Approximately 9,128,550 J of heat is needed to change the cold ice to hot steam at 1100°C.
To calculate the amount of heat required to change the cold ice to hot steam, we need to consider the different phases and energy changes involved.
First, we need to calculate the heat required to raise the temperature of the ice from -15°C to its melting point (0°C). This can be done using the specific heat capacity of ice, which is approximately 2.09 J/g°C. Since we have 3 kg of ice, which is equivalent to 3000 g, the heat required for this phase transition can be calculated as follows:
Q1 = (3000 g) × (2.09 J/g°C) × (0°C - (-15°C)) = 94,050 J.
Next, we need to calculate the heat required to melt the ice, which is known as the heat of fusion. The heat of fusion of ice is 333.5 J/g. Therefore, the heat required for this phase change can be calculated as:
Q2 = (3000 g) × (333.5 J/g) = 1,000,500 J.
Furthermore, we need to calculate the heat required to raise the temperature of the resulting water from 0°C to its boiling point (100°C). The specific heat capacity of water is approximately 4.18 J/g°C. Thus, the heat required for this phase transition can be calculated as:
Q3 = (3000 g) × (4.18 J/g°C) × (100°C - 0°C) = 1,254,000 J.
Finally, we need to calculate the heat required to change the water into steam, which is known as the heat of vaporization. The heat of vaporization of water is 2260 J/g. Therefore, the heat required for this phase change can be calculated as:
Q4 = (3000 g) × (2260 J/g) = 6,780,000 J.
Summing up all the heats required for each phase transition:
Total heat required = Q1 + Q2 + Q3 + Q4 = 94,050 J + 1,000,500 J + 1,254,000 J + 6,780,000 J = 9,128,550
Thus, approximately 9,128,550 J of heat is needed to change the cold ice to hot steam at 1100°C.