Question

A stainless-steel-bottomed kettle, its bottom 22cm cm in diameter and 2.2 mmmm thick, sits on a burner. The kettle holds boiling water, and energy flows into the water from the kettle bottom at 800 WW .What is the temperature of the bottom surface of the kettle? Thermal conductivity of stainless steel is 14 W/(m?K).

Answer 1

Answer:

103.3°C

Explanation:

k = Thermal conductivity of stainless steel = 14 W/m² K

P = Power = 800 W

d = Diameter = 22 cm

t = Thickness of kettle = 2.2 mm

$\Delta T$ = Change in temperature = $(T_2-100)$

100°C boiling point of water

Power is given by

$P=\dfrac{kA\Delta T}{t}\\\Rightarrow P=\dfrac{kA(T_2-T_1)}{t}\\\Rightarrow T_2=\dfrac{Pt}{kA}+T_1\\\Rightarrow T_2=\dfrac{800\times 2.2\times 10^{-3}}{14\times \dfrac{\pi}{4} 0.22^2}+100\\\Rightarrow T_2=103.3\ ^{\circ}C$

The temperature of the bottom of the surface 103.3°C