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Question
A metal sphere cools from 80 °C to 60 °C in 6 min. How much time with it take to cool from 60 °C to 40 °C if the room temperature is 30 °C?
Solution
Given: T1 = 80 °C, T2 = 60 °C, T3 = 40 °C, T0 = 30 °C, (dt)1 = 6 min.
To find: Time taken in cooling (dt)2
Formula: `"dT"/"dt" = "C"("T" - "T"_0)`
Calculation: From formula,
`("dT"/"dt")_1 = "C"("T"_1 - "T"_0)`
∴ `(80 - 60)/6` = C(80 - 30)
∴ C = `20/(6 xx 50) = 1/15`/min
Now, `("dT"/"dt")_2 = "C"("T"_2 - "T"_0)`
∴ `(60 - 40)/("dt")_2 = 1/15 (60 - 30)`
∴ `"dt"_2 = (60 - 40)/30 xx 15`
∴ `"dt"_2 = 20/30 xx 15`
∴ `"dt"_2 = 300/30`
∴ `"dt"_2` = 10 min
Time taken in cooling is 10 min.
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