Three identical rod are joined together to form a equilateral triangle as shown, lateral surfaces of rod are insulated. Temperature of end $A$ and $B$ are maintained at $100°\mathrm{C}$ and $200°\mathrm{C}$ respectively as shown in figure. If temperature at point $P$ which is mid point of rod $BC,$ is $T°\mathrm{C}$ then value of $\left(\frac{T}{25}\right)$ in ${}^{\circ }\mathrm{C}$ ?

Refer to the diagram, walls of the vessel are insulated, surrounding temperature is less than zero $\left(-T°\mathrm{C}\right)$ due to which $H$ thickness of ice has already been formed. If rate of increase of thickness of ice at this instant is $\left(\frac{NkT}{5H\rho L_f}\right)$ $L_f\to$ Latent heat of fusion, $\rho$-density of ice and water, $k\to$ thermal conductivity of ice, $A\to$ Cross-sectional area of vessel), then value of $N$ is

Two spherical objects (I) and (II) are placed in same surrounding, their emissivity (e) and radius are shown in figure. If in some time interval, $100 \mathrm{J}$ of energy is absorbed by the object (I), then amount of energy absorbed) by object (II) in same time interval comes out to be $\left(100N\right)\mathrm{J},$ find $N.$

Consider a hollow cylinder of inner radius $a$ and outer radius $2a,$ lateral surface of cylinder is insulated and there is a temperature difference of $\Delta T$ between its ends, and $E_0=\frac{N\pi a^{2}k\Delta T}{L}$ is the rate of energy flow, then value of $N$ is ( k : Thermal conductivity of material)