Q. No.A cup of coffee cools from \(90^{\circ}\text{C}\) \(80^{\circ}\text{C}\) in \(t\) minutes, when the room temperature is \(20^{\circ}\text{C}.\) The time taken by a similar cup of coffee to cool from \(80^{\circ}\text{C}\) \(60^{\circ}\text{C}\) at room temperature same at \(20^{\circ}\text{C}\) is:
1. \(\frac{10}{13}t\)
2. \(\frac{5}{13}t\)
3. \(\frac{13}{10}t\)
4. \(\frac{13}{5}t\)
1. \(\frac{10}{13}t\)
2. \(\frac{5}{13}t\)
3. \(\frac{13}{10}t\)
4. \(\frac{13}{5}t\)
Two conducting slabs of heat conductivity \(K_{1} ~\text{and}~K_{2}\) are joined as shown in figure. If the temperature at the ends of the slabs are \(\theta_{1}~\text{and}~\theta_{2} \ (\theta_{1} > \theta_{2} ), \) then the final temperature \( \left(\theta\right)_{m} \) of the junction will be:
| 1. | \(\frac{K_{1} \theta_{1} + K_{2} \theta_{2}}{K_{1} + K_{2}}\) | 2. | \(\frac{K_{1} \theta_{2} + K_{2} \theta_{1}}{K_{1} + K_{2}}\) |
| 3. | \(\frac{K_{1} \theta_{2} + K_{2} \theta_{1}}{K_{1} - K_{2}}\) | 4. | None |
A slab of stone with an area \(0.36~\text{m}^{2}\) and thickness of \(0.1~\text{m}\) is exposed on the lower surface to steam at \(100^\circ\text{C}.\) A block of ice at \(0^{\circ}\text{C}\) rests on the upper surface of the slab. In one hour \(4.8~\text{kg}\) of ice is melted. The thermal conductivity of the slab will be:
(Given latent heat of fusion of ice \(= 3.36\times10^{5}~\text{JKg}^{-1}\))
1. \(1.29~\text{J/m/s/}^{\circ}\text{C}\)
2. \(2.05~\text{J/m/s/}^{\circ}\text{C}\)
3. \(1.02~\text{J/m/s/}^{\circ}\text{C}\)
4. \(1.24~\text{J/m/s/}^{\circ}\text{C}\)
The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:
| 1. | \(-40^\circ\) | 2. | \(40^\circ\) |
| 3. | \(0^\circ\) | 4. | \(50^\circ\) |
1. \(T_A>T_B>T_C\)
2. \(T_B>T_C>T_A\)
3. \(T_C>T_B>T_A\)
4. \(T_A>T_C>T_B\)
1. \(1:4\)
2. \(3:1\)
3. \(1:2\)
4. \(6:1\)
Which of the curves in the figure represents the relation between Celsius and Fahrenheit temperature?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
| 1. | \(\dfrac{4T}{5}\) | 2. | \(T\) |
| 3. | \(\dfrac{T}{2}\) | 4. | \(\dfrac{5T}{4}\) |
| 1. | increases by a factor of \(4\) |
| 2. | increases by a factor of \(2\) |
| 3. | remains unchanged |
| 4. | decreases by a factor of \(2\) |
| Assertion (A): | In a pressure cooker the water is brought to a boil. The cooker is then removed from the stove. Now on removing the lid of the pressure cooker, the water starts boiling again. |
| Reason (R): | The impurities in water bring down its boiling point. |
| 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. | Both (A) and (R) are False. |
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