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A Body Cools from 80° C to 70° C in 5 Minutes and to 62° C in the Next 5 Minutes. Calculate the Temperature of the Surroundings. - Physics

Sum

A body cools from 80° C to 70° C in 5 minutes and to 62° C in the next 5 minutes. Calculate the temperature of the surroundings.

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Solution

Average Temperature,
T1 = 80 +70/2 = 75°C
Average Temperature,
T2 = 70 + 62/2 = 66°C

We know, that `"dT"/"dt"` = − k (T − T0)
Where, T is a average temperature
T0 is surrounding temperature
`10/5` = − k (75 − T0) ..............(1)
`8/5` = − k (66 − T0) ............(2)
Dividing (1) and (2)
`10/8=(75-"T"_0)/(66-"T"_0)`
T0 = 30°C

Concept: Temperature and Heat
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