A revolutionary new diet advertises that one can lose weight simply by eating ice. When one eats ice,chemical energy in the body is used to melt the ice and then raise the temperature of the melted ice to the temperature of the body, 37 degrees Celsius.Past scientific studies have confirmed that the expenditure of 1.806 J of energy is necessary to metabolize 0.5kg of body fat.How many grams of ice at 0 degrees celsius would one have to eat to lose 0.5kg of body fat?

To determine the amount of ice one would have to eat to lose 0.5kg of body fat, we need to calculate the amount of energy required to melt the ice and raise its temperature to match the body temperature.

First, let's convert the body fat from kilograms to grams:
0.5 kg = 500 g

Next, we need to calculate the total energy required to metabolize 500 g of body fat:
Energy required = (metabolism energy expenditure per mass) * (mass of body fat)
Energy required = 1.806 J/g * 500 g
Energy required = 903 J

Now, let's calculate the energy needed to melt the ice and raise its temperature:
Energy required to melt the ice = (heat of fusion of ice) * (mass of ice)
Energy required to melt the ice = (334 J/g) * (mass of ice)

To find the mass of ice needed, we equate the energy required to melt the ice with the total energy required:
334 J/g * mass of ice = 903 J

Solving for the mass of ice:
mass of ice = 903 J / 334 J/g
mass of ice ≈ 2.7 g

Therefore, one would have to eat approximately 2.7 grams of ice at 0 degrees Celsius to lose 0.5 kg of body fat.