Question

How much heat energy is required to change a 0.3kg ice cube from a solid at -20°C to steam at 129°C?

Answer 1

To determine the amount of heat energy required to change the state of a substance from one phase to another, you need to consider the specific heat capacity and latent heat of the substance at each phase transition. Here's the breakdown of the heat energy required for each phase transition in the given scenario:

1. Heating the ice cube from -20°C to 0°C (solid to solid at its melting point): The specific heat capacity of ice is approximately 2.09 J/g°C. The mass of the ice cube is 0.3 kg, which is equivalent to 300 grams. The temperature change is from -20°C to 0°C, which is 20°C. The heat energy required for this phase transition is: Q = (mass) x (specific heat capacity) x (temperature change) = 300 g x 2.09 J/g°C x 20°C = 12,540 J

2. Melting the ice cube at 0°C (solid to liquid): The latent heat of fusion (melting) for ice is approximately 334,000 J/kg. The mass of the ice cube is 0.3 kg. The heat energy required for this phase transition is: Q = (mass) x (latent heat of fusion) = 0.3 kg x 334,000 J/kg = 100,200 J

3. Heating the water from 0°C to 100°C (liquid to liquid at its boiling point): The specific heat capacity of water is approximately 4.18 J/g°C. The mass of the water is still 0.3 kg, or 300 grams. The temperature change is from 0°C to 100°C, which is 100°C. The heat energy required for this phase transition is: Q = (mass) x (specific heat capacity) x (temperature change) = 300 g x 4.18 J/g°C x 100°C = 125,400 J

4. Boiling the water at 100°C to steam at 100°C (liquid to gas): The latent heat of vaporization for water is approximately 2,260,000 J/kg. The mass of the water is still 0.3 kg. The heat energy required for this phase transition is: Q = (mass) x (latent heat of vaporization) = 0.3 kg x 2,260,000 J/kg = 678,000 J

5. Heating the steam from 100°C to 129°C (gas to gas): The specific heat capacity of steam is approximately 2.03 J/g°C. The mass of the steam is still 0.3 kg, or 300 grams. The temperature change is from 100°C to 129°C, which is 29°C. The heat energy required for this phase transition is: Q = (mass) x (specific heat capacity) x (temperature change) = 300 g x 2.03 J/g°C x 29°C = 17,697 J

To determine the total heat energy required, add up the values calculated for each phase transition:

Total heat energy = 12,540 J + 100,200 J + 125,400 J + 678,000 J + 17,697 J = 933,837 J

Therefore, approximately 933,837 Joules (J) of heat energy are required to change a 0.3 kg ice cube from a solid at -20°C to steam at 129°C.