Question

How much heat energy is required to change 500 g of ice at 0°C into water at 20°C? The latent heat of the fusion of water is 80 cal/g, and the heat capacity is 1 cal/g.

Answer 1

To calculate the heat energy required to change 500 g of ice at 0°C into water at 20°C, we need to consider two steps:

1. The heat energy required to melt the ice at 0°C (latent heat of fusion).
2. The heat energy required to raise the temperature of the water from 0°C to 20°C (specific heat capacity).

Let's calculate each step:

Step 1: Heat energy to melt the ice The latent heat of fusion of water is given as 80 cal/g. Since we have 500 g of ice, the heat energy required to melt it can be calculated as: Q1 = mass × latent heat of fusion = 500 g × 80 cal/g

Step 2: Heat energy to raise the temperature of the water The specific heat capacity of water is given as 1 cal/g. We need to find the heat energy required to raise the temperature of the water from 0°C to 20°C. Since there is no phase change involved, we can use the formula: Q2 = mass × specific heat capacity × temperature change = 500 g × 1 cal/g°C × (20°C - 0°C)

Now, let's calculate the values:

Q1 = 500 g × 80 cal/g = 40,000 cal

Q2 = 500 g × 1 cal/g°C × 20°C = 10,000 cal

Finally, to find the total heat energy required, we sum up Q1 and Q2:

Total heat energy = Q1 + Q2 = 40,000 cal + 10,000 cal = 50,000 cal

Therefore, the heat energy required to change 500 g of ice at 0°C into water at 20°C is 50,000 calories.