calculation of peak-temperature in linear gas tungsten arc welding

Question

In liner gas tungsten arc welding of two places of the same material, the peak temperature T (in K) is given as T = C₁q / α, where q is the heat input per unit length (in J/m) of weld, α is the thermal diffusivity (in m²/s) of the plate materials and C₁ is a constant independent of process parameters and material types. Two welding cases are given below.

Case I:

V = 15 V, I = 200 A, v = 5 mm/s,

K = 150 W/mK, ρ = 3000 kg/m³,

C = 900 J/kg-K

Case II:

V = 15 V, I = 3ii A, v = 10 mm/s,

K = 50 W/mK, ρ = 8000 kg/m³,

C = 450 J/kg-K

Where, V is welding voltage, I is welding current, v is welding speed, and k, ρ and C refer to the thermal conductivity, the density and the specific heat of the plate materials respectively. Consider that electrical energy is completely converted to thermal energy. All other conditions remain same.

The ratio of the peak temperature in Case I to that in Case II is

(a) $\frac{1}{3}$                         (b)$\frac{1}{2}$

(c) 1                                           (d) 2