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 \(A_P\) \(A_Q\) respectively, have the same temperature difference across their ends. If \(k_P\) \(k_Q\) 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 \(0^{\circ}\text{C}~\text{and}~90^{\circ}\text{C},\) respectively. The temperature at the junction of the three rods will be:
1. \(45^{\circ}\text{C}\)
2. \(60^{\circ}\text{C}\)
3. \(30^{\circ}\text{C}\)
4. \(20^{\circ}\text{C}\)
Mud houses are cooler in the summer and warmer in the winter because:
1. | the mud is a superconductor of heat. |
2. | the mud is a good conductor of heat. |
3. | the mud is a bad conductor of heat. |
4. | None of the above |
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 figure. If the temperature at the ends of the slabs are \(\theta_{1}~\text{and}~\theta_{2} \ (\theta_{1} > \theta_{2} ), \) 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 |
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 and . The thermal conductivity of the composite rod will be:
1.
2.
3.
4.
Four rods of the same material with different radii \(r\) and length \(l\) are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?
1. \(r = \frac{1}{3}~\text{cm}, l = \frac{1}{9}~\text{cm}\)
2. \(r =3~\text{cm}, l =9~\text{cm}\)
3. \(r =4~\text{cm}, l =8~\text{cm}\)
4. \(r =1~\text{cm}, l =1~\text{cm}\)
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:
1. | Conduction of heat at different points of the rod stops because the temperature is not increasing |
2. | The rod is a bad conductor of heat |
3. | Heat is being radiated from each point of the rod |
4. | Each point of the rod is giving heat to its neighbour at the same rate at which it is receiving heat |
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. \(85^{\circ}\mathrm{C}\)