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Q. No.A piece of alloy of mass \(250~\text{g}\) (specific heat capacity \(=0.1 \times\) that of water) is placed in a furnace and then put into a calorimeter containing \(240~\text{g}\) of water at \(20^\circ\text{C}.\) The water equivalent of the calorimeter is \(10~\text{g}\). The final temperature of the mixture is \(50^\circ\text{C}.\) The temperature of the furnace is (nearly):
1.
\(250^\circ\text{C}\)
2.
\(350^\circ\text{C}\)
3.
\(600^\circ\text{C}\)
4.
\(800^\circ\text{C}\)
Subtopic: Ā Calorimetry |
Ā 68%
Level 2: 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: Ā Thermal Expansion |
Level 3: 35%-60%
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If the ends of the meter stick are maintained at \(\theta_1\)\(^\circ \text{C}\) and \(\theta_2\)\(^\circ \text{C},\) the temperatures measured at the \(25\) cm and \(80\) cm marks are observed to be \(35^\circ \text{C}\) and \(68^\circ \text{C}\) respectively. Then the temperatures of the left end
(\(\theta_1\)\(^\circ \text{C}\)) and the right end (\(\theta_2\)\(^\circ \text{C}\)) are:
(\(\theta_1\)\(^\circ \text{C}\)) and the right end (\(\theta_2\)\(^\circ \text{C}\)) are:
| 1. | \(\theta_{1}=0, ~\theta_{2}=90\) |
| 2. | \(\theta_{1}=10,~\theta_{2}=85\) |
| 3. | \(\theta_{1}=20, ~\theta_{2}=80\) |
| 4. | \(\theta_{1}=30, ~\theta_{2}=100\) |
Subtopic: Ā Conduction |
Ā 71%
Level 2: 60%+
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When the temperature difference between a body and its surroundings is \(20^{\circ}\text{C}\), it loses heat to the surroundings at a rate of \(40\) W. If the temperature difference increases to \(25^{\circ}\text{C}\), the rate of loss of heat is:
1. \(45\) W
2. \(50\) W
3. \(60\) W
4. \(80\) W
1. \(45\) W
2. \(50\) W
3. \(60\) W
4. \(80\) W
Subtopic: Ā Newton's Law of Cooling |
Ā 77%
Level 2: 60%+
Hints
When the logarithm of the temperature difference between a body and its surroundings is plotted as a function of time, the graph is a:
| 1. | straight line with positive slope. |
| 2. | straight line with negative slope. |
| 3. | exponentially decaying curve. |
| 4. | parabola. |
Subtopic: Ā Newton's Law of Cooling |
Ā 64%
Level 2: 60%+
Hints
Two liquids flow through a heat exchanger and exchange heat energy.
The first liquid has a mass flow rate \(\left(\dfrac{dm}{dt}\right)=r_1,\) and its temperature rises by \(\Delta\theta_1.\) For the second liquid, the flow rate \(\left(\dfrac{dm}{dt}\right)=r_2,\) and the temperature fall is \(\Delta\theta_2.\) The ratio of their specific heat capacities is:
The first liquid has a mass flow rate \(\left(\dfrac{dm}{dt}\right)=r_1,\) and its temperature rises by \(\Delta\theta_1.\) For the second liquid, the flow rate \(\left(\dfrac{dm}{dt}\right)=r_2,\) and the temperature fall is \(\Delta\theta_2.\) The ratio of their specific heat capacities is:
| 1. | \(\dfrac{\Delta\theta_1}{\Delta\theta_2}\) | 2. | \(\dfrac{r_1}{r_2}\) |
| 3. | \(\dfrac{r_2\Delta\theta_2}{r_1\Delta\theta_1}\) | 4. | \(\dfrac{r_2\Delta\theta_1}{r_1\Delta\theta_2}\) |
Subtopic: Ā Calorimetry |
Ā 74%
Level 2: 60%+
Hints
The moment of inertia of a metallic rod of length \(L,\) about an axis passing through its centre-of-mass and perpendicular to the rod, is \(I_0.\) When the temperature is raised by \(\Delta\theta,\) it increases by \(\Delta I_0. \) The coefficient of linear expansion of the rod's material is:
| 1. | \(\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
| 2. | \(\dfrac12\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
| 3. | \(\dfrac15\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
| 4. | \(2\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
Subtopic: Ā Thermal Expansion |
Ā 63%
Level 2: 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: Ā Conduction |
Ā 51%
Level 3: 35%-60%
Hints
A body cools from \(52^\circ \text{C}\) to \(48^\circ \text{C}\) in \(6\) minutes. How much time will the same body take to cool from \(53^\circ \text{C}\) to \(47^\circ \text{C}?\) Assume cooling is linear with time.
1. \(12\) minutes
2. \(9\) minutes
3. \(8\) minutes
4. \(7\) minutes
1. \(12\) minutes
2. \(9\) minutes
3. \(8\) minutes
4. \(7\) minutes
Subtopic: Ā Newton's Law of Cooling |
Ā 82%
Level 1: 80%+
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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: Ā Convection |
Ā 51%
Level 3: 35%-60%
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