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Question

In a room where the temperature is 30oC, a body cools from 61oC to 59oC in 4 minutes. The time taken by the body to cool from 51oC to 49oC will be

A
4 min
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B
5 min
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C
6 min
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D
8 min
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Solution

The correct option is C 6 min
The equation given by Newton's law of cooling:
dTdt=bA(TT0)
dTTT0=bAdt integrating between appropriate limits.
1tln(T2T0T1T0)=constant
Substituting the appropriate conditions:
14ln(59306130)=1tln(49305130)
Solving for t, we get t=6 minutes.

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