Mike has to cook mashed potatoes for Thanksgiving, and needs to get the water bo

Question

Mike has to cook mashed potatoes for Thanksgiving, and needs to get the water boiling. He puts 6 L (= 6 kg) of water in a steel pot on the stove. The steel is 1 cm thick and has a thermal conductivity of 50 W/(m K) Assume that the water is bring stirred and is thus able to stay at a uniform temperature, and assume that the pot has negligible heat capacity. If the burner surface is 10 cm^2 at 500 degree C and the water starts at 25 degree C, what is the initial rate of heat flow into the water? (Your answer should have units Watts.) At that heal flow rate, given water's heat capacity of 4186 J/(kg K), how long will it take for the water to reach 100 degree C?

Explanation / Answer

Here,

volume , V = 6 L

thickness , t = 1 cm

t = 0.01 m

thermal conductivity , k = 50 W/(m.K)

a)

for the initial rate of heat flow

initial rate of heat flow = k * Area * temperature difference/thickness

initial rate of heat flow = 50 * 10 *10^-4 * (500 - 25)/.01

initial rate of heat flow = 2375 W

the initial rate of heat flow is 2375 W

b)

let the time taken is t

initial rate of heat flow * time = heat needed to change temperature of water to 100 degree

2375 * t = 6 * 4186 * (100 - 25)

t = 793 s

the time taken for water to reach 100 degree C is 793 s

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