Heat Conduction in One Dimension

$1.56\times {10}^5 \mathrm{J}$ of heat is conducted through $2 {\mathrm{m}}^2$ wall of $12 \mathrm{cm}$ thickness in $1 \mathrm{h}$. Temperature difference between the two sides of the wall is $20 °\mathrm{C}$. The thermal conductivity of the material of the wall is (in ${\mathrm{W} \mathrm{m}}^{-1\mathrm{ }}{\mathrm{K}}^{-1}$) $\alpha$. Write the value of $100\alpha$.

A metal rod of length $2 \mathrm{m}$ has cross sectional areas $2A$ and $A$ as shown in the figure. The ends are maintained at temperatures $100°\mathrm{C}$ and $70°\mathrm{C}$. The temperature at middle point $C$ is___$°\mathrm{C}$.

The end $A$ of a rod $AB$ of length $1 \mathrm{m}$ is maintained at $100 °\mathrm{C}$ and the end $B$at $10 °\mathrm{C}$. What is the temperature (in $°\mathrm{C}$) at a distance of $60 \mathrm{cm}$ from the end $B$?

Two heater coils separately take $10 \min$ and $5 \min$ to boil a certain amount of water. If both the coils are connected in series, the time taken to boil water is

Cloudy nights are usually warmer than clear ones, because clouds 

SI unit of temperature gradient is

Which one of the following is not the example of the athermanous medium.

Which one of the following is not the example of the diathermanous medium.

Three rods (lengths $2l, l, l)$ made of the same material and having the same area of cross-section are joined as shown in figure. The end points $A, B$ and $C$ are maintained at constant temperatures $100°\mathrm{C}, 50°\mathrm{C}$ and $0°\mathrm{C},$ respectively. Assuming that there is no loss of heat from the surface of the rods, find the temperature that the junction $P$ ultimately reaches.

Two rods of the same length and diameter having thermal conductivities $K_1$ and $K_2$ are joined in parallel. The equivalent thermal conductivity of the combination is

A long metallic bar is carrying heat from one of its ends to the other end under a steady state. The variation of temperature $\mathrm{\theta }$ along the length $x$ of the bar from its hot end is best described by which of the following figure?

Two rods (one semi-circular and other straight) of the same material and of same cross-sectional area are joined as shown in the diagram. The points $\mathrm{A}$ and $\mathrm{B}$ are maintained at different temperatures. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross-section of the straight rod in a given time is

If the power consumption is $400 \mathrm{W}$,

The thermal conductivity of air is:

The lengths and radii of two rods made of same material are in the ratios $1\text{:}2$and $2\text{:}3$, respectively. If the temperature difference between the ends for the two rods be the same, then in steady state, the amount of heat flowing per second through them will be in the ratio,

A partition wall has two layers of different materials $\mathrm{A}$ and $\mathrm{B}$ in contact with each other. They have the same thickness but the thermal conductivity of layer $\mathrm{A}$ is twice that of $\mathrm{B}$. At steady state, if the temperature difference across the layer $\mathrm{B}$ is $50 \mathrm{K}$, then the corresponding temperature difference across the layer $\mathrm{A}$ is

The thermal conductivity of air is:

Three rods $AB, BC$ and $BD$ of same length $l$ and cross-sectional area $A$ are arranged as shown. The end $D$ is immersed in ice whose mass is $440 \mathrm{g}$ and is at $0{}^{\circ }\mathrm{C}$. The end $C$ is maintained at $100°\mathrm{C}$. Heat is supplied at constant rate of $200 \mathrm{cal} {\mathrm{s}}^{-1}$. Thermal conductivities of $AB, BC$ and $BD$ are $K, 2K$ and $\frac{K}{2}$, respectively. Time after which whole ice will melt is $\left(K=100 \mathrm{cal}/\mathrm{m}-\mathrm{s}-{}^{\circ }\mathrm{C}, A=10{ \mathrm{cm}}^2, l=1 \mathrm{m}\right)$

In the given diagram, the possible direction of heat energy transformation is

Explain athermanous medium with an example.