A slab of stone of area $0.36\;m ^2$ and thickness $0.1 \;m$ is exposed on the lower surface to steam at $100^{\circ} C$. A block of ice at $0^{\circ} C$ rests on the upper surface of the slab. In one hour $4.8\; kg$ of ice is melted. The thermal conductivity of slab is .......... $J / m / s /{ }^{\circ} C$ (Given latent heat of fusion of ice $=3.36 \times 10^5\; J kg ^{-1}$)

$Assertion :$ Two thin blankets put together are warmer than a single blanket of double the thickness.
$Reason :$ Thickness increases because of air layer enclosed between the two blankets.

Two conducting rods $A$ and $B$ of same length and cross-sectional area are connected $(i)$ In series $(ii)$ In parallel as shown. In both combination a temperature difference of $100^o C$ is maintained. If thermal conductivity of $A$ is $3K$ and that of $B$ is $K$ then the ratio of heat current flowing in parallel combination to that flowing in series combination is

The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances $R _{1}$ and $R _{2}$ as well as top and bottom temperatures $\theta_{1}$ and $\theta_{2}$ (as shown in figure) is given by

One end of a copper rod of uniform cross-section and of length $3.1$ m is kept in contact with ice and the other end with water at $100°C $ . At what point along it's length should a temperature of $200°C$ be maintained so that in steady state, the mass of ice melting be equal to that of the steam produced in the same interval of time. Assume that the whole system is insulated from the surroundings. Latent heat of fusion of ice and vaporisation of water are $80 cal/gm$ and $540$ cal/gm respectively

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