An aluminum electric tea kettle with a mass of 500 g is heated with a 500-W heating coil.How long will it take to change the temperature of 1.0 kg of water from 18°C to 98°C in the tea kettle? The specific heat of aluminum is 900 J/kg ∙ K and that of water is 4186 J/kg ∙ K.

Question

Quizplus · Accepted Answer

The first step is to calculate the amount of heat energy required to raise the temperature of 1.0 kg of water from 18°C to 98°C using the specific heat equation:

Q = m * c * ΔT

where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.

Q = 1.0 kg * 4186 J/(kg ∙ K) * (98°C - 18°C)
Q = 350,280 J

Next, we can use the same equation to calculate the amount of heat energy supplied by the heating coil to the aluminum tea kettle:

Q = m * c * ΔT
Q = 0.5 kg * 900 J/(kg ∙ K) * (98°C - 18°C)
Q = 36,000 J

Now, we can use the equation for power:

P = Q/t

where P is power, Q is energy, and t is time.

We want to solve for t, so we rearrange the equation:

t = Q/P

t = 350,280 J / 500 W + 36,000 J / 500 W
t = 701 s + 72 s
t = 773 s or 12.9 minutes

Therefore, the best choice is C) 12 minutes.

An Aluminum Electric Tea Kettle with a Mass of 500