A body cools from 80°C to 60°C in 5 minutes. The surroundings are at 20°C. Using the approximation applied in the source solution, the time to cool from 60°C to 40°C is:
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Question

A body cools from 80°C to 60°C in 5 minutes. The surroundings are at 20°C. Using the approximation applied in the source solution, the time to cool from 60°C to 40°C is:

G1 Physics · Accepted Answer

Using the average-excess-temperature form of Newton's law of cooling: For 80°C → 60°C in 5 min, rate = 20/5 = k[(80+60)/2 - 20] = k(50) For 60°C → 40°C in time t, rate = 20/t = k[(60+40)/2 - 20] = k(30) Divide the equations: (20/5)/(20/t) = 50/30 t/5 = 5/3 t = 25/3 min = 500 s Hence option A follows.