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)
V Vakul

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

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