Answer:
153.0815W/m.K
Explanation:
Heat transferred in phase is changed is expressed as:
[tex]Q=\pm mL[/tex] (m-mass, Q-heat, L-Latent heat of phase change)
Latent heat is the heat required to change the phase of 1kg of the material.
#The rate of heat flow(by conduction) per unit time:
[tex]H=\frac{\bigtriangleup Q}{\bigtriangleup t}=kA\frac{T_H-T_C}{L}\\\\L_f=334\times10^3J/kj\\\\H_{ice}=\frac{Q_{ice}}{t}=\frac{m_{ice}L_f}{t}[/tex] #Heat flowing through melting ice.
[tex]H_{ice}=\frac{5.0\times10^-^3kg)334\times10^3J/kg)}{10\times60s}\\\\=2.7833J/s[/tex]
To solve for k:
[tex]H=\frac{\bigtriangleup Q }{\bigtriangleup t}\\\\=kA\frac{T_H-T_C}{L}[/tex][tex]H=\frac{\bigtriangleup Q }{\bigtriangleup t}\\\\=kA\frac{T_H-T_C}{L}[/tex][tex]H=\frac{\bigtriangleup Q }{\bigtriangleup t}\\\\=kA\frac{T_H-T_C}{L}\\\\k=\frac{H}{A\frac{T_H-T_C}{L}}=\frac{HL}{A(T_H-T_C)}[/tex]
[tex]=\frac{(2.7833J/s\times 0.55)}{1.00\times10^-^4m^2\times 100K}\\\\=153.0815W/m.K[/tex]
The thermal conductivity k of the metal is 153.0815W/m.K
