The temperature of a body in air falls from 40° C to 24° C in 4 minutes. The temperature of the air is 16° C. The temperature of the body in the next 4 minutes will be :

Solution

Physics sir · 4 steps

Track how far the body is above the air: that gap shrinks by the same factor every 4 minutes.

1. Excess over air. Newton's law says the excess temperature θ - θ₀ decays exponentially. So in equal time intervals it is multiplied by the same factor.

   θ - θ₀ = (θᵢ - θ₀) e⁻ᵏᵗ

2. First 4 minutes. The excess falls from 40 - 16 = 24 °C to 24 - 16 = 8 °C. So every 4 minutes the excess becomes 8/24 = 1/3 of what it was.
3. Next 4 minutes. The excess drops from 8 °C to 8/3 °C. The body's temperature is then 16 + 8/3 = 56/3 °C ≈ 18.7 °C.
4. So. The temperature after the next 4 minutes is 56/3 °C, option (b). The average-temperature form of Newton's law gives the same value here.

The idea to keep. In Newton's cooling, equal time intervals shrink the excess over the surroundings by the same ratio. Find that ratio from the first interval, then apply it again.

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