If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously will be
$32$
$16$
$4$
$64$
A body cools in a surrounding which is at a constant temperature of $\theta _0$ . Assuming that it obeys Newton's law of cooling, its temperature $\theta $ is plotted against time $t$ . Tangents are drawn to the curve at the points $A(\theta = \theta _1)$ and $B(\theta = \theta _2)$ . These tangents meet the time-axis at angles $\alpha _1$ and $\alpha _2$ as shown in the graph then
Two diagonally opposite comers of a square made of a four thin rods of same material, same dimensions are at temperature $40^{\circ} C$ and $10^{\circ} C$. If only heat conduction takes place, then the temperature difference between other two corners will be .......... $^{\circ} C$
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 The ratio of the thermal resistance of the rod is
A wall is made up of two layers $A$ and $B.$ The thickness of the two layers is the same, but materials are different. The thermal conductivity of $A$ is double than that of $B.$ In thermal equilibrium the temperature difference between the two ends is $36\,^oC.$ Then the difference of temperature at the two surfaces of $A$ will be......... $^oC$
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