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 \(0^{\circ}\mathrm{C}\) \(90^{\circ}\mathrm{C}\), 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. \(20^{\circ}\mathrm{C}\)
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 |
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 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.
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 identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of the composite plate will be:
1. 5
2. 2.4
3. 1.5
4. 1.2
Four rods of the same material with different radii r and length are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?
1.
2. r = 3 cm, = 9 cm
3. r = 4 cm, = 8 cm
4. r = 1 cm, = 1 cm