A body cools from 80° C to 60° C in 5 minutes. The temperature of the surrounding is 20° C. The time it takes to cool from 60° C to 40° C is :

Solution

Physics sir · 4 steps

Use the average-temperature form of Newton's law for each interval, then divide the two equations.

1. The working rule. Over a short drop, the rate of cooling is proportional to the excess of the average temperature over the surroundings. Here T₀ = 20°C.

   (T₁ - T₂)/t = k((T₁ + T₂)/2 - T₀)

2. First interval. From 80°C to 60°C in 5 min, the average is 70°C. So 20/5 = k(70 - 20), which gives k = 0.08 min⁻¹.
3. Second interval. From 60°C to 40°C, the average is 50°C. So 20/t = 0.08 × (50 - 20) = 2.4, which gives t = 25/3 min.
4. So. t = 25/3 × 60 s = 500 s, which is option (a).

The idea to keep. For equal temperature drops, the time is inversely proportional to (average temperature minus surroundings). A lower average temperature means slower cooling, so the second interval always takes longer.

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