JEE Main 2023 · 6 April · evening · Single correct · +4 / −1

A body cools in 7 minutes from 60° C to 40° C. The temperature of the surrounding is 10° C. The temperature of the body after the next 7 minutes will be:

  1. (a) 34° C
  2. (b) 28° C
  3. (c) 32° C
  4. (d) 30° C
Answer and solution

Answer (b) 28° C

Solution

Physics sir · 4 steps

Track the excess over the surroundings: in equal times it shrinks by the same fraction.

  1. Excess temperature. Newton's law of cooling acts on θ = T - T₀, the excess of the body over the 10°C surroundings. This excess decays exponentially, so in equal time intervals it is multiplied by the same factor.

    θ(t) = θ₀ e⁻ᵏᵗ ⇒ θ₁₄/θ₇ = θ₇/θ₀

  2. First 7 minutes. The excess goes from 60 - 10 = 50°C to 40 - 10 = 30°C. So the factor for 7 minutes is 30/50 = 3/5.
  3. Next 7 minutes. Apply the same factor again: the new excess is 30 × 3/5 = 18°C. The body is then at 10 + 18 = 28°C.
  4. So. After the next 7 minutes the temperature is 28°C, option (b). The average-temperature form of the law gives the same answer here.

The idea to keep. In cooling problems, always subtract the surrounding temperature first. Equal time intervals multiply the excess temperature by the same factor, so a simple ratio gives the next reading.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Heat Transfer

Asked about 30 times in JEE Main since 2020. This question is from 2023.