 \times 10^{10} kJ / kg \right)(0.1 kg )=6.73 \times 10^{9} kJ

of heat, which is sufficient to meet the energy needs of the car for

\text { No. of days }=\frac{\text { Energy content of fuel }}{\text { Daily energy use }}=\frac{6.73 \times 10^{9} kJ }{165,000 kJ / \text { day }}=40,790 \text { days }

which is equivalent to about 112 years. Considering that no car will last more than 100 years, this car will never need refueling. It appears that nuclear fuel of the size of a cherry is sufficient to power a car during its lifetime.

Discussion Note that this problem is not quite realistic since the necessary critical mass cannot be achieved with such a small amount of fuel. Further, all of the uranium cannot be converted in fission, again because of the critical mass problems after partial conversion.