A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$

A wall consists of alternating blocks of length $d$ and coefficient of thermal conductivity $K_{1}$ and $K_{2}$ respectively as shown in figure. The cross sectional area of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between left and right is

In which case the thermal conductivity increases from left to right

he ratio of the coefficient of thermal conductivity of two different materials is $5 : 3$ . If the thermal resistance of the rod and thickness of these materials is same, then the ratio of the length of these rods will be

Aring consisting of two parts $ADB$ and $ACB$ of same conductivity $k$ carries an amount of heat $H$. The $ADB$ part is now replaced with another metal keeping the temperatures $T_1$ and $T_2$ constant. The heat carried increases to $2H$. What $ACB$ should be the conductivity of the new$ADB$ part? Given $\frac{{ACB}}{{ADB}}= 3$

The ratio of the diameters of two metallic rods of the same material is $2 : 1$ and their lengths are in the ratio $1 : 4$ . If the temperature difference between their ends are equal, the rate of flow of heat in them will be in the ratio