Question

On a trip, you notice that a 3.50-kg bag of ice lasts an average of one day in your cooler. What is the average power in watts entering the ice if it starts at 0ºC and completely melts to 0ºC water in exactly one day? (1 watt = 1 joule/second)

a) 40 W
b) 117,600 W
c) 1,440,000 W
d) 3,600 W

Answer 1

The average power in watts entering the ice is approximately 0.0268 W.

Step-by-step explanation:

To calculate the average power in watts entering the ice, we need to determine the total energy required to melt the ice and the time it takes to do so. The energy required to melt the ice can be calculated using the specific heat capacity of ice and the latent heat of fusion. The specific heat capacity of ice is 2.09 J/g°C, and the latent heat of fusion is 334 J/g. Given that the bag of ice is 3.50 kg, the total energy required to melt the ice is:

Energy = mass x specific heat capacity x temperature change + mass x latent heat of fusion

Energy = (3.50 kg x 2.09 J/g°C x 0 - 0°C) + (3.50 kg x 334 J/g)

Energy = 2317 J

Since the ice completely melts in exactly one day, the time is 24 hours, which is equal to 86400 seconds. Therefore, we can calculate the average power in watts entering the ice by dividing the energy by the time:

Average Power = Energy / Time

Average Power = 2317 J / 86400 s

Average Power ≈ 0.0268 W