Final answer:
Upon cooling 5.0 g of water from 25°C to 0°C, the water loses 525 J of energy, which in turn melts approximately 1.544 g of ice, taking into account the latent heat of fusion of ice.
Step-by-step explanation:
To solve this physics problem, we need to calculate the amount of energy lost by the 5.0 g of water as it cools to 0°C and then determine how much of this energy is used to melt the ice. The steps involve calculating the heat energy lost by the water using its specific heat capacity, then using the specific latent heat of fusion of ice to calculate the mass of ice that melts.
Step 1: Calculating the energy lost by the water
Firstly, calculate the energy (Q) lost by the water when it cools from 25°C to 0°C using the formula:
Q = mass × specific heat capacity × change in temperature
Q = 5.0 g × 4.2 J/(g°C) × (0°C - 25°C)
Q = 5.0 g × 4.2 J/(g°C) × (-25°C)
Q = -525 J (negative sign indicates loss of energy)
Step 2: Calculating the mass of ice that melts
Next, use the specific latent heat of fusion of ice to determine how much ice melts with the energy removed from the water:
mass of ice melted = energy lost by water / specific latent heat of fusion
mass of ice melted = 525 J / 340 J/g
mass of ice melted = 1.544 g (approximately)
Thus, the mass of ice that melts is approximately 1.544 g.