Embibe Experts Solutions for Chapter: Heat Transfer, Exercise 2: Exercise - 2

Two rods of same dimensions, but made of different materials are joined end to end with their free ends being maintained at $100°C$ and $0°C$ respectively. The temperature of the junction is $70°C$. Then the temperature of the junction if the rods are interchanged will be equal to $T°C$ Find $T$:

A spherical tungsten piece of radius $1.0 \mathrm{cm}$ is suspended in an evacuated chamber maintained at $300 \mathrm{K}$. The piece is maintained at$1000 \mathrm{K}$ by heating it electrically. The rate at which the electrical energy must be supplied. The emissivity of tungsten is $0.30$ and the Stefan constant $\left(\mathrm{\sigma }\right) \mathrm{is} 6.0 \times {10}^{–8} \mathrm{W} {\mathrm{m}}^{-2}{\mathrm{k}}^{-4}$. 

Assume transmitivity $t\to 0$ for all the cases:

A hollow and a solid sphere of same material and having identical outer surface are heated under the identical condition to the same temperature at the same time (both have same $e\mathit{,}\mathit{ }a$) :

The solar constant is the amount of heat energy received per second per unit area of a perfectly black surface placed at a mean distance of the Earth from the Sun, in the absence of Earth's atmosphere, the surface being held perpendicular to the direction of Sun's rays. Its value is $1388 \mathrm{W} {\mathrm{m}}^{-2}$. If the solar constant for the earth is $s$. The surface temperature of the sun is $T \mathrm{K}, D$ is the diameter of the Sun, $R$ is the mean distance of the Earth from the Sun. The sun subtends a small angle$‘\mathrm{\theta }’$ at the earth. Then correct options is/are :

A heated body emits radiation which has a maximum intensity at frequency $v_{\mathit{m}}$. If the temperature of the body is doubled: 

Two identical rods made of two different metals $A\mathit{ }$and $B$ with thermal conductivities $K_A$ and $K_B$ respectively are joined end to end. The free end of $A$ is kept at a temperature $T_1$ while the free end of $B$ is kept at a temperature $T_2 (< T_1)$. Therefore, in the steady-state

A small pond of depth $0.5 \mathrm{m}$ is exposed to a cold winter with outside temperature of $263 \mathrm{K}.$ Thermal conductivity of ice is $K=2.2 \mathrm{W} {\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, latent heat is $L=3.4\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}$, and density is $\rho =0.9\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Take the temperature of the pond to be $273 \mathrm{K}.$ The time taken for the whole pond to freeze is about.