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Question

The temperature of a body falls from 40C to 36C in 5 minutes when placed in a surrounding of constant temperature 16C . Find the time taken for the temperature of the body to become 32C.


A

8.1 min

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B

6.1 min

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C

5.3 min

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D

5.1 min

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Solution

The correct option is B

6.1 min


As the temperature differences are small, we can use Newton's law of cooling.

dθdt=k(θθ0)dθθθ0=kdt ...(i)
Where k is a constant,θ is the temperature of the body at time t and θ0 = 16C is the temperature of the surrounding. We have,

360c400cdθθθ0=k(5min)In360c160c400c160c=k(5min)

or, k=In(5/6)5min

or, If t be the time required for the temperature to fall from 360C to 320C then by (i),

320c360cdθθθ0=ktIn320c16c360c160=In(5/6)t5mint=In(4/5)In(5/6)×5min=6.1min


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