There are two identical vessels filled with equal amounts of ice. The vessels are made of different metals. If the ice melts in the two vessels in $20$ and $35$ minutes respectively,the ratio of the coefficients of thermal conductivity of the two metals is:

Two plates $A$ and $B$ have thermal conductivities $84 \, W m^{-1} K^{-1}$ and $126 \, W m^{-1} K^{-1}$ respectively. They have the same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $A$ and $B$ are kept at $100^{\circ} C$ and $0^{\circ} C$ respectively,then the temperature of the surface of contact in steady state is $.......... \, ^{\circ} C$.

$A$ metallic rod of cross-sectional area $9.0 \, cm^2$ and length $0.54 \, m$,with the surface insulated to prevent heat loss,has one end immersed in boiling water and the other in an ice-water mixture. The heat conducted through the rod melts the ice at the rate of $1 \, g$ for every $33 \, s$. The thermal conductivity of the rod is ....... $W m^{-1} K^{-1}$.

The coefficients of thermal conductivity of copper,mercury,and glass are respectively $K_c, K_m$,and $K_g$ such that $K_c > K_m > K_g$. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $X_c, X_m$,and $X_g$,then:

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

$A$ 'thermacole' icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. $A$ cubical icebox of side $30 \,cm$ has a thickness of $5.0 \,cm$. If $4.0 \,kg$ of ice is put in the box,estimate the amount of ice (in $kg$) remaining after $6 \,h$. The outside temperature is $45 \,^{\circ}C$,and the coefficient of thermal conductivity of thermacole is $0.01 \,J \,s^{-1} \,m^{-1} \,K^{-1}$. Heat of fusion of water $= 335 \times 10^{3} \,J \,kg^{-1}$.