Soda pop cane are made of aluminum having thickness of 0.12 mm. They are typically kept at a temperature of 4°C in refrigerator. Such cane has height of 4.83 inch and diameter of 2.6 inch. Suppose you bought such a cold soda pop and brought into the class where the temperature is 25°C. Required:
Calculate the rate of heat transfer of the coke cane to the surroundings.

Explanation:

For flow of heat through conduction , the formula is

Q = KA( T₂ -T₁ ) / d where K is thermal conductivity of material , A is surface area , T₂ - T₁ is temp diff .

Thermal conductivity of aluminum is 205 W /m.s

Surface area of cane = 2π r² + 2π r h where r is radius and h is height of cane .

A = 2π r ( r + h )

= 2 x 3.14 x 1.3 x .0254 ( 1.3 x .0254 + 4.83 x .0254 )

= .20736 ( .033 + .12268 )

A = .03228 m²

thickness d = .12 x 10⁻³ m

Putting the values ,

Q = 205 x .03228 x ( 25 - 4 ) / .12 x 10⁻³

= 1158 x 10³ J /s