Newton's Law of Cooling PYQs: JEE Mains Physics

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1. 1. A cup of coffee cools from \(90^{\circ} \mathrm{C}\) to \(80^{\circ} \mathrm{C}\) in t minutes when the room temperature is \(20^{\circ} \mathrm{C}\). The time taken by the similar cup of coffee to cool from \(80^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\) at the same room temperature is : 2025 Medium
2. 2. The temperature of a body in air falls from \(40^{\circ} \mathrm{C}\) to \(24^{\circ} \mathrm{C}\) in 4 minutes. The temperature of the air is \(16^{\circ} \mathrm{C}\). The temperature of the body in the next 4 minutes will be: 2025 Medium
3. 3. A body cools from \(60^{\circ} C\) to \(40^{\circ} C\) in \(6\) minutes. If, temperature of surroundings is \(10^{\circ} C\). Then, after the next 6 minutes, its temperature will be \(.........{ }^{\circ} C\). 2023 Medium
4. 4. A body cools from \(80^{\circ}\,C\) to \(60^{\circ}\,C\) in \(5\) minutes. The temperature of the surrounding is \(20^{\circ} C\). The time it takes to cool from \(60^{\circ}\,C\) to \(40^{\circ}\,C\) is........... \(s\) 2023 Medium
5. 5. A body cools in \(7\) minutes from \(60^{\circ}\,C\) to \(40^{\circ}\,C\). The temperature of the surrounding is \(10^{\circ}\,C\). The temperature of the body after the next \(7\) minutes will be 2023 Medium
6. 6. A bowl filled with very hot soup cools from \(98^{\circ}\,C\) to \(86^{\circ}\,C\) in \(2\) minutes when the room temperature is \(22^{\circ}\,C\). \(..........\,minutes\) long it will take to cool from \(75^{\circ}\,C\) to \(69^{\circ}\,C\) ? 2023 Medium
7. 7. In an experment ot verify Newton's law of cooling, a graph is plotted between, the temperature difference \((\Delta T )\) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as \(80^{\circ} \,C\). The value of \(t _{2}\) as mentioned in the graph will be...........
   2022 Hard
8. 8. Read the following statements: \(A.\) When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. \(B.\) Two bodies \(P\) and \(Q\) having equal surface areas are maintained at temperature \(10^{\circ}\,C\) and \(20^{\circ}\,C\). The thermal radiation emitted in a given time by \(P\) and \(Q\) are in the ratio \(1: 1.15\) \(C.\) A carnot Engine working between \(100\,K\) and \(400\,K\) has an efficiency of \(75 \%\) \(D.\) When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below : 2022 Hard
9. 9. A body takes \(4\, {min}\). to cool from \(61^{\circ} {C}\) to \(59^{\circ} {C}\). If the temperature of the surroundings is \(30^{\circ} {C}\), the time taken by the body to cool from \(51^{\circ} {C}\) to \(49^{\circ} {C}\) is \(....\,min\) 2021 Medium
10. 10. In \(5\, minutes,\) a body cools from \(75^{\circ} {C}\) to \(65^{\circ} {C}\) at room temperature of \(25^{\circ} {C}\). The temperature of body at the end of next \(5\, minutes\) is \(......\,{ }^{\circ} {C} .\) 2021 Medium
11. 11. A metallic sphere cools from \(50^{\circ} C\) to \(40^{\circ} C\) in \(300 \,s.\) If atmospheric temperature around is \(20^{\circ} C ,\) then the sphere's temperature after the next \(5\) minutes will be close to\(.....C\) 2020 Medium
12. 12. A body takes \(10\, minutes\) to cool from \(60\,^oC\) to \(50\,^oC\). The temperature of surroundings is constant at \(25\,^oC\). Then, the temperature of the body after next \(10\, minutes\) will be approximately ....... \(^oC\) 2018 Medium
13. 13. A black coloured solid sphere of radius \(R\) and mass \(M\) is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature \(T_0\). The initial temperature of the sphere is \(3T_0\). If the specific heat of the material of the sphere varies as \(\alpha T^3\) per unit mass with the temperature \(T\) of the sphere, where \(\alpha \) is a constant, then the time taken for the sphere to cool down to temperature \(2T_0\) will be ( \(\sigma \) is Stefan Boltzmann constant) 2014 Hard
14. 14. A hot body, obeying Newton's law of cooling is cooling down from its peak value \(80\,^oC\) to an ambient temperature of \(30\,^oC\) . It takes \(5\, minutes\) in cooling down from \(80\,^oC\) to \(40\,^oC\).  ........  \(\min.\) will it take to cool down from \(62\,^oC\) to \(32\,^oC\) ? (Given \(ln\, 2\, = 0.693, ln\, 5\, = 1.609\)) 2014 Hard
15. 15. Hot water cools from \(60\,^oC\) to \(50\,^oC\) in the first \(10\,minutes\) and to \(42\,^oC\) in the next \(10\,minutes.\) The temperature of the surroundings is ...... \(^oC\) 2014 Hard

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