Calculate The Energy Needed To Vaporize 75g Of Water.

Calculating the Energy Needed to Vaporize 75g of Water: A Comprehensive Guide

Understanding the energy requirements for phase transitions, such as vaporizing water, is crucial in various scientific and engineering applications. This comprehensive guide will walk you through the process of calculating the energy needed to vaporize 75g of water, explaining the underlying principles and offering practical examples. We'll explore the relevant concepts, demonstrate the calculation, and delve into potential applications of this knowledge.

Understanding Phase Transitions and Latent Heat

Water exists in three primary phases: solid (ice), liquid (water), and gas (steam). Transitions between these phases involve energy exchange. When a substance changes phase, it absorbs or releases energy without changing its temperature. This energy is called latent heat. The specific latent heat varies depending on the type of phase transition. For water, we are interested in the latent heat of vaporization.

Latent Heat of Vaporization

The latent heat of vaporization (L_v) is the amount of heat energy required to change one unit of mass of a substance from a liquid to a gas at its boiling point. For water at 100°C (212°F) and atmospheric pressure, the latent heat of vaporization is approximately 2260 kJ/kg or 2260 J/g. This means it takes 2260 Joules of energy to vaporize 1 gram of water at its boiling point.

The Importance of Specific Heat Capacity (Optional but Helpful)

While not directly involved in the vaporization process itself, understanding specific heat capacity is helpful for complete calculations involving temperature changes before the phase transition occurs. The specific heat capacity (c) represents the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree Celsius (or one Kelvin). For water, the specific heat capacity is approximately 4.18 J/g°C. This means it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1°C. This becomes relevant if your water isn't already at 100°C.

Calculating the Energy Needed to Vaporize 75g of Water

Now, let's calculate the energy required to vaporize 75g of water, assuming the water is already at its boiling point (100°C).

The formula for calculating the energy (Q) required for a phase transition is:

Q = m × L_v

Where:

• Q is the heat energy (in Joules)
• m is the mass of the substance (in grams)
• L_v is the latent heat of vaporization (in J/g)

1. Input Values:

• m = 75g (mass of water)
• L_v = 2260 J/g (latent heat of vaporization of water)

2. Calculation:

Q = 75g × 2260 J/g = 169500 J

Therefore, the energy required to vaporize 75g of water at its boiling point is 169,500 Joules or 169.5 kJ.

What if the Water is Not at 100°C? A More Complex Scenario

If the water is not already at its boiling point (100°C), we need to consider the energy required to heat the water to 100°C before calculating the energy for vaporization. This involves two steps:

Step 1: Heating the water to 100°C

The formula for calculating the energy required to heat a substance is:

Q₁ = m × c × ΔT

Where:

• Q₁ is the heat energy (in Joules)
• m is the mass of the substance (in grams)
• c is the specific heat capacity (in J/g°C)
• ΔT is the change in temperature (in °C)

Let's assume the initial temperature of the water is 25°C. Then:

• m = 75g
• c = 4.18 J/g°C
• ΔT = 100°C - 25°C = 75°C

Q₁ = 75g × 4.18 J/g°C × 75°C = 23512.5 J

Step 2: Vaporizing the water at 100°C

This is the same calculation as before:

Q₂ = 75g × 2260 J/g = 169500 J

Step 3: Total Energy

The total energy required is the sum of the energy needed to heat the water and the energy needed to vaporize it:

Q_total = Q₁ + Q₂ = 23512.5 J + 169500 J = 193012.5 J or approximately 193 kJ

Applications of Latent Heat Calculations

Understanding and calculating latent heat has numerous applications across various fields:

• Power Generation: Steam power plants rely on the latent heat of vaporization to generate electricity. The energy released when steam condenses back into water is harnessed to drive turbines.

• HVAC Systems: Air conditioning and refrigeration systems use refrigerants that undergo phase transitions, absorbing heat during evaporation and releasing heat during condensation. Accurate calculations are essential for efficient system design.

• Meteorology: Understanding latent heat is crucial for weather forecasting models. Evaporation and condensation processes significantly influence atmospheric energy transfer and weather patterns.

• Chemical Engineering: Many industrial processes involve phase transitions, such as distillation and evaporation. Precise energy calculations are vital for efficient and safe operation.

• Cooking: Boiling and steaming food rely on the latent heat of vaporization. Understanding this allows for efficient and consistent cooking.

• Medical Applications: Some medical treatments, such as sterilization and wound care, utilize steam and vaporization processes.

Beyond the Basics: Factors Affecting Latent Heat

While we've used standard values for the latent heat of vaporization, it's important to note that this value can vary slightly depending on factors such as:

• Pressure: The latent heat of vaporization decreases as pressure decreases. At higher altitudes, where atmospheric pressure is lower, water boils at a lower temperature and requires less energy to vaporize.

• Impurities: The presence of dissolved substances in water can slightly affect the latent heat of vaporization.

• Temperature: While we've assumed the water is at its boiling point, slight variations around 100°C will have minimal impact.

Conclusion: Mastering Latent Heat Calculations

Calculating the energy needed to vaporize water, or any substance for that matter, is a fundamental concept in thermodynamics with wide-ranging applications. By understanding the principles of latent heat and utilizing the appropriate formulas, we can accurately predict and manage energy requirements in various scenarios. This understanding is crucial for advancements in various fields, from sustainable energy production to improved cooking techniques. This guide provided a clear walkthrough of the calculation and highlighted its practical significance, emphasizing the importance of considering factors beyond the simplified model for more complex and accurate predictions. Remember to always account for any pre-vaporization temperature changes for the most precise results.