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In general, the temperature at a point (x) varies with time (t) i.e., it is a function $T(x,t)$. In the steady state, the temperature depends on x but not on time t i.e., $T(x,t)=T(x)$. In this state, the heat that reaches any cross-section is transmitted to the next without accumulation. The discussion in this article is limited conduction heat transfer in the steady state.

The rate of heat transfer through a rod of length x and cross-section area A whose two ends are maintained at a temperature T_{1} and T_{2} is given by
\begin{align}
\frac{\mathrm{d}Q}{\mathrm{d}t}=\frac{KA}{x}(T_1-T_2)
\end{align}
where K is the thermal conductivity of the material of the rod. The SI unit of thermal conductivity is W/(m-K). The dimensional formula of the thermal conductivity is MLT^{-3}K^{-1}. Note that heat is transferred from the end at higher temperature T_{1} to the end at the lower temperature T_{2}.

The quantity dQ/dt is also called heat current or the rate of flow of heat. The quantity $(T_1-T_2)/x$ (and its differential form dT/dx) is called temperature gradient. The thermal resistance of a body is defined as the ratio of temperature difference to the heat current \begin{align} R=\frac{\Delta T}{\mathrm{d}Q/\mathrm{d}t}=\frac{x}{KA}. \end{align} In electrical circuits, equivalents of heat current, temperature difference and thermal resistance is electric current, potential difference and electrical resistance, respectively.

Consider two rods of thermal resistances $R_1$ and $R_2$. The effective thermal resistance of a system of two rods connected in series is given by \begin{align} R_s=R_1+R_2 \end{align} If these rods are of same physical dimensions and of thermal conductivities $K_1$ and $K_2$ then effective thermal conductivity of the system is \begin{align} K_s=\frac{K_1K_2}{K_1+K_2}. \end{align} The effective thermal resistance of a system of two rods connected in parallel is given by \begin{align} R_p=\frac{R_1R_2}{R_1+R_2}. \end{align} If rods is parrallel are of same physical dimensions but thermal conductivities $K_1$ and $K_2$ then effective thermal conductivity of the system is \begin{align} K_p=K_1+K_2. \end{align}

In general, a substance that is a good conductor of heat is also a good conductor of electricity. At a given temperature T, the ratio of thermal conductivity (K) to the electrical conductivity (σ) is constant i.e., K/σT= L (a constant). This is known as Wiedemann-Franz Law.

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**Question 1:** For cooking the food, which of the following type of utensil is most suitable

**Question 2:** Two conducting walls of thickness d_{1} and d_{2}, and thermal conductivity K_{1} and K_{2} are joined together. If temperatures on the outside surfaces are T_{1} and T_{2} then the temperature of common surface is

**Question 3:** Ice has formed on a shallow pond, and a steady state has been reached, with the air above the ice at -5.0°C and the bottom of the pond at 4°C. If the total depth of ice + water is 1.4 m, then he thickness of ice layer is (Assume that the thermal conductivities of ice and water are 0.40 and 0.12 cal/(m-°C), respectively.)