On a trip, you notice that a 4.56 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 0°C and completely melts to 0°C water in exactly one day? (1 watt = 1 joule/second or 1 W = 1 J/s.)

17.63W

Explanation:

The total energy supplied to the ice is used to melt the ice. Since the ice starts to melt at and also melts completely at the same temperature, the latent heat of fusion will be the focus in solving this problem.

Latent heat of fusion is defined as the amount of energy that changes a solid substance to liquid state without any change in temperature. It is given by the following relationship;

where m is the mass of the substance and l is the specific latent heat of fusion of the substance.

The specific latent heat of fusion of ice is approximately.

The total heat supplied to the ice was used to melt the ice and is calculated using equation (1), given that m = 4.56kg.

The total energy supplied to the ice is equivalent to the average power P entering the ice multiplied by the time t for which the power is supplied. Therefore;

where t = 1 day and 1 day = 24 hours.

24 hours = 60 x 60 x 24s =86400s.

Hence, t = 86400s.

Substituting into equation (2), we get the following;