$A$ copper rod and a steel rod of equal cross-sections and lengths $L$ are joined side by side and connected between two heat baths as shown in the figure. If heat flows through them from $x = 0$ to $x = 2L$ at a steady rate and thermal conductivities of the metals are $K_{Cu}$ and $K_{Steel}$ $(K_{Cu} > K_{Steel})$,then the temperature varies as (convection and radiation are negligible):

On a cold morning,a metal surface feels colder than a wooden surface because:

$A$ cylindrical metallic rod in thermal contact with two heat reservoirs at its two ends conducts an amount of heat '$Q_1$' in time '$t$'. The metallic rod is melted and the material is formed into a rod of length four times the length of the original rod. The amount of heat conducted by the new rod when placed in thermal contact with the same two reservoirs in time '$t$' is '$Q_2$'. Then $\frac{Q_1}{Q_2}$ is:

Same quantity of ice is filled in each of the two metal containers $P$ and $Q$ having the same size, shape, and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in $P$ melts completely in time $t_{1}$ whereas in $Q$ it takes a time $t_{2}$. The ratio of thermal conductivities of the materials of $P$ and $Q$ is

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$. The rate of heat transfer,$\frac{dQ}{dt}$ through the rod in a steady state is given by:

Heat current is maximum in which of the following (rods are of identical dimension)?