Two rods of same length and material transfer a given amount of heat in $12\, seconds$ , when they are joined end to end. But when they are joined in series, then they will transfer same heat in same conditions in…….. $\sec$

It takes $10$ minutes to cool a liquid from $61^{\circ} C$ to $59^{\circ} C$. If room temperature is $30^{\circ} C$ then time taken in cooling from $51^{\circ} C$ to $49^{\circ} C$ is ………. $min$ 

Three rods $A, B,$ and $C$ of thermal conductivities $K, 2K$ and $4K$ and equal, cross-sectional areas and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100\ ^oC, 50\ ^oC,$ and $0\ ^oC$ respectively, then the temperature $\theta$ of the junction is

A cylindrical metallic rod, in thermal contact with two reservoirs of heat at its two ends, conducts an amount of heat $Q$ in time $t.$ The metallic rod is melted and the  material is formed into a rod of half the radius of the original rod. Amount of heat  conducted by the new rod, when placed in thermal contact with same two reservoirs in  time $t$ , is

A glass flask of volume $1$ litre is fully filled with mercury at $0\,^oC$. Both the flask and mercury are now heated to $100\,^oC$. If the coefficient of volume expansion of mercury is $1.82\times10^{-4}/^oC$, volume coefficient of linear expansion of glass is $10\times10^{-6}/^oC$, the amount of mercury which is spilted out is ………… $\mathrm{ml}$