Embibe Experts Solutions for Chapter: Heat Transfer, Exercise 3: Exercise-3

Two metal cubes with $3 \mathrm{cm}$-edge of copper and aluminium are arranged as shown in figure. Find

 The total thermal current from one reservoir to the other. The thermal conductivity of copper is $401 \mathrm{W}/\mathrm{m}-\mathrm{K}$ and that of aluminium is $237 \mathrm{W}/\mathrm{m}-\mathrm{K}$. 

Calculate ${\theta }_1$ and ${\theta }_2$ in shown situation.

An electric heater is used in a room of total wall area $137 {\mathrm{m}}^2$ to maintain a temperature of $+20 °\mathrm{C}$ inside it, when the outside temperature is $-10 °\mathrm{C}$. The walls have three different layers of materials. The innermost layer is of wood of thickness $2.5 \mathrm{c}\mathrm{m}$, the middle layer is of cement of thickness $1.0 \mathrm{c}\mathrm{m}$ and the outermost layer is of brick of thickness $25.0 \mathrm{c}\mathrm{m}$. The power of electric heater (in $\mathrm{W}$) is $x\times {10}^3 \mathrm{W}$. Write the value of $x$ to the nearest integer. Assume that there is no heat loss through the floor and the ceiling. The thermal conductivities of wood, cement and brick are $0.125, 1.5$ and $1.0 \mathrm{W} {\mathrm{m}}^{-1} °{\mathrm{C}}^{-1}$, respectively.

The figure shows the face and interface temperature of a composite slab consisting of four layers of two materials having identical thickness. Under steady state condition, find the value of temperature $\theta$ in${}^{o}C$.

A lagged stick of cross-section area $1 {\mathrm{cm}}^2$ length are $1 {\mathrm{cm}}^2$ and length $1 \mathrm{m}$ is initially at a temperature of $0^{°}\mathrm{C}$. It is then kept between $2$ resevoirs of temperature ${100}^{°}\mathrm{C}$ and $0^{°}\mathrm{C}.$ Specific heat capacity is $10 \mathrm{J} {\mathrm{kg}}^{°}\mathrm{C}$ and linear mass density is $2 \mathrm{kg} {\mathrm{m}}^{-1}$.

(i) If temperature gradient along the rod in steady state is $-50 \mathrm{n} °\mathrm{C} {\mathrm{m}}^{-1}$ then find the value of $n$. 

(ii) If total heat absorbed by the rod to reach steady state is $250 \mathrm{n} \mathrm{J}$ then find the value of $n$.

Calculate the temperature of the black body from given graph.