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  • Give answer! 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:

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

 

Answers (1)

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{ heta_{1}- heta_{2}}{t} ight ]=kleft[frac{ heta_{1}+ heta_{2}}{2}- heta_{0} ight ]

- wherein

heta_{av}=frac{ heta_{1}+ heta_{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

Posted by

Vakul

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