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 $\frac{{ACB}}{{ADB}}= 3$

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at ${0^o}C$ and ${90^o}C$ respectively. The temperature of the junction of the three rods will be ...... $^oC$

A cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$. The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is

The only possibility of heat flow in a thermos flask is through its cork which is $75 cm^2$ in area and $5 cm$ thick. Its thermal conductivity is $0.0075 cal/cmsec^oC$. The outside temperature is$ 40^oC$ and latent heat of ice is $80 cal g^{-1}$. Time taken by $500 g$ of ice at $0^oC$ in the flask to melt into water at $0^oC$ is ....... $hr$

For cooking the food, which of the following type of utensil is most suitable

Three rods of the same dimension have thermal conductivities $3K$ , $2K$ and $K$ . They are arranged as shown in fig. Given below, with their ends at $100^oC, 50^oC $and $20^oC$. The temperature of their junction is ......... $^oC$