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Newton's law of cooling with the average-temperature method: time or temperature over an interval

This type of question, asked 10 times: May 2021 S1, 9 May 2023 S2, 10 May 2023 S2, 20 Apr 2025 S1, 21 Apr 2025 S2, 25 Apr 2025 S1, 11 Apr 2026 S2, 15 Apr 2026 S1, 16 Apr 2026 S2, 18 Apr 2026 S2. All 10 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    May 2021 S1

    39
    The temperature of a liquid drops from 365 K to 361 K in 2 min. Find the time during which temperature of the liquid drops from 344 K to 342 K. (Take, room temperature = 293 K)

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  2. Question 2

    9 May 2023 S2

    40
    The temperature of a liquid falls from 365 K to 359 K in 3 minutes. The time during which temperature of this liquid falls from 342 K to 338 K is [Let the room temperature be 296 K]

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  3. Question 3

    10 May 2023 S2

    42
    An ordinary body cools from '4θ4\theta' to '3θ3\theta' in 't' minutes. The temperature of that body after next 't' minutes is (Assume Newton's law of cooling and room temperature is θ\theta)

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  4. Question 4

    20 Apr 2025 S1

    19
    A body cools from 60∘C60^{\circ}C to 40∘C40^{\circ}C in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is 10∘C10^{\circ}C )

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  5. Question 5

    21 Apr 2025 S2

    20
    Hot water cools from 80∘C80^{\circ}C to 60∘C60^{\circ}C in 1 minutes. In cooling from 60∘C60^{\circ}C to 50∘C50^{\circ}C it will take (room temperature =30∘C=30^{\circ}C )

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  6. Question 6

    25 Apr 2025 S1

    26
    A body cools from 80∘C80^{\circ}C to 50∘C50^{\circ}C in 5 min. In the next time of ' tt ' in, the body continues to cool from 50∘C50^{\circ}C to 30∘C30^{\circ}C. The total time taken by the body to cool from 80∘C80^{\circ}C to 30∘C30^{\circ}C is [The temperature of the surroundings is 20∘C20^{\circ}C.]

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  7. Question 7

    11 Apr 2026 S2

    112
    A body cools in 77 minutes from 60∘60^\circC to 40∘40^\circC. What time (in minutes) does it take to cool from 40∘40^\circC to 28∘28^\circC, if its surrounding temperature is 10∘10^\circC ? (Newton's law of cooling holds good)

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  8. Question 8

    15 Apr 2026 S1

    112
    An ordinary body cools from 4θ4\theta to 3θ3\theta in 't' minutes. The temperature of the body after next 't' minutes is (Assume Newton's law of cooling and room temperature as θ\theta)

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  9. Question 9

    16 Apr 2026 S2

    112
    A bowl filled with very hot water cools from 98∘C98^\circ\mathrm{C} to 86∘C86^\circ\mathrm{C} in 2 minutes when the room temperature is 22∘C22^\circ\mathrm{C}. How long it will take to cool from 75∘C75^\circ\mathrm{C} to 69∘C69^\circ\mathrm{C} ?

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  10. Question 10

    18 Apr 2026 S2

    113
    A body cools from a temperature 3θ3\theta to 2θ2\theta in 10 minute. The room temperature is θ\theta. The temperature of the body at the end of the next 10 minute is 'xx'. Assuming that Newton's law of cooling is applicable, the value of 'xx' will be

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