Answer:
![k=105.0359\times 10^4\,W.m^{-1}.K^{-1}](https://tex.z-dn.net/?f=k%3D105.0359%5Ctimes%2010%5E4%5C%2CW.m%5E%7B-1%7D.K%5E%7B-1%7D)
Explanation:
Given:
temperature at the hotter end, ![T_H=100^{\circ}C](https://tex.z-dn.net/?f=T_H%3D100%5E%7B%5Ccirc%7DC)
temperature at the cooler end, ![T_C=0^{\circ}C](https://tex.z-dn.net/?f=T_C%3D0%5E%7B%5Ccirc%7DC)
length of rod through which the heat travels, ![dx=0.7\,m](https://tex.z-dn.net/?f=dx%3D0.7%5C%2Cm)
cross-sectional area of rod, ![A=1.1\times 10^{-4}\,cm^2](https://tex.z-dn.net/?f=A%3D1.1%5Ctimes%2010%5E%7B-4%7D%5C%2Ccm%5E2)
mass of ice melted at zero degree Celsius, ![m=8.7\times 10^{-3}\,kg](https://tex.z-dn.net/?f=m%3D8.7%5Ctimes%2010%5E%7B-3%7D%5C%2Ckg)
time taken for the melting of ice, ![t=15\times60=900\,s](https://tex.z-dn.net/?f=t%3D15%5Ctimes60%3D900%5C%2Cs)
thermal conductivity k=?
By Fourier's Law of conduction we have:
......................................(1)
where:
=rate of heat transfer
dT= temperature difference across the length dx
Now, we need the total heat transfer according to the condition:
we know the latent heat of fusion of ice, ![L = 334000\,J.kg^{-1}](https://tex.z-dn.net/?f=L%20%3D%20334000%5C%2CJ.kg%5E%7B-1%7D)
![Q=m.L](https://tex.z-dn.net/?f=Q%3Dm.L)
![Q=8.7\times 10^{-3}\times 334000](https://tex.z-dn.net/?f=Q%3D8.7%5Ctimes%2010%5E%7B-3%7D%5Ctimes%20334000)
![Q=2905.8\,J](https://tex.z-dn.net/?f=Q%3D2905.8%5C%2CJ)
Now the heat rate:
![\dot{Q}=\frac{Q}{t}](https://tex.z-dn.net/?f=%5Cdot%7BQ%7D%3D%5Cfrac%7BQ%7D%7Bt%7D%20)
![\dot{Q}=\frac{2905.8}{900}](https://tex.z-dn.net/?f=%5Cdot%7BQ%7D%3D%5Cfrac%7B2905.8%7D%7B900%7D%20)
![\dot{Q}=3.2287\,W](https://tex.z-dn.net/?f=%5Cdot%7BQ%7D%3D3.2287%5C%2CW)
Now using eq,(1)
![3.2287=k\times 1.1\times 10^{-4} \times \frac{100}{0.7}](https://tex.z-dn.net/?f=3.2287%3Dk%5Ctimes%201.1%5Ctimes%2010%5E%7B-4%7D%20%5Ctimes%20%5Cfrac%7B100%7D%7B0.7%7D)
![k=205.4606\,W.m^{-1}.K^{-1}](https://tex.z-dn.net/?f=k%3D205.4606%5C%2CW.m%5E%7B-1%7D.K%5E%7B-1%7D)