# Solve the following problem. 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? - Physics

Sum

Solve the following problem.

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//15) = 10 min

Time taken in cooling is 10 min.

Concept: Newton’s Laws of Cooling
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#### APPEARS IN

Balbharati Physics 11th Standard Maharashtra State Board
Chapter 7 Thermal Properties of Matter
Exercises | Q 3. (xv) | Page 141