Question 369: Properties of Matter

Question

Certain quantity of water cools from 70
o
C to 60
o
C in the first 5 minutes and to 54
o
C in the next 5 minutes. The temperature of the surroundings is

Accepted Answer

Let the temperature of surroundings be $${	heta _0}$$
By Newton's law of cooling
$${{{	heta _1} - {	heta _2}} \over t} = k\left[ {{{{	heta _1} - {	heta _2}} \over 2} - {	heta _0}} ight]$$
$$ \Rightarrow {{70 - 60} \over 5} = k\left[ {{{70 + 60} \over 2} - {	heta _0}} ight]$$
$$ \Rightarrow 2 = k\left[ {65 - {	heta _0}} ight]$$
Similarly, $${{60 - 54} \over 5} = k\left[ {{{60 + 54} \over 2} - {	heta _0}} ight]$$
$$ \Rightarrow {6 \over 5} = k\left[ {57 - {	heta _0}} ight]$$
By dividing (i) by (ii) we have
$${{10} \over 6} = {{65 - {	heta _0}} \over {57 - {	heta _0}}} \Rightarrow {	heta _0} = {45^o}$$

Answer

45
o
C

Answer

20
o
C

Answer

42
o
C

Answer

10
o
C

Properties of Matter

Certain quantity of water cools from 70 o C to 60 o C in the first 5 minutes and to 54 o C in the next 5 minutes. The temperature of the surroundings is

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