Evaporation is the process by which water changes from a liquid to a gas or vapor. When water is heated to its boiling point, evaporation accelerates significantly. This accelerated process is crucial in various scientific and industrial applications, from cooking to power generation.
The rate at which water evaporates depends on several factors, including the surface area exposed to the air, the temperature of the water and its surroundings, and the energy input driving the process. In the context of boiling, the heat source plays a direct role in supplying the energy required for the phase transition from liquid to gas.
Factors Affecting Evaporation Rate:
Surface Area: A larger surface area allows more water molecules to escape into the air, increasing the evaporation rate.
Temperature: Higher temperatures, both of the water and the ambient air, increase the kinetic energy of water molecules, making them more likely to escape into the vapor phase. Boiling water (100°C at standard pressure) has molecules with high kinetic energy.
Heat Input: The amount of heat supplied directly influences how quickly water reaches its boiling point and how vigorously it boils, both of which are critical for evaporation.
Humidity: While not directly included in this simplified calculator, high ambient humidity can slow down evaporation as the air is already saturated with water vapor.
Air Movement: Wind or air currents can carry away humid air near the surface, replacing it with drier air, thus promoting further evaporation.
The Physics Behind the Calculation:
This calculator estimates the evaporation rate by considering the energy balance. The heat supplied by the heat source is used to raise the water temperature to boiling and then to convert liquid water into steam. The amount of energy required for this phase change (latent heat of vaporization) is a key component. We also factor in the heat loss to the surroundings, although this simplified model focuses primarily on the energy used for evaporation driven by the heat source.
The calculation broadly follows these principles: energy supplied by the heat source minus energy lost to heat the water to boiling and then minus energy lost to the environment (simplified here) equals energy used for evaporation. From the energy used for evaporation, we can determine the mass of water evaporated, and subsequently, the volume and rate.
Note: This calculator provides an estimation. Real-world evaporation can be influenced by factors not precisely modeled here, such as atmospheric pressure, wind speed, and the exact heat transfer efficiency of the container and heat source.
function calculateEvaporationRate() {
var initialVolumeL = parseFloat(document.getElementById("waterVolume").value);
var surfaceAreaM2 = parseFloat(document.getElementById("surfaceArea").value);
var ambientTempC = parseFloat(document.getElementById("ambientTemperature").value);
var waterTempC = parseFloat(document.getElementById("waterTemperature").value);
var timeHours = parseFloat(document.getElementById("timeDuration").value);
var heatPowerWatts = parseFloat(document.getElementById("heatSourcePower").value);
var latentHeatJPerKg = parseFloat(document.getElementById("latentHeatEvaporation").value);
var waterDensityKgPerL = parseFloat(document.getElementById("waterDensity").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(initialVolumeL) || isNaN(surfaceAreaM2) || isNaN(ambientTempC) || isNaN(waterTempC) || isNaN(timeHours) || isNaN(heatPowerWatts) || isNaN(latentHeatJPerKg) || isNaN(waterDensityKgPerL)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (waterTempC < 100 && heatPowerWatts <= 0) {
resultDiv.innerHTML = "Heat source power must be positive if water is not boiling.";
return;
}
// Constants and Conversions
var secondsPerHour = 3600;
var timeSeconds = timeHours * secondsPerHour;
var initialMassKg = initialVolumeL * waterDensityKgPerL;
// Simplified approach: Assume all heat input is used for evaporation after reaching boiling point
// In a more complex model, we'd account for heat needed to reach boiling and heat loss.
// Here, we simplify by assuming the heat source power is directly contributing to evaporation
// and that the water is already at or near boiling.
// Energy supplied by heat source during the duration
var totalEnergySuppliedJ = heatPowerWatts * timeSeconds;
// Energy required to evaporate water: E = m * L
// We need to find 'm' (mass evaporated)
// m = E / L
// Mass of water that *could* be evaporated with the supplied energy
var potentialMassEvaporatedKg = totalEnergySuppliedJ / latentHeatJPerKg;
// The actual mass evaporated is limited by the initial mass of water available
var actualMassEvaporatedKg = Math.min(potentialMassEvaporatedKg, initialMassKg);
// Calculate the volume evaporated
var volumeEvaporatedL = actualMassEvaporatedKg / waterDensityKgPerL;
// Calculate evaporation rate per hour
var evaporationRateLPerHour = volumeEvaporatedL / timeHours;
// Calculate remaining water volume
var remainingVolumeL = initialVolumeL – volumeEvaporatedL;
if (remainingVolumeL 0) ? (volumeEvaporatedL / initialVolumeL) * 100 : 0;
resultDiv.innerHTML = `
Results:
Mass of water potentially evaporated: ${potentialMassEvaporatedKg.toFixed(3)} kg
Actual mass evaporated: ${actualMassEvaporatedKg.toFixed(3)} kg
Volume of water evaporated: ${volumeEvaporatedL.toFixed(3)} Liters
Evaporation Rate: ${evaporationRateLPerHour.toFixed(3)} Liters/Hour
Remaining Water Volume: ${remainingVolumeL.toFixed(3)} Liters
Percentage of water evaporated: ${percentageEvaporated.toFixed(2)} %
`;
}