Answer:
The mass of the juice responsible for melting the ice is 949.043 grams.
Explanation:
By the First Law of Thermodynamics, we understand that juice releases heat to the ice, which turns into water under the assumption that interactions between the ice-juice system and surroundings are negligible and energy processes are done in steady-state. Since juice is done with water, its specific heat will be taken as of the water. The process is described by the following formula:
(1)
Where:
- Mass of ice, in grams.
- Mass of the juice, in grams.
- Specific heat of ice, in joules per gram-degree Celsius.
- Specific heat of water, in joules per gram-degree Celsius.
- Latent heat of fusion, in joules per gram.
- Initial temperature of ice, in degrees Celsius.
- Melting point of water, in degrees Celsius.
- Final temperature of the ice-juice system, in degrees Celsius.
- Initial temperature of the juice, in degrees Celsius.
If we know that , , , , , , and , then the mass of the juice is:
The mass of the juice responsible for melting the ice is 949.043 grams.