A gallon of gasoline releases about 2.0 ×10^8 J of energy when it is burned. How many gallons of

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A gallon of gasoline releases about 2.0 ×10^8 J of energy...

A gallon of gasoline releases about $2.0 \times 10^{8}$ J of energy when it is burned. How many gallons of gas must be burned to release the same amount of energy as is released when 1.0 lb of ${ }_{92}^{23} \mathrm{U}$ undergoes fission. (Assume that each fission reaction in 235 U releases 173 MeV.)

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Key Concepts

Nuclear Fission

Nuclear fission is a process whereby the nucleus of a heavy atom, such as uranium, splits into smaller nuclei, releasing a large amount of energy in the process. This released energy originates from the change in nuclear binding energy during the transition from a heavier nucleus to lighter nuclear fragments.

Energy Unit Conversion

Energy from nuclear reactions is often expressed in units like mega electron-volts (MeV), while chemical energies, such as those from gasoline combustion, are given in Joules. Converting between these units is crucial for comparing different forms of energy quantitatively.

Mole Concept and Avogadro’s Number

When calculating the total energy released in a nuclear reaction from a given mass of a substance, the mole concept and Avogadro’s number are used to determine the number of atoms present. This allows one to scale the per-reaction energy release to the entire mass undergoing fission.

Chemical Energy in Fossil Fuels

Chemical energy in fossil fuels, such as gasoline, is characterized by its energy density, meaning the amount of energy released per unit of fuel (e.g., per gallon). Understanding these values is important when comparing the energy obtained from nuclear fission to that from conventional chemical combustion.

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