To calculate the total amount of heat needed to change a substance from one state to another, you need to consider the heat required for each phase transition and for raising the temperature within each phase. The specific heat capacity of each substance is also necessary. Here's how you can calculate the total heat needed to change the given quantities:
Heat to raise the temperature of ice from -10°C to 0°C: Q1 = mass × specific heat capacity × temperature change Q1 = 345 kg × 2.09 kJ/kg°C × (0°C - (-10°C))
Heat to melt the ice at 0°C: Q2 = mass × heat of fusion of ice Q2 = 345 kg × 333.5 kJ/kg
Heat to raise the temperature of water from 0°C to 100°C: Q3 = mass × specific heat capacity × temperature change Q3 = 345 kg × 4.18 kJ/kg°C × (100°C - 0°C)
Heat to vaporize the water at 100°C: Q4 = mass × heat of vaporization of water Q4 = 345 kg × 2260 kJ/kg
Heat to raise the temperature of steam from 100°C to 120°C: Q5 = mass × specific heat capacity × temperature change Q5 = 0.500 kg × 2.03 kJ/kg°C × (120°C - 100°C)
The total amount of heat needed is the sum of these individual heat values:
Total heat = Q1 + Q2 + Q3 + Q4 + Q5
Simply plug in the values and calculate each term to obtain the total amount of heat needed.