(a) Calculate the energy (in kilowatt-hours) released if 1.00 kg of 239 Pu undergoes complete fi

(a) Calculate the energy (in kilowatt-hours) released if...

(a) Calculate the energy (in kilowatt-hours) released if 1.00 $\mathrm{kg}$ of 239 $\mathrm{Pu}$ undergoes complete fission and the energy released per fission event is 200 $\mathrm{MeV}$ . (b) Calculate the energy (in electron volts) released in the deuteriumtritium fusion reaction $$ _{1}^{2} \mathrm{H}+_{1}^{3} \mathrm{H} \quad \rightarrow \quad_{2}^{4} \mathrm{He}+_{0}^{1} \mathrm{n} $$ (c) Calculate the energy (in kilowatt-hours) released if 1.00 $\mathrm{kg}$ of deuterium undergoes fusion according to this reaction. (d) What If? Calculate the energy (in kilowatt- hours) released by the combustion of 1.00 $\mathrm{kg}$ of coal if each $\mathrm{C}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}$ reaction yields 4.20 $\mathrm{eV}$ . (e) List advantages and disadvantages of each of these methods of energy generation.

(a) Calculate the energy (in kilowatt-hours) released if 1.00 $\mathrm{kg}$ of 239 $\mathrm{Pu}$ undergoes complete fission and the energy released per fission event is 200 $\mathrm{MeV}$ . (b) Calculate the energy (in electron volts) released in the deuteriumtritium fusion reaction
$$
_{1}^{2} \mathrm{H}+_{1}^{3} \mathrm{H} \quad \rightarrow \quad_{2}^{4} \mathrm{He}+_{0}^{1} \mathrm{n}
$$
(c) Calculate the energy (in kilowatt-hours) released if 1.00 $\mathrm{kg}$ of deuterium undergoes fusion according to this reaction. (d) What If? Calculate the energy (in kilowatt- hours) released by the combustion of 1.00 $\mathrm{kg}$ of coal if each $\mathrm{C}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}$ reaction yields 4.20 $\mathrm{eV}$ . (e) List advantages and disadvantages of each of these methods of energy generation.

Key Concepts

Energy Unit Conversion

This concept involves converting energy from one unit system to another, such as from electron volts (eV) or mega-electron volts (MeV) to joules or kilowatt-hours. It requires knowledge of the conversion factors (for example, 1 eV = 1.602×10?¹? joules) and an understanding of how to consistently apply these conversions when computing large-scale energy releases. Mastery of these conversions is essential for comparing energies across different physical processes.

Nuclear Fission

Nuclear fission is a process in which a heavy atomic nucleus splits into two or more lighter nuclei, accompanied by the release of a significant amount of energy. The energy comes predominantly from the binding energy differences between the initial and final products. Calculating the total energy released involves multiplying the energy per fission event by the total number of fission events, which requires a conversion between mass and the number of nuclei.

Nuclear Fusion

Nuclear fusion is the process that combines lighter nuclei to form a heavier nucleus, releasing energy due to a difference in nuclear binding energy. In fusion reactions, the energy per event is determined by the mass defect and binding energies of the isotopes involved in the reaction. Fusion energy calculations involve careful evaluation of the energy yield per reaction and require conversion of this microscopic energy amount to macroscopic energy units for practical applications.

Stoichiometric Calculations in Reaction Energetics

Stoichiometry in the context of energy calculations involves determining the number of reacting particles (atoms or molecules) from a given mass and using this count to calculate the total energy released. Both nuclear and chemical reactions rely on precise stoichiometric relationships to scale the energy release from a single event to a bulk amount, thereby linking microscopic reaction details with macroscopic energy output.

Chemical Combustion Energy

Chemical combustion energy refers to the energy released during a chemical reaction, such as the oxidation of carbon. Unlike nuclear reactions, chemical reactions typically involve energy changes in the electron arrangement rather than the nuclear structure. Calculations here require knowledge of the reaction enthalpy per molecule or per mole, and subsequent conversion into desired energy units, highlighting the comparative lower energy density of chemical processes.

Evaluation of Energy Generation Methods

This concept involves critically assessing different energy production methods by weighing their respective advantages and disadvantages. Factors include energy density, safety, environmental impact, waste management, and resource availability. Evaluating nuclear versus chemical processes requires an understanding of the fundamental differences in reaction mechanisms as well as the practical implications for energy generation, infrastructure, and policy.

Transcript

00:02 Hi everyone, in the first part it is given, calculate the energy released in kilowatt hour if 1 kg of plutonium 239 undergoes complete fission and energy per fission is 200 mega -lequence bolt.

00:41 Let us solve it.

00:43 Number of plutonium nuclei first we will calculate.

00:46 Mass of plutonium atomic weight into avogazard number.

00:51 Mass is given 1 kg.

00:53 Plutonium is 0 .239 kg into avogadra number 6 .023.

01:03 So it is to be 3 .324.

01:19 10 to the power 25.

01:23 So total energy release.

01:26 Is called to number of nuclei into energy per fission that is 3 .324 10 to the power 25 into 200 mega electron bolt so it is to be 5 .04 into 10 to the power 26 mega electron bolt let me correct here it is 10 to the power 24 here also we have to convert in kilowatt hour so it is to be 5 .04 10 to the power 26 mega electron bolt into 4 .44 10 to the power minus 20 kilowatt hour per mega electron bolt.

02:40 So you will get 2 .24 into 10 to the power 7 kilo watt hour.

02:49 Now in b part we have to calculate energy release in deuterium fusion reaction q in 1 h2 plus 1h3 is equal to 2h4 plus neutron.

03:13 So energy release will be equal to mass effect of the reaction into 931 .56 mega electron bolt.

03:23 Mass effect is mass of 1h2, mass of 1h3, mass of 2, mass of 2h3, mass of 2h3, mass of 2h3 ,000...

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