To solve this problem, we need to consider the energy required to warm the ice cube from -18.5°C to 0°C, the energy required to melt the ice cube, and the energy required to warm the melted water from 0°C to 55°C. Let's calculate the energy for each step and determine the number of ice cubes needed.
Warming the ice cube to 0°C:
The specific heat capacity of ice is 2.05 J/g°C. The temperature change is from -18.5°C to 0°C. Therefore, the energy required to warm the ice cube can be calculated as:
Energy = mass × specific heat capacity × temperature change
Energy = 24 g × 2.05 J/g°C × (0°C - (-18.5°C))
Energy = 24 g × 2.05 J/g°C × 18.5°C = 899.4 J
Melting the ice cube:
The heat of fusion (specific latent heat of fusion) of water is 334 J/g. We need to determine the energy required to melt the ice cube. The mass of the ice cube is 24 g, so the energy required can be calculated as:
Energy = mass × heat of fusion
Energy = 24 g × 334 J/g = 8016 J
Warming the melted water from 0°C to 55°C:
The specific heat capacity of water is 4.184 J/g°C. We need to determine the energy required to warm the melted water from 0°C to 55°C. The mass of the melted water can be calculated by subtracting the mass of the ice cube that melted from the initial mass of the ice cube (24 g).
Mass of melted water = 24 g - 24 g = 0 g (since all the ice melted)
Therefore, no additional energy is required for this step.
Now, let's add up the energy required for each step to determine the total energy needed to cool the coffee from 85°C to 55°C:
Total energy required = Energy to warm the ice cube to 0°C + Energy to melt the ice cube
Total energy required = 899.4 J + 8016 J = 8915.4 J
Given that each ice cube provides 8915.4 J of energy, we can determine the number of ice cubes needed to cool the coffee.
Energy per ice cube = 8915.4 J
Energy required to cool the coffee = Total energy required = 8915.4 J
The number of ice cubes needed = Energy required to cool the coffee / Energy per ice cube
Number of ice cubes needed = 8915.4 J / 8915.4 J = 1
Therefore, you would need to add 1 ice cube to your 355 mL cup of coffee to bring it to 55°C.
The correct answer is A. 1.