Figure shows a lagged copper bar AB whose ends are pressed against metal tanks at $100^\circ\text{C}$ and $0^\circ\text{C}$, but are separated from them by layers of dirt. The length of the bar is $10\,\text{cm}$ and the dirt layers are $0.1\,\text{mm}$ thick. The conductivity of dirt is $0.001$ times that of copper. The temperature difference across the copper bar is