Para resolver este problema es necesario aplicar los conceptos relacionados a la conductividad térmica, para lo cual se tiene matematicamente que
[tex]k=\frac{\Delta Q}{\Delta t} \frac{1}{A} \frac{x}{\Delta T}[/tex]
Where,
K = thermal conductivity
A = Cross-sectional Area
[tex]\Delta T[/tex]= Change at temperature
x = Distance
[tex]\Delta t[/tex]= Difference of time
[tex]\Delta Q[/tex] = Heat exchange energy
Our values are given as follow,
[tex]t=4hours (\frac{3600s}{1hour}) = 14400s[/tex]
The total heat required to change the phase of ice would be
[tex]H = L_f*m \rightarrow[/tex] Where Lf Latent heat of fussion and m is the mass.
[tex]H = 80*500g[/tex]
[tex]H =40000 cal[/tex]
[tex]A= 600cm^2[/tex]
[tex]\Delta T = 20\° C[/tex]
[tex]x = 1cm[/tex]
Replacing we would have:
[tex]k=\frac{\Delta Q}{\Delta t} \frac{1}{A} \frac{x}{\Delta T}[/tex]
[tex]k=\frac{40000}{14400} \frac{1}{600} \frac{1}{20}[/tex]
[tex]K = 2.3*10^{-4} cal/s\cdot cm\cdot \°C[/tex]
Therefore the correct answer is D.
