Dinner (2) Mike has to cook mashed potatoes for thanksgiving, and needs to get t

Question

Dinner (2) 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 being 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 th water? (Your answer should have units Watts.) (Hint : draw a picture of the simplified heat flow model.) at that heat 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

mass of the wtare m=6kg

thick ness of the steel, l=1cm

thermal conductivity of steel, k=50 w/m.k

a)

area A=10cm^2

T1=500 oC

T2=25 oC

now,

rate of heat flow, P=Q/t=k*A*(dT)/l

P=50*(10*10^-4)*(500-25)/(1*10^-2)

====> P=2375 W

heat flow rate P=2375 W

b)

heat capacity of water C=4186 J/kg*k

boiling point T3=100 oC

heat enegry required Q=m*C*dT

but,

heat flow rate P=Q/t

P=(m*C*dT)/t

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

==> t=793.14 sec

time taken t=793.14 sec or t=13.22 min

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