To calculate the heat energy required to change the state of a substance from one phase to another, we need to consider the specific heat capacity and the latent heat of the substance at each phase transition. In the case of ice, we have the following phases: solid (ice) at -20°C, liquid (water) at 0°C, and gas (steam) at 100°C.
The energy required can be calculated as the sum of three parts:
Heating the ice from -20°C to 0°C: Energy = mass × specific heat capacity of ice × temperature change
Melting the ice at 0°C: Energy = mass × latent heat of fusion of ice
Heating the water from 0°C to 100°C: Energy = mass × specific heat capacity of water × temperature change
Vaporizing the water at 100°C: Energy = mass × latent heat of vaporization of water
Heating the steam from 100°C to 129°C: Energy = mass × specific heat capacity of steam × temperature change
Let's calculate each part step by step:
- Heating the ice from -20°C to 0°C: Energy1 = 0.3 kg × specific heat capacity of ice × (0°C - (-20°C))
The specific heat capacity of ice is approximately 2,090 J/(kg·°C).
- Melting the ice at 0°C: Energy2 = 0.3 kg × latent heat of fusion of ice
The latent heat of fusion of ice is approximately 334,000 J/kg.
- Heating the water from 0°C to 100°C: Energy3 = 0.3 kg × specific heat capacity of water × (100°C - 0°C)
The specific heat capacity of water is approximately 4,180 J/(kg·°C).
- Vaporizing the water at 100°C: Energy4 = 0.3 kg × latent heat of vaporization of water
The latent heat of vaporization of water is approximately 2,260,000 J/kg.
- Heating the steam from 100°C to 129°C: Energy5 = 0.3 kg × specific heat capacity of steam × (129°C - 100°C)
The specific heat capacity of steam is approximately 2,010 J/(kg·°C).
Now we can calculate the total energy required by summing up all the individual energy components:
Total Energy = Energy1 + Energy2 + Energy3 + Energy4 + Energy5
After performing the calculations, you will obtain the total heat energy required to change the ice cube from -20°C to steam at 129°C.