How to calculate the pressure in nuclear reactions?

[beruniy]

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...

 

[phyzguy]

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.

 

[beruniy]

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.

 

[phyzguy]

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.

 

[beruniy]

But the problem asks to calculate the "maximal" pressure in ampule. Doesn't it mean exactly transient pressure at the moment?

 

[phyzguy]

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.

 

[beruniy]

Okay, thank you very much. May be, somebody has another point of view?