A system S receives heat continuously from an electrical heater of power $10 \mathrm{W}$. The temperature of $S$ becomes constant at $50°\mathrm{C}$ when the surrounding temperature is $20°\mathrm{C}$. After the heater is switched off, $S$ cools from $35.1°\mathrm{C}$ to $34.9°\mathrm{C}$ in $1$ minute. The heat capacity of $S$ is:-

Two identical square rods of metal are welded end to end as shown in figure (a) $20$ calories of heat flows. through it in $4$ minutes. If the rods are welded as shown in figure (b), the same amount of heat will flow through the rods in :-

Three rods of the same dimensions are arranged as shown in the figure, they have thermal conductivities $K_1,K_2$ and $K_3$. The points $P$ and $Q$ are maintained at different temperatures for the heat to flow at the same rate along $PRQ$ and $PQ$

The temperature of the two outer surface of a composite slab, consisting of two materials having coefficient of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$, respectively are $T_2$ and $T_2$ $\left(T_2>T_1\right)$. The rate of heat transfer through the slab, in a steady state is $\left(\frac{A\left(T_2-T_1\right)K}{x}\right)f$, with $f$ equals to

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$ and $T_2$ respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to