Final answer:
The final temperature of the water after transferring 4,200 J of thermal energy to the ice cube is 5°C. The water cooled down by 5°C from its initial temperature of 10°C due to the thermal energy transferred to the ice.
Step-by-step explanation:
The question asks about the change in temperature of water after it has transferred a certain amount of thermal energy to an ice cube. To find the final temperature of the water, we will use the formula that links the thermal energy transferred (Q), the mass of the water (m), the specific heat capacity of the water (C), and the change in temperature (ΔT): Q = m·C·ΔT.
Given that the specific heat capacity of water is 4,200 J/kg°C (which can also be expressed as 4.2 J/g°C since 1 kg = 1000 g),
we can rearrange the formula to solve for the change in temperature:
ΔT = Q / (m·C).
Plugging in the values,
we have ΔT = 4,200 J / (200 g · 4.2 J/g°C).
After simplifying, we find ΔT = 5°C. Since the initial temperature of the water was 10°C and thermal energy transfer tends to lower the temperature of the source, the final temperature of the water would be the initial temperature minus the change in temperature: 10°C - 5°C = 5°C.
Therefore, the final temperature of the water after transferring 4,200 J of thermal energy to the ice cube is 5°C.