To calculate the heat energy that needs to be removed to change water at 25°C into ice at 4°C, we need to consider the following steps:
- Cooling the water from 25°C to 0°C (to reach the freezing point of water).
- Removing the heat of fusion to convert the water at 0°C into ice at 0°C.
- Cooling the ice from 0°C to 4°C.
Let's calculate the energy required for each step:
Step 1: Cooling water from 25°C to 0°C. The specific heat capacity of water is approximately 4.186 J/g°C. The temperature change is 25°C - 0°C = 25°C.
Heat energy required = mass × specific heat capacity × temperature change Heat energy = 200g × 4.186 J/g°C × 25°C = 20,930 J
Step 2: Removing the heat of fusion to convert water at 0°C into ice at 0°C. The heat of fusion for water is approximately 334 J/g.
Heat energy required = mass × heat of fusion Heat energy = 200g × 334 J/g = 66,800 J
Step 3: Cooling the ice from 0°C to 4°C. The specific heat capacity of ice is approximately 2.09 J/g°C. The temperature change is 4°C - 0°C = 4°C.
Heat energy required = mass × specific heat capacity × temperature change Heat energy = 200g × 2.09 J/g°C × 4°C = 1676 J
Now, let's add up the heat energies from all the steps:
Total heat energy required = 20,930 J + 66,800 J + 1676 J ≈ 89,406 J
So, approximately 89,406 Joules of heat energy need to be removed to change 200g of water at 25°C into ice at 4°C.