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A container holds 650 kg of ice at a temperature of −27 ∘ C. It is heated at a rate of 15.6 kW for a period of 55 minutes. How much of the ice will have melted?

User Tom Hennen
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Answer: All 650 kg of ice will have melted.

Step-by-step explanation:

To determine how much of the ice will melt, we need to consider the heat energy required to raise the temperature of the ice from -27°C to its melting point (0°C), and then the heat energy required to convert the ice into water at 0°C.

First, let's calculate the heat energy required to raise the temperature of the ice:

Q1 = m * c * ΔT

Where:

Q1 = Heat energy required

m = Mass of ice

c = Specific heat capacity of ice

ΔT = Change in temperature

The specific heat capacity of ice is approximately 2.09 J/g°C.

Converting the mass from kg to grams:

m = 650 kg * 1000 = 650,000 g

ΔT = 0°C - (-27°C) = 27°C

Q1 = 650,000 g * 2.09 J/g°C * 27°C = 36,261,000 J

Next, let's calculate the heat energy required to convert the ice into water:

Q2 = m * L

Where:

Q2 = Heat energy required

m = Mass of ice

L = Latent heat of fusion for ice

The latent heat of fusion for ice is approximately 334 J/g.

Q2 = 650,000 g * 334 J/g = 217,100,000 J

Now, let's calculate the total heat energy supplied to the ice:

Q_total = Power * Time

Converting the power from kW to W:

Power = 15.6 kW * 1000 = 15,600 W

Converting the time from minutes to seconds:

Time = 55 minutes * 60 seconds/minute = 3,300 seconds

Q_total = 15,600 W * 3,300 s = 51,480,000 J

Finally, we can determine the amount of ice that will melt:

Q_total = Q1 + Q2 + Q_melted

Q_melted = Q_total - Q1 - Q2

Q_melted = 51,480,000 J - 36,261,000 J - 217,100,000 J = -201,881,000 J

The negative sign indicates that the system lost heat energy. In this case, it means that all the ice will have melted.

Therefore, all 650 kg of ice will have melted.

User Amazing Angelo
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