Review problem. A nuclear power plant operates by using the...

Review problem. A nuclear power plant operates by using the energy released in nuclear fission to convert $20^{\circ} \mathrm{C}$ water into $400^{\circ} \mathrm{C}$ steam. How much water could theoretically be converted to steam by the complete fissioning of 1.00 $\mathrm{g}$ of $^{235} \mathrm{U}$ at 200 $\mathrm{MeV} /$ fission?

Key Concepts

Latent Heat of Vaporization

The latent heat of vaporization is the amount of energy required to change a substance from its liquid phase to its gaseous phase at constant temperature. In thermodynamics, this concept highlights the energy needed to overcome intermolecular forces without raising the temperature, and it is essential for calculating the energy required to produce steam from water.

Stoichiometric Conversion of Mass to Number of Atoms

When determining the total energy released from a given mass of a material, it is essential to calculate the number of atoms present using its molar mass and Avogadro’s number. This conversion ties the microscopic energy release per nucleus to a macroscopic quantity by converting mass units into a count of nuclei, enabling the total energy yield to be determined.

Nuclear Fission

Nuclear fission is a process in which a heavy atomic nucleus splits into two or more smaller nuclei, releasing a large amount of energy in the process. This energy comes from the conversion of mass into energy, as described by the principle of mass–energy equivalence, and is quantified by the difference in binding energy between the original nucleus and its fission fragments.

Energy Unit Conversion

In nuclear and particle physics, energy is commonly expressed in mega–electronvolts (MeV). For engineering and thermodynamics applications, it is often necessary to convert energy from MeV to joules using the conversion factor where 1 electronvolt equals approximately 1.602 × 10?¹? joules. This allows the energy yield from nuclear reactions to be applied in calculations involving conventional energy units.

Transcript

00:01 For this question, we are calculating how much can 1 gram of uranium 235 convert steam, convert water at 20 degrees into steam at 400 degrees celsius.

00:22 Alright, to start off, we will need to find out what is the energy being released by 1 gram of uranium 235.

00:31 We are given that 200 m .ev is released per fission reaction.

00:38 So what we just have to do is to find how many, what is the number of nucleus in 1 gram or uranium 235, then we can calculate what is the total energy.

00:54 So to find the total energy released, we take the total mass which is 1 gram divided by the molar mass which is 2035 grams per mole this will give us the number of moles multiplied by avocado's constant and this will give us the number of atoms or number of uranium 235 nuclei next we multiply by the energy released per nuclei which is 200 mep.

01:36 Then we will want to convert it into joules for si units.

01:41 So multiply by 1 .6 times 10 power minus 13 joules per mep.

01:52 So our total energy that's released by 1 gram or if you're in 235 is 8 .2 times 10 to the power of 10 joules.

02:06 Now we want to consider a unknown mass of water, m.

02:16 And we want to find what is the energy required to convert this amount of mass m of water at 20 degrees to 400 degrees celsius steam so amount of energy required let us just play as q first is to raise the water from 20 degrees to 100 degrees so this is the first part mc delta t where m is the mass of water cw is the specific heat capacity of water...

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