Please help me solve this thermal physics problem?

Because the phase change is happening slowly, I assume that this phase change is occurring reversible (i.e., arbitrarily close to equilibrium conditions). At equilibrium, the free energy change for a reaction is zero. Assuming this reaction is at constant pressure and temperature then:

ΔG = 0 = ΔH - T*ΔS, so, at equilibrium,

T = ΔH/ΔS

where ΔH and ΔS are the enthalpy and entropy changes for the liquid -> solid reaction.

The question tells you that ΔS = -3830 J/K. The heat released in the reaction is another way of saying that ΔH = -1.28*10^6 J (the sign of ΔH is negative because heat is released, i.e., this is the heat or enthalpy of solidification, which is equal to minus the enthalpy of fusion. Solidification reactions are always exothermic).

Putting this together, we have that:

T = (-1.28*10^6 J )/(-3.83*10^3 J/K)

T = 334 K = 61.0 C (to the correct number of significant digits)

to sparkling up this difficulty thermal conductivity of aluminium and that of iron are required.regrettably that are actually not provided. the easy equation for the quantity of warmth carried out by using a rod of length ' l ' and of portion of pass area ' a ' in a time ' t ' seconds is given by skill of the equation , Q =ok a (T1 - T2) t/l .the place T1 and T2 are the temperature between its ends.