Q. No.| 1. | density gradient |
| 2. | temperature gradient |
| 3. | velocity gradient |
| 4. | none of these |
The two ends of a rod of length \(L\) and a uniform cross-sectional area \(A\) are kept at two temperatures \(T_1\text{ and }T_2~ (T_1> T_2).\) The rate of heat transfer \(\dfrac{dQ}{dt}\) through the rod in a steady state is given by:
1. \(\dfrac{dQ}{dt} = \dfrac{KL \left(\right. T_{1} - T_{2} \left.\right)}{A}\)
2. \(\dfrac{dQ}{dt} = \dfrac{K \left(\right. T_{1} - T_{2} \left.\right)}{LA}\)
3. \(\dfrac{dQ}{dt} = KLA \left(\right. T_{1} - T_{2} \left.\right)\)
4. \(\dfrac{dQ}{dt} = \dfrac{KA \left(\right. T_{1} - T_{2} \left.\right)}{L}\)
1. \(18^\circ \text{C}\)
2. \(14^\circ \text{C}\)
3. \(45^\circ \text{C}\)
4. \(150^\circ \text{C}\)
| Assertion (A): | Thermal conduction occurs only in the presence of a temperature gradient. |
| Reason (R): | In the absence of a temperature gradient (i.e., no temperature difference in space), thermal energy – which is transferred due to molecular (or particle) collisions, cannot be transferred in any particular direction. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
| 1. | \(45^\circ \text{C}\) | 2. | \(60^\circ \text{C}\) |
| 3. | \(30^\circ \text{C}\) | 4. | \(20^\circ \text{C}\) |
Which of the following circular rods, (given radius \(r\) and length \(l\)) each made of the same material and whose ends are maintained at the same temperature will conduct the most heat:
| 1. | \(r=2r_0;~l=2l_0\) |
| 2. | \(r=2r_0;~l=l_0\) |
| 3. | \(r=r_0;~l=2l_0\) |
| 4. | \(r=r_0;~l=l_0\) |
The thermal conductivity of a rod depends on
1. length
2. mass
3. area of cross section
4. material of the rod.
1. \(60^\circ\text{C}\)
2. \(20^\circ\text{C}\)
3. \(50^\circ\text{C}\)
4. \(10^\circ\text{C}\)
The two ends of a metal rod are maintained at temperatures \(100~^\circ\text{C}\) and \(110~^\circ\text{C}.\) The rate of heat flow in the rod is found to be \(4.0\) J/s. If the ends are maintained at temperatures \(200~^\circ \text{C}\) and \(210 ~^\circ \text{C},\) 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 |
| 1. | \(A\) and \(L\) | 2. | \(A\) and \(1/L\) |
| 3. | \(1/A\) and \(L\) | 4. | \(1/A\) and \(1/L\) |
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