The two ends of a metal rod are maintained at temperatures \(100^{\circ}\mathrm{C}\) and \(110^{\circ}\mathrm{C}\). The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures \(200^{\circ}\mathrm{C}\) and \(210^{\circ}\mathrm{C}\), the rate of heat flow will be:
1. 44.0 J/s
2. 16.8 J/s
3. 8.0 J/s
4. 4.0 J/s

Two rods \(\mathrm{P}\) and \(\mathrm{Q}\)  of equal length and having cross-sections \(A_P\)$\mathrm{ and}$ \(A_Q\) respectively, have the same temperature difference across their ends. If \(k_P\) $\mathrm{and}$ \(k_Q\) are their thermal conductivities, then the condition for their equal rate of conduction of heat will be:
1. \(k_PA_P = k_QA_Q\)
2. \(\frac{\sqrt{k_P}}{A_P} - \frac{\sqrt{k_Q}}{A_Q}\)
3. \(k_PA_Q = k_QA_P\)
4. \(k^2_PA_P = k^2_QA_Q\)

Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod has the same length. The left and right ends are kept at \(0^{\circ}\mathrm{C}\) $and$ \(90^{\circ}\mathrm{C}\), respectively. The temperature at the junction of the three rods will be:

         
1. \(45^{\circ}\mathrm{C}\)
2. \(60^{\circ}\mathrm{C}\)
3. \(30^{\circ}\mathrm{C}\)
4. \(20^{\circ}\mathrm{C}\)$$

Mud houses are cooler in the summer and warmer in the winter because:

The temperature of the hot and cold ends of a 20 cm long rod in a thermal steady state is at \(100^{\circ}\mathrm{C}\) and \(20^{\circ}\mathrm{C}\) respectively. The temperature at the centre of the rod will be:
1. \(50^{\circ}\mathrm{C}\)
2. \(60^{\circ}\mathrm{C}\)
3. \(40^{\circ}\mathrm{C}\)
4. \(30^{\circ}\mathrm{C}\)

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:

Two rods, A and B, of different materials having the same cross-sectional area are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:

1. $\frac{K_1+K_2}{2}$
2. $\frac{3\left(K_1+K_2\right)}{2}$
3. $K_1+K_2$
4. $2\left(K_1+K_2\right)$

Four rods of the same material with different radii r and length $\mathcal{l}$ are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?

1. $r=\frac{1}{3}\mathrm{cm},$ $\mathcal{l}=\frac{1}{9}\mathrm{cm}$

2. r = 3 cm, $\mathcal{l}$ = 9 cm

3. r = 4 cm, $\mathcal{l}$ = 8 cm

4. r = 1 cm, $\mathcal{l}$ = 1 cm

When two ends of a rod wrapped with cotton are maintained at different temperatures and, after some time, every point of the rod attains a constant temperature, then:

Two slabs A and B of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab A is twice that of B. The coefficient of thermal conductivity of slab A is twice that of B. The first surface of slab A is maintained at \(100^{\circ}\mathrm{C}\)$,$ while the second surface of slab B is maintained at \(25^{\circ}\mathrm{C}\)$$. The temperature at the common surface will be:
1. \(62.5^{\circ}\mathrm{C}\)
2. \(45^{\circ}\mathrm{C}\)
3. \(55^{\circ}\mathrm{C}\)
4. \(85^{\circ}\mathrm{C}\)