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Q. No.A rod \(\mathrm{A}\) has a coefficient of thermal expansion \((\alpha_A)\) which is twice of that of rod \(\mathrm{B}\) \((\alpha_B)\). The two rods have length \(l_A,~l_B\) where \(l_A=2l_B\). If the two rods were joined end-to-end, the average coefficient of thermal expansion is:
1.
\(\alpha_A\)
2.
\(\dfrac{2\alpha_A}{6}\)
3.
\(\dfrac{4\alpha_A}{6}\)
4.
\(\dfrac{5\alpha_A}{6}\)
Subtopic: Thermal Expansion |
61%
Level 2: 60%+
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A metal ball of mass \(2\) kg is heated by a \(30~\text{W}\) heater, in a room at \(20^{\circ}\text{C}\). The temperature of the metal becomes steady at \(50^{\circ}\text{C}\). The rate of loss of heat from the ball when the temperature is \(50^{\circ}\text{C}\) is:
1. \(0~\text{W}\)
2. \(50~\text{W}\)
3. \(25~\text{W}\)
4. \(30~\text{W}\)
Subtopic: Newton's Law of Cooling |
Level 3: 35%-60%
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A glass vessel of volume \(V_0\) contains a liquid which fills \(20\%\) of its volume. When the temperature of the system is raised by \(10^\circ\text C,\) the volume of the unfilled portion is found to remain constant. If the coefficient of linear expansion of glass is \(\alpha,\) the coefficient of expansion of the liquid is:
| 1. | \(5 \alpha \) | 2. | \(\dfrac{3 \alpha}{5} \) |
| 3. | \(\dfrac{5 \alpha}{3} \) | 4. | \(15 \alpha\) |
Subtopic: Thermal Expansion |
Level 3: 35%-60%
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A hot body \((A)\) at a temperature of \(2000~ \text K\) radiates like a blackbody, at a rate of \(160 ~\text W.\) It is placed in a furnace which is heated to a temperature of \(1000~ \text K,\) the interior of the furnace behaving like a blackbody. At the initial instant, when the hot body \(A\) is at \(2000~ \text K,\) the net rate of loss of heat from \(A\) due to radiation is:
1. \(160 ~\text W\)
2. \(150 ~\text W\)
3. \(60 ~\text W\)
4. \(10 ~\text W\)
1. \(160 ~\text W\)
2. \(150 ~\text W\)
3. \(60 ~\text W\)
4. \(10 ~\text W\)
Subtopic: Radiation |
55%
Level 3: 35%-60%
Please attempt this question first.
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Please attempt this question first.
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%
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
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 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
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 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%
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