Embibe Experts Solutions for Chapter: Heat Transfer, Exercise 4: Exercise-4

Heat flows radially outward through a spherical shell of outside radius $R_2$ and inner radius $R_1.$ The temperature of inner surface of the shell is ${\theta }_1$ and that of outer is ${\theta }_2.$ The radial distance from the centre of shell where the temperature is just half way between ${\theta }_1$ and ${\theta }_2$ is

A metallic sphere having radius $0.08 \mathrm{m}$ and mass $m=10 \mathrm{kg}$ is heated to a temperature of $227°\mathrm{C}$ and suspended inside a box whose walls are at a temperature of $27°\mathrm{C}$. The maximum rate at which its temperature will fall is :

(Take $e= 1$, Stefan’s constant $\mathrm{\sigma }= 5.8 \mathrm{x} {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2} {\mathrm{K}}^{-4}$and specific heat of the metal $s= 90 \mathrm{cal} {\mathrm{kg}}^{-1}{\mathrm{deg}}^{-1},\mathit{ }\mathrm{J} = 4.2 \mathrm{Joules} {\mathrm{Calorie}}^{-1}$)

Solar constant for the earth is $2.0 \mathrm{cal} {\mathrm{cm}}^{-2} {\min }^{-1}.$ Stefan's constant is $\sigma =5.7\times {10}^{-12} \mathrm{watt} {\mathrm{cm}}^{-2}-{\mathrm{K}}^{-4}.$ Temperature of sun is $6000 \mathrm{K}.$ Angular diameter of sun as seen from the earth is 

Prevost's theory of heat exchange tells that a body radiates thermal energy 

Fraunhofer lines are found in 

A solid black sphere of radius $R$ and a solid black cylinder of same material and radius with height equal to the radius, are at the same temperature. These are allowed to cool in the same surroundings. The ratio of the rates of fall of their temperature will be-