Hi ,please I need something to finish this problem:
The specific heat s of a material in [J/(kg deg C] is the amount of energy in joules required to raise the temperature of 1[kg] of material by one degree C. The density ρ of a material in [kg/m3] is the mass in [kg] per cubic meter. If a current density J exists inside a material for a time Δt, show that the rise in temperature Δ T in degree C given the formula (σ is conductivity of the material):
Δ T=(J^2* Δ t)/(s* σ* ρ)
This is how I started:
J=σ*E (E electric field) --> E=J/σ
Now the power density.
to have the enegy density(Eg), I multiply by Δ t (t is the time).
Then I said that: ΔT=Eg/s
where s is the specific heat and T the temperature.
--> ΔT=J^2*Δt/(s* σ)
Now since I have been woking with the energy density. To have the energy, I divide by the density ρ.
If I do that I got the expression, but i would like to know if my reasonning is right.