Certain quantity of water cools from $70\,^oC$ to $60\,^oC$ in the first $5\, minutes$ and  to $54\,^oC$ in the next $5\, minutes$. The temperature of the surroundings is......... $^oC$

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

The intensity of radiation emitted by the sun has its maximum value at a wavelength of $510\,nm$ and that emitted by the north star has the maximum value at $350\,nm$. If these stars behave like black bodies, then the ratio of thesurface temperature of the sun and north star is

A wall is made of two layers of thickness $1\  cm$ and $4\  cm$ and thermal conductivities $K$ and $3K$ respectively. If temperature difference for the wall is $50\ ^oC$ then temperature difference for the thin layer will be

Two rods $A$ and $B$ of same cross-sectional are $A$ and length $l$ connected in series between a source $(T_1 = 100^o C)$ and a sink $(T_2 = 0^o C)$ as shown in figure. The rod is laterally insulated  If $T_A$ and $T_B$ are the temperature drops across the rod $A$ and $B$, then 

In a composite rod, when two rods of different lengths $l_1$ and $l_2$ and of the same cross-sectional area are joined from end to end then if $K$ is the effective coefficient of thermal conductivity,  the value of $(l_1 + l_2)/K$ is