SUMMARY
The energy required to change one quarter of 8.0 kg of water at 25°C into steam is calculated using the formula Q = mcΔT + mL_v, where m is the mass of water, c is the specific heat capacity, ΔT is the temperature change, and L_v is the latent heat of vaporization. The specific calculations yield Q = 2,520,000 J for heating the water to 100°C, and an additional 4,600,000 J for vaporizing 2.0 kg of water, resulting in a total energy requirement of 7,120,000 J. The discussion clarifies the importance of using the correct latent heat value for vaporization rather than fusion.
PREREQUISITES
- Understanding of specific heat capacity (c) and its units (J/(kg·°C))
- Knowledge of latent heat of vaporization (L_v) and its value (2,300,000 J/kg)
- Ability to perform basic algebraic calculations involving mass and energy
- Familiarity with temperature conversion and the Celsius scale
NEXT STEPS
- Study the concept of latent heat and its applications in phase changes
- Learn about specific heat capacities of various substances
- Explore thermodynamic principles related to energy transfer in heating and phase changes
- Practice solving problems involving energy calculations for different states of matter
USEFUL FOR
Students studying thermodynamics, physics educators, and anyone looking to understand energy calculations in phase changes of water.