Question

A body cools from 60°c to 40°c in 7 minutes.What will be its temperature after next 7 minutes if the temperature of its surrounding is 10°C​

Answer 1

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Question;-

A body cools from 60°c to 40°c in 7 minutes.What will be its temperature after next 7 minutes if the temperature of its surrounding is 10°C.

Answer:-

Given,

• A body cools from 60°C to 40°C in 7 minutes.

To Find,

• The temperature after next 7 minutes If the temperature of its surroundings is 10°C.

Calculations,

In first case,

Initial temperature, T1 = 60°C

Final temperature, T2 = 40°C

Time of cooling, t1 = 7minutes

= 7×60 = 420s

Temperature of surroundings

$t_{o} = 10c$

From Newtons law of cooling we can write,

$\frac{dT}{dt}$= K $\frac{T1-T2}{2}$ - $T_{0}$

$\frac{60 - 40}{420} = k( \frac{60 + 40}{2} - 10)$

$= \frac{20}{420} = k \times 40 - - - - (1)$

In second case:-

Initial temperature , T1 =40°C

Time of cooling , t1 = 7minutes

= 7×60 =420s

Again from Newtons law of cooling we can write,

$\frac{50 - t}{420} = k( \frac{50 + t}{2} - 10) - - - - (2)$

From equation (1) and (2)

We get

T=34°C

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