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Q. No.A metallic rod of length \(l\) (at \(0^\circ\text C\)) expands by \(\Delta l\) when its temperature is increased by \(100^\circ\text C.\) This rod is kept on a surface with its left end maintained at \(0^\circ\text C,\) and its right end at \(100^\circ\text C.\) The rod is insulated along its length, so heat can only be exchanged at the ends. The length of the rod is:
1.
\(l+\Delta l\)
2.
\(l+\dfrac{\Delta l}{2}\)
3.
\(l+\dfrac{\Delta l}{4}\)
4.
\(l+\dfrac{3\Delta l}{4}\)
Subtopic: Thermal Expansion |
Level 3: 35%-60%
Hints
A heater supplying constant power \(P\) watts is switched on at time \(t=0\) minutes to raise the temperature of a liquid kept in a calorimeter of negligible heat capacity. A student records the temperature of the liquid \(T(t)\) at equal time intervals. A graph is plotted with \(T(t)\) on the \(y\)-axis versus \(t\) on the \(x\)-axis. Assume that there is no heat loss to the surroundings during heating. Then:
| 1. | The graph is a straight line parallel to the time axis. |
| 2. | The heat capacity of the liquid is inversely proportional to the slope of the graph. |
| 3. | If some heat were lost at a constant rate to the surroundings during heating, the graph would be a straight line but with a larger slope. |
| 4. | The internal energy of the liquid increases quadratically with time. |
Subtopic: Temperature and Heat |
59%
Level 3: 35%-60%
Please attempt this question first.
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Please attempt this question first.
Mercury, with a coefficient of thermal expansion \(\gamma\), is poured into a thin glass tube, which does not expand on heating. The length of the mercury column is \(L.\) If the temperature is raised by \(\theta,\) the new length of the mercury column will be:
| 1. | \(L(1+\gamma\theta)\) | 2. | \(L\left(1+\dfrac\gamma2\theta\right)\) |
| 3. | \(L\left(1+\dfrac\gamma3\theta\right)\) | 4. | \(L\left(1+\dfrac{2\gamma}3\theta\right)\) |
Subtopic: Thermal Expansion |
57%
Level 3: 35%-60%
Hints
If the temperature (in \(^\circ\text C\)) of a blackbody is increased \(2\)-fold, then the rate of radiation from the body will become:
| 1. | \(16\)-fold | 2. | \(4\)-fold |
| 3. | less than \(16\)-fold | 4. | more than \(16\)-fold |
Subtopic: Stefan-Boltzmann Law |
Level 4: Below 35%
Hints
A calorimeter contains \(270\) g of ice at \(0^\circ\)C (specific latent heat \(80\) cal/g). Steam (specific latent heat \(540\) cal/g) at \(100^\circ\)C is continuously passed through it, and the excess steam is allowed to escape. Assume negligible loss of heat to the surroundings, except due to excess steam being allowed to escape. Also, ignore the heat capacity of the calorimeter. The final mass of water in the calorimeter is:
1. \(40\) g
2. \(90\) g
3. \(310\) g
4. \(360\) g
1. \(40\) g
2. \(90\) g
3. \(310\) g
4. \(360\) g
Subtopic: Calorimetry |
Level 3: 35%-60%
Hints
Two rods having coefficient of linear expansion \(\alpha,3\alpha\) are connected end-on-end. The average coefficient of thermal expansion for the composite rod:
| 1. | is \(2\alpha\) |
| 2. | is \(4\alpha\) |
| 3. | can be any value between \(\alpha\) and \(3\alpha\) |
| 4. | can be any value between \(2\alpha\) and \(3\alpha\) |
Subtopic: Thermal Expansion |
55%
Level 3: 35%-60%
Hints
A solid non-expanding tank contains air (at atm pressure \({\large p}_0~\&~0^{\circ}\text{C}\)) and mercury, the mercury filling half the tank. Let coefficient of expansion of mercury be \({\Large\gamma}_L.\) If the temperature is raised by \(\theta\) (a few degrees Celsius), the pressure of air increases by (nearly):
| 1. | \({\Large\gamma}_L\theta\times{\large p}_0 ~\) | 2. | \({\Large\frac{\theta}{273}}{\large p}_0\) |
| 3. | \({\dfrac{{\Large\gamma}_L\theta}{273}}{\large p}_0\) | 4. | \(\Big({\Large\gamma}_L\theta+{\Large\frac{\theta}{273}}\Big){\large p}_0 \) |
Subtopic: Thermal Expansion |
54%
Level 3: 35%-60%
Hints
Blackbody radiation emerging from a body at an absolute temperate \(T\) is allowed to fall on an ideal gas enclosed in a transparent vessel until its temperature reaches a steady state value of \(T_1.\) Then:
1. \(T_1=T\)
2. \(T_1>T\)
3. \(T_1<T\)
4. any of the above may be true.
1. \(T_1=T\)
2. \(T_1>T\)
3. \(T_1<T\)
4. any of the above may be true.
Subtopic: Stefan-Boltzmann Law |
53%
Level 3: 35%-60%
Hints
A vessel containing water is heated from the top by means of a heater, just above the water surface. Assume that the temperature of the water was just above \(0^\circ\text{C},\) in the beginning. The temperature \((\theta_A)\) at the bottom is measured as a function of time. Which of the following shows the correct plot?
| 1. | \(a\) | 2. | \(b\) |
| 3. | \(c\) | 4. | \(d\) |
Subtopic: Convection |
51%
Level 3: 35%-60%
Hints
Two bodies \(A,B\) are maintained at temperatures \(\theta_A=100^\circ\text C\) and \(\theta_B=0^\circ\text C.\) Two thermally conducting rods \((P,~Q)\) of different conductivities and of different dimensions are connected between \(A\) and \(B.\) The conductivity of \(P\) is twice that of \(Q.\) The sides of the rods are insulated. If the mid-points of the two rods are connected to each other by a thin conducting wire (after equilibrium is reached),
| 1. | heat would flow from \(P\) to \(Q\). |
| 2. | heat would flow from \(Q\) to \(P\). |
| 3. | no flow of heat occurs between \(P\) & \(Q\). |
| 4. | flow of heat may occur back and forth between \(P\) & \(Q,\) varying with time. |
Subtopic: Conduction |
Level 3: 35%-60%
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