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The 'Kangri' is an earthen pot used to stay warm in Kashmir during the winter months. Assume that the 'Kangri' is spherical and of surface area $7 \times 10^{-2} \,m ^{2}$. It contains $300 g$ of a mixture of coal, wood and leaves with calorific value of $30 \,kJ / g$ (and provides heat with $10 \%$ efficiency). The surface temperature of the 'Kangri' is $60^{\circ} C$ and the room temperature is $0^{\circ} C$. Then, a reasonable estimate for the duration $t$ (in h) that the 'Kangri' heat will last is (take the 'Kangri' to be a black body)
Wires $A$ and $B$ have identical lengths and have circular cross-sections. The radius of $A$ is twice the radius of $B$ $i.e.$ ${r_A} = 2{r_B}$. For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by
A body takes $5$ minutes for cooling from ${50^o}C$ to ${40^o}C.$ Its temperature comes down to ${33.33^o}C$ in next $5$ minutes. Temperature of surroundings is ....... $^oC$
A black body radiates energy at the rate of $E$ $W/m^2$ at a high temperature $TK$ . When the temperature is reduced to $\frac{T}{2}K$, the radiant energy will be
Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2\ T$ and $3\ T$ respectively. The temperature of the middle ($i.e.$ second) plate under steady state condition is