How to calculate the pressure in nuclear reactions?

In summary, the conversation discusses the irradiation of a Lithium-6 sample in a nuclear reactor with neutrons, resulting in the production of hydrogen and helium gases. The problem at hand is to calculate the maximal pressure in the reactor, given the energy released from the reaction. The participants consider various methods of calculating the pressure, including using thermodynamic laws and considering the energy dissipation and temperature equilibrium of the ampule. Ultimately, it is determined that there is not enough information provided to calculate the pressure accurately.
  • #1
beruniy
7
0
A Lithium-6 sample (m = 12,0 mg) which was isolated in ampule V = 200 cm3,was loaded in nuclear reactor and irradiated by neutrons for a long time. Calculate the maximal pressure in reactor, T = 400 K.

The equation is
Li + n = T + α

I calculated the energy of this reaction using formula ΔE = -Δmc2
4,78 MeV for 1 particle, and then calculated it for 12 mg of Lithium.
How can I transfer energy to pressure? I tried to use the kinetic energy but nothing came out of it. May be it is possible to use thermodynamic laws? If you know please help me solve this task...
 
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  • #2
I think you are supposed to assume that all of the lithium has been converted to T and α - i.e. into hydrogen and helium, which are both gases. You should be able to calculate how many moles of gas are produced, and since you know the temperature and volume, you should be able to calculate the pressure.
 
  • #3
Yes, I consider that all Lithium is converted to T and He, but it is incorrectly to think that we can use Mendeleev-Klapeiron equation in this case. This is simply equation for perfect gas but you must take into account that nuclear reaction gives us huge energy (9,21×105 kJ) and exactly this energy creates pressure. Otherwise we'll calculate pressure as if nuclear reaction didn't progress.
 
  • #4
Of course, but eventually this energy is dissipated and the ampule reaches temperature equilibrium with its surroundings. The problem tells you that the temperature of the ampule is 400K. Note that it says "for a long time", meaning you can ignore the transient temperature rise due to the energy of the nuclear reactions.
 
  • #5
But the problem asks to calculate the "maximal" pressure in ampule. Doesn't it mean exactly transient pressure at the moment?
 
  • #6
I don't think you have nearly enough information to do the calculation you are proposing. You would need to know the neutron flux, so you could calculate the rate at which energy was being generated. You would also need to know the thermal transfer characteristics of the ampule so you could calculate the rate of heat transfer from the ampule to the surroundings. You are not given either one of these, so I think what I proposed is the only way you can answer the problem.
 
  • #7
Okay, thank you very much. May be, somebody has another point of view?
 

FAQ: How to calculate the pressure in nuclear reactions?

How is pressure calculated in nuclear reactions?

The pressure in nuclear reactions is calculated using the ideal gas law, which states that pressure is equal to the product of the number of moles, the gas constant, and the temperature, divided by the volume of the container. In nuclear reactions, the number of moles and the gas constant can be determined based on the reactants and products involved, while the temperature and volume must be measured experimentally.

What is the role of pressure in nuclear reactions?

Pressure plays a crucial role in nuclear reactions as it determines the rate and efficiency of the reaction. As the pressure increases, the molecules in the reaction become more closely packed, leading to a higher number of collisions and a faster reaction rate. Additionally, pressure can also affect the stability of certain nuclei, making it an important factor in controlling nuclear reactions.

How does pressure change during a nuclear reaction?

In most cases, the pressure will increase during a nuclear reaction due to the release of energy and the production of gaseous byproducts. However, in some types of reactions such as fusion reactions, the pressure may decrease due to the conversion of matter into energy. The exact change in pressure will depend on the specific reaction and its conditions.

Can pressure be used to control nuclear reactions?

Yes, pressure can be used to control nuclear reactions to some extent. By varying the pressure, the rate of the reaction and the stability of the nuclei can be altered. Additionally, in nuclear power plants, pressure is used to control the flow of coolant and prevent overheating of the reactor, which could lead to a runaway reaction.

How is pressure related to nuclear fission and fusion reactions?

In nuclear fission reactions, pressure is used to control the rate of the reaction and prevent a chain reaction from getting out of control. On the other hand, in nuclear fusion reactions, pressure is used to overcome the repulsive forces between nuclei and bring them close enough to fuse together. In both types of reactions, pressure plays a crucial role in the success and safety of the reaction.

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