$A$ slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio $1 : 4$. If the free face of brass is at $100^\circ C$ and that of copper at $0^\circ C$,the temperature of the interface is ........ $^\circ C$.

$A$ slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} C$ and that of copper at $100^{\circ} C$. If the thermal conductivities of brass and copper are in the ratio $1: 4$,then the temperature of the interface is (in $^{\circ} C$)

$A$ 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:

$A$ 'thermacole' icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. $A$ cubical icebox of side $30 \,cm$ has a thickness of $5.0 \,cm$. If $4.0 \,kg$ of ice is put in the box,estimate the amount of ice (in $kg$) remaining after $6 \,h$. The outside temperature is $45 \,^{\circ}C$,and the coefficient of thermal conductivity of thermacole is $0.01 \,J \,s^{-1} \,m^{-1} \,K^{-1}$. Heat of fusion of water $= 335 \times 10^{3} \,J \,kg^{-1}$.

The thickness of a metallic plate is $0.4 \ cm$. The temperature difference between its two surfaces is $20^{\circ}C$. The quantity of heat flowing per second is $50 \ \text{calories}$ through an area of $5 \ cm^2$. In the $CGS$ system,the coefficient of thermal conductivity is:

$A$ deep rectangular pond of surface area $A$,containing water (density $=\rho$,specific heat capacity $=s$),is located in a region where the outside air temperature is at a steady value of $-26^{\circ}C$. The thickness of the frozen ice layer in this pond at a certain instant is $x$. Taking the thermal conductivity of ice as $K$ and its specific latent heat of fusion as $L$,the rate of increase of the thickness of the ice layer at this instant would be given by: