An iron kettle contains 3.1 kg of ice at -4 deg C. The pot is 2.2 kg and initial

Question

An iron kettle contains 3.1 kg of ice at -4 deg C. The pot is 2.2 kg and initially has a temperature of 18 deg C. The pot stands on a hot plate, delivering 2.3 kW, and the voltage is 220 V.

a) What is the current in the hot plate?

b) How long does it take until the ice is melted (0 deg C)?

c) You now want to boil the water in the kettle in exactly 15 minutes. The voltage is still 220 V. How much current must flow through the hot plate in order to get this done?

You do not have to consider loss of heat to the surroundings.

Explanation / Answer

a)

Power = voltage x current

I = P/V = 2300/220 = 10.45 A

b)

Latent heat (L) = 334 kJ/kg ; specific heat (c) = 2.1 kJ/kgK

Q = mcdT + mL

= 3.1 x 2.1 x 4 + 3.1 x 334 = 1061.44 kJ

But Q = P x t

t = Q/P =1061.44/2.3 = 461.5 sec

c)

specific heat for water = 4.2 kJ/kgK

Q = mcdT = 3.1 x 4.2 x 100 = 1302 kJ

P = Q/t = 1302 /(15x60) = 1.45 kW

VI = 1450

I = 1450/220 = 6.57 A

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