Answer:
14.46°C
Step-by-step explanation:
Given:
- Mass of ice = 28 g = 0.028 kg
- Mass of water = 562 g = 0.562 kg
- Mass of copper calorimeter = 80 g = 0.08 kg
- Specific heat of copper = 387 J/(kg°C)
- Specific heat of water = 4186 J/(kg°C)
- Specific heat of ice = 2090 J/(kg°C)
- Latent heat of fusion of water = 3.33 x 10^5 J/kg
- Initial temperature of ice = -78°C
- Melting point of ice = 0°C
- Initial temperature of water and copper calorimeter = 21°C
Find:
- The final temperature of the mixture
Solution:
1. Calculate the heat required to warm the ice from its initial temperature to its melting point: Heat to warm ice = Mass of ice * Specific heat of ice * (Melting point of ice - Initial temperature of ice) Heat to warm ice = 0.028 kg * 2090 J/(kg*°C) * (0°C - (-78°C)) = 4579.44 J
2. Calculate the heat required to melt the ice at its melting point: Heat to melt ice = Mass of ice * Latent heat of fusion of water Heat to melt ice = 0.028 kg * 3.33e5 J/kg = 9324 J
3. Calculate the heat lost by the water and calorimeter as they cool down to the final temperature: Heat lost by water and calorimeter = Mass of water * Specific heat of water * (Initial temperature of water and copper calorimeter - Final temperature) + Mass of copper calorimeter * Specific heat of copper * (Initial temperature of water and copper calorimeter - Final temperature)
4. The total heat gained by the ice must be equal to the total heat lost by the water and calorimeter: Heat to warm ice + Heat to melt ice + Mass of ice * Specific heat of water * (Final temperature - Melting point of ice) = Heat lost by water and calorimeter 4579.44 J + 9324 J + 0.028 kg * 4186 J/(kg°C) * (Final temperature - 0°C) = [0.562 kg * 4186 J/(kg°C) + 0.080 kg * 387 J/(kg*°C)] * (21°C - Final temperature)
Solving for the final temperature, we get: Final temperature ≈ 14.46°C
So, the final temperature of the system is approximately 14.46°C