# Certain quantity of water cools from 70oC to 60oC in the first 5 minutes and to 54oC in the next 5 minutes. The temperature of the surroundings is: Option 1) 45oC Option 2) 20oC Option 3) 42oC Option 4) 10oC

As we learnt in

Newton's Law of Cooling -

Rate of cooling is directly proportional to temperature difference between the body and its surrouding.

-

When body Cools by Radiation from theta1 degree c to theta two degree c in time t -

$\left[\frac{\theta_{1}-\theta_{2}}{t} \right ]=k\left[\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0} \right ]$

- wherein

$\theta_{av}=\frac{\theta_{1}+\theta_{2}}{2}$

Let temperature of the surrounding is T

$then \frac{70-60}{5}=K\left [ \frac{70+60}{2} -T\right ]....(1)$

$and\ \: \frac{60-54}{5}=K\left [ \frac{60+54}{2} -T\right ]....(2)$

Divide (1) and 2)

$\frac{10}{6}=\frac{65-T}{57-T}\ \: \: or\ \: \: 285-5T=195-3T$

or $2T=90$

$or T=45^{\circ}c$

Correct option is 1

Option 1)

45oC

This option is correct

Option 2)

20oC

This option is incorrect

Option 3)

42oC

This option is incorrect

Option 4)

10oC

This option is incorrect

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