Generating Electricity from Evaporated Water: An Analysis

Introduction

Generating electricity from the evaporation of water might seem like a promising avenue for renewable energy. However, the process is not as straightforward as one might think. In this article, we will delve into the physics behind using evaporated water to generate electricity and evaluate its practicality.

The Energy Required for Evaporation

Evaporation of water requires a significant amount of energy to overcome the attractive forces between water molecules and convert the liquid phase into a vapor. This energy is known as the latent heat of vaporization. For water, this amount is approximately 2260 kJ/kg at 100°C. Therefore, for 1 kg of water, the energy required for evaporation is calculated as follows:

Q m × L_v
Q 1 kg × 2260 kJ/kg 2260 kJ

Converting Thermal Energy to Electricity

The next step is converting this thermal energy into electrical energy. Modern steam power plants have efficiencies ranging from 30% to 40%. For the purpose of this calculation, we will assume an efficiency of 35%.

Electrical Energy Output Q × Efficiency
Electrical Energy Output 2260 kJ × 0.35 ≈ 791 kJ

To convert this energy from kJ to kWh, we use the conversion factor 1 kWh 3600 kJ.

Electrical Energy Output in kWh 791 kJ / 3600 kJ/kWh ≈ 0.2197 kWh

Conclusion

From evaporating 1 kg of water, approximately 0.22 kWh of electricity can be generated, assuming a conversion efficiency of about 35%. This quantity is less than the initial energy used to evaporate the water, highlighting the inefficiency of the process.

A Deeper Look at Thermal Efficiency

Phil Karn points out that the efficiency of a heat engine in extracting energy from a temperature difference is limited by the thermodynamic limits of efficiency. This means that if we start with 100°C water, the maximum efficiency can be achieved by increasing the temperature of the heat sink (the cold reservoir). According to the efficiency formula, ( eta 1 - frac{T_{cold}}{T_{hot}} ), where temperatures are in Kelvin: For an efficiency of 25%, ( T_{hot} ) 373 K / (1 - 0.25) 497 K or 224°C. For an efficiency of 50%, ( T_{hot} ) 373 K / (1 - 0.5) 746 K or 473°C. For an efficiency of 75%, ( T_{hot} ) 373 K / (1 - 0.75) 1492 K or 1219°C. For an efficiency of 80%, ( T_{hot} ) 373 K / (1 - 0.8) 1865 K or 1592°C. For an efficiency of 90%, ( T_{hot} ) 373 K / (1 - 0.9) 3730 K or 3457°C. As shown, increasing the efficiency by 5% requires a temperature difference of 250°C, but increasing it by 10% from 80% to 90% requires a temperature increase of almost 2000°C, illustrating the challenges and diminishing returns in increasing efficiency.

Summary

While the idea of generating electricity from evaporated water is intriguing, the practical implementation faces significant challenges due to the low initial efficiency and the considerable temperature differences required for high efficiency. Understanding the thermodynamic limits and practical applications is crucial for evaluating the feasibility of this technology.