First slide

Radiation

Question

In a room, where the temperature is 30⁰C, a body cools from 61⁰C to 59⁰C in 4 min. The time taken by the body to cool from 51⁰C to 49⁰C will be [MP PMT 2013)

Moderate

A

4 min
B

5 min
C

6 min
D

8 min

Solution

According to Newton's law of cooling,
$\frac{61 - 59}{4} = K (\frac{61 + 59}{2} - 30)$
$\Rightarrow \frac{2}{4} = K \times 30$
$Similarly, \frac{51 - 49}{t} = K (\frac{51 + 49}{2} - 30)$
$\Rightarrow \frac{2}{t} = K \times 20$
Solving Eqs. (i) and (ii), we get
t = 6 min

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