A body cools from 60°C to 40°C in 6 minutes. If, temperature of surroundings is 10°C. Then, after the next 6 minutes, its temperature will be ____________°C.

Solution

Physics sir · 4 steps

Track the excess over 10°C: it shrinks by the same factor in every equal 6-minute interval.

1. Use excess temperature. Newton's law says the excess over the surroundings, θ - θ₀, decays exponentially with time. So in equal time intervals the excess is multiplied by the same factor.

   (θ₁ - θ₀)/(θᵢ - θ₀) = (θ₂ - θ₀)/(θ₁ - θ₀)

2. First 6 minutes. The excess goes from 60 - 10 = 50 to 40 - 10 = 30. The factor for 6 minutes is 30/50 = 0.6.
3. Next 6 minutes. The excess becomes 30 × 0.6 = 18. So the temperature is 10 + 18 = 28°C. The average-temperature form of the law gives the same 28 here.
4. So. After the next 6 minutes the body is at 28°C.

The common slip: 20. Assuming the body falls by the same 20°C again gives 20. The fall slows as the body gets closer to the surroundings.

The idea to keep. In Newton's cooling, equal times multiply the excess over the surroundings by the same factor. Always subtract the surrounding temperature first.

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