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.
\(800^\circ\text{C}\)
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| 1. | \(5 \alpha \) | 2. | \(\dfrac{3 \alpha}{5} \) |
| 3. | \(\dfrac{5 \alpha}{3} \) | 4. | \(15 \alpha\) |
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(\(\theta_1\)\(^\circ \text{C}\)) 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. | \(\theta_{1}=30, ~\theta_{2}=100\) |
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1. \(45\) W
2. \(50\) W
3. \(60\) W
4. \(80\) W
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| 1. | straight line with positive slope. |
| 2. | straight line with negative slope. |
| 3. | exponentially decaying curve. |
| 4. | parabola. |
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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. | \(\dfrac{r_2\Delta\theta_1}{r_1\Delta\theta_2}\) |
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| 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. | \(2\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\) |
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| 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. |
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1. \(12\) minutes
2. \(9\) minutes
3. \(8\) minutes
4. \(7\) minutes
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| 1. | \(a\) | 2. | \(b\) |
| 3. | \(c\) | 4. | \(d\) |
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