What is athermanous medium$?$

A metallic prong consists of $4$ rods made of the same material, cross-section, and same lengths as shown.



The three forked ends are kept at ${100}^{\mathrm{o}}\mathrm{C}$ and the handle end is at $0^{\mathrm{o}}\mathrm{C}.$ The temperature of the junction is

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be

The filament of a light bulb has surface area $64 {\mathrm{mm}}^2.$ The filament can be considered as a black body at temperature $2500 \mathrm{K}$ emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of $100 \mathrm{m}$. Assume the pupil of the eyes of the observer to be circular with radius $3 \mathrm{mm}$. Then:

(Take Stefan-Boltzmann constant $=5.67\times {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2} {\mathrm{K}}^{-4},$ Wiens' displacement constant $=2.90\times {10}^{-3} \mathrm{m} \mathrm{K}$, Planck's constant $=6.60\times {10}^{-34} \mathrm{J} \mathrm{s}$, speed of light in vacuum $=3.00\times {10}^8 \mathrm{m}{\mathrm{s}}^{-1}$)

A container with $1 \mathrm{kg}$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 \mathrm{W} {\mathrm{m}}^{-2}$ and it is absorbed by the water over an effective area of $0.05 {\mathrm{m}}^2.$ Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${}^{\circ }\mathrm{C}$) in the temperature of water and the surroundings after a long time will be_________. (Ignore effect of the container, and take constant for Newton's law of cooling $=0.001 {\mathrm{s}}^{-1},$ Heat capacity of water $=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

(Approximate the answer to two decimal place)

Consider a ball of mass $100 \mathrm{g}$ attached to one end of a spring $\left(k=800 \mathrm{N} {\mathrm{m}}^{-1}\right)$ and immersed in $0.5 \mathrm{kg}$ water. Assume the complete system is in thermal equilibrium. The spring is now stretched to $20 \mathrm{cm}$ and the mass is released so that it vibrates up and down. Estimate the change in temperature of water before the vibrations stop.

(Specific heat of the material of the ball $=400 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ and Specific heat of water $=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)