Calculating Temperature Increase in Nuclear Fusion Reaction

[Dalaran]

Hi all,

I've been given an assignment to calculate the temperature increase of the fusion reactor walls in some theoretical event. It is a 30keV plasma energy in which the heat of the entire plamsa is instantaneously dropped on the wall. I can calculate volume of the wall and have the given density as well as specific heat.

My approach:

Cp = specific heat (J/kg*K) = 460
rho = density (kg/m³) = 7600
V = volume (m³) = 29.61
P = plasma energy (eV) = 30,000
and q is conversion of eV to J (1.602x10^-19)

T increase = (P * q) / (Cp * rho * V)

I end up some ridiculously low # of x10^-24 degree celsius (or K) increase. I know that these are using very little mass at any given time, but with a plasma temperature of ~3X10⁸ I expected some reasonable value. Is what I am doing correct or am I way out in left field with my thinking?

Appreciate the help.

 

[Aidan Davis]

Hi,
This is extremely late, but whatever.
30 KeV refers to energy per particle in the plasma. Your formula is correct on a per particle basis, and it gives 4.643*10^-23 K increase per particle of plasma. Extrapolating to, for example, on mole of plasma, gives 27.962 K increase. These numbers are small because youre heating a few hundred tons of wall material.