Two conducting slabs of heat conductivity \(K_{1} ~  \text{and}   ~K_{2}\) are joined as shown in fig. If the temperature at the ends of the slabs are \(\theta_{1}\  and\  \theta_{2} \ (\theta_{1}   >   \theta_{2} ),  \)then the final temperature \( \left(\theta\right)_{m} \)of the junction will be:

              

1.	\(\frac{K_{1} \theta_{1}   +   K_{2} \theta_{2}}{K_{1}   +   K_{2}}\)	2.	\(\frac{K_{1} \theta_{2}   +   K_{2} \theta_{1}}{K_{1}   +   K_{2}}\)
3.	\(\frac{K_{1} \theta_{2}   +   K_{2} \theta_{1}}{K_{1}   -   K_{2}}\)	4.	None

Which of the following is closest to an ideal black body?

A cylindrical rod has temperatures ${\mathrm{T}}_1$ $\mathrm{and}$ ${\mathrm{T}}_2$ at its ends. The rate of flow of heat is $Q_1$ cal/sec. If all the linear dimensions are doubled while keeping the temperature constant, then the rate of flow of heat $Q_2$ will be:

1. $4Q_1$

2. $2Q_1$

3. $\frac{Q_1}{4}$

4. $\frac{Q_1}{2}$

Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities K and 2K, respectively. The equivalent thermal conductivity of the slab will be:

1. $2/6$ $\mathrm{K}$

2. $\sqrt{2}$ $\mathrm{K}$

3. $3\mathrm{K}$

4. $4/3$ $\mathrm{K}$

A pan filled with hot food cools in 2 minutes from \(94^{\circ}\mathrm{C}\) to \(86^{\circ}\mathrm{C}\) when the room temperature is \(20^{\circ}\mathrm{C}\). How long will it take to cool from \(71^{\circ}\mathrm{C}\) to \(69^{\circ}\mathrm{C}\)?

A slab of stone with an area \(0.36~\text{m}^{2}\)${\mathrm{}}^{}$ and thickness of \(0.1~\text{m}\) is exposed on the lower surface to steam at \(100​​^{\circ}\mathrm{C}\)$$. A block of ice at \(0^{\circ}\mathrm{C}\) rests on the upper surface of the slab. In one hour \(4.8~\text{kg}\) of ice is melted. The thermal conductivity of the slab will be: (Given latent heat of fusion of ice \(= 3.36\times10^{5}~\text{JKg}^{-1}\)${\mathrm{}}^{}$)
1. \(1.29~\text{J/m/s/}^{\circ}\text{C}\)
2. \(2.05~\text{J/m/s/}^{\circ}\text{C}\)
3. \(1.02~\text{J/m/s/}^{\circ}\text{C}\)
4. \(1.24~\text{J/m/s/}^{\circ}\text{C}\)

Three stars \(A,\) \(B,\) and \(C\) have surface temperatures \(T_A,~T_B\)and \(T_C\) respectively. Star \(A\) appears bluish, star \(B\) appears reddish and star \(C\) yellowish. Hence,

A piece of iron is heated in a flame. If it becomes dull red first, then becomes reddish yellow, and finally turns to white hot, the correct explanation for the above observation is possible by using:

The diagram shows a bimetallic strip used as a thermostat in a circuit. Copper expands more than Invar for the same temperature rise.

What will be switched on when the bimetallic strip becomes hot?

In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at \(150^{\circ}\mathrm{C}\) is dropped in a copper calorimeter (of water equivalent of 0.025 kg) containing 150 \(c m^{3}\) of water at \(27^{\circ}\mathrm{C}\). The final temperature is \(40^{\circ}\mathrm{C}\). The specific heat of the metal will be: (Heat   losses   to   the   surroundings   are   negligible)
1. \(0 . 40  ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
2. \(0 . 43  ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
3. \(0 . 54 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
4. \(0 . 61 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)