Consider two rods of same length and different specific heats $(S_{1}, S_{2})$,conductivities $(K_{1}, K_{2})$ and area of cross-sections $(A_{1}, A_{2})$ and both having temperatures $T_{1}$ and $T_{2}$ at their ends. If the rate of loss of heat due to conduction is equal,then:

The area of a glass window is $10 \ m^2$ and its thickness is $2 \ mm$. The outside and inside temperatures are $40^{\circ}C$ and $20^{\circ}C$ respectively. The thermal conductivity in $MKS$ units is $0.2$. The heat conducted per second into the room is ......

Two rods,one made of copper and the other of steel,having the same length and cross-sectional area,are joined together. The thermal conductivity of copper is $385 \, J s^{-1} m^{-1} K^{-1}$ and that of steel is $50 \, J s^{-1} m^{-1} K^{-1}$. If the copper end is held at $100^{\circ} C$ and the steel end is held at $0^{\circ} C$,the junction temperature is ........... $^{\circ} C$ (Assuming no other heat losses).

$A$ slab of stone of area $3600 \, cm^2$ and thickness $10 \, cm$ is exposed on the lower surface to steam at $100^{\circ} C$. $A$ block of ice at $0^{\circ} C$ rests on the upper surface of the slab. In one hour, $4.8 \, kg$ of ice is melted. The thermal conductivity of the stone in $J \, s^{-1} \, m^{-1} \, K^{-1}$ is (Latent heat of ice $= 3.36 \times 10^5 \, J/kg$)

If the thermal conductivity of aluminum is $0.5 \ cal/cm \cdot s \cdot ^\circ C$,then the temperature gradient required to conduct $10 \ cal/s \cdot cm^2$ in the steady state is ...... $^\circ C/cm$.

One end of a copper rod of length $1.0 \; m$ and area of cross-section $10^{-3} \; m^2$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $92 \; cal/(m \cdot s \cdot ^\circ C)$ and the latent heat of ice is $8 \times 10^4 \; cal/kg$,then the amount of ice which will melt in one minute is: