Latent Heat Formula

What is Latent Heat Formula?

Latent heat is a critical concept in physics, particularly when studying the changes in the state of matter, such as melting or boiling. The latent heat formula helps calculate the amount of energy absorbed or released during these phase changes without a change in temperature. This formula is especially useful in understanding how much energy substances require to change from solid to liquid or from liquid to gas and vice versa.

The latent heat formula is expressed as

𝑄 = 𝑚 x 𝐿
or

L = Q / m

• Q represents the heat absorbed or released
• m is the mass of the substance
• L is the latent heat capacity, indicating the amount of heat needed to change the phase of one kilogram of the substance.

The concept of latent heat was first introduced by Joseph Black, a Scottish physicist, in the 18th century. He made significant contributions to thermodynamics, distinguishing between heat that changes temperature and heat that changes physical state.

Derivation of Latent Heat Formula

To derive the latent heat formula, let’s begin with the understanding that during a phase change, such as ice melting into water or water vaporizing into steam, the temperature of the substance does not change. Instead, the energy provided goes into changing the state of the substance. This energy change is what we refer to as latent heat.

First, consider the relationship between energy and mass in the context of phase changes. The amount of energy required to change the phase of a substance depends on how much of the substance you have. This means that the energy involved in the phase change is directly proportional to the mass of the substance. We express this relationship as:

𝑄∝𝑚

Where:

• 𝑄 is the total energy absorbed or released during the phase change
• 𝑚 is the mass of the substance.

Next, we introduce a proportionality constant, L is known as the latent heat capacity. This constant represents the amount of energy required to change the phase of one kilogram of a substance without changing its temperature.

By replacing the proportionality with an equality, we get the latent heat formula:

𝑄=𝑚 x 𝐿

Where:

• L is the latent heat capacity, measured in joules per kilogram (J/kg).

Thus, the latent heat formula 𝑄=𝑚L effectively quantifies how much energy is absorbed or released when a specific mass of a substance undergoes a phase change. This formula is essential in physics for calculating energy transformations in processes like melting, boiling, or condensing.

Applications of Latent Heat Formula

1. Weather Prediction: Meteorologists use the latent heat formula to calculate the energy involved in water vapor condensing into clouds, which is essential for predicting weather patterns and rainfall.
2. Heating and Cooling Systems: Engineers design HVAC systems using the latent heat formula to ensure efficient phase changes in refrigerants, which help in heating or cooling buildings effectively.
3. Food Industry: In the food industry, the latent heat formula helps in designing processes like freezing and thawing, ensuring that foods are preserved or processed without altering their properties too drastically.
4. Energy Sector: The formula is crucial in power generation, particularly for steam turbines, as it efficiently boils and condenses water to generate electricity.
5. Climatology: Researchers apply the latent heat concept to study global warming and the melting of ice caps by calculating the energy required for ice to melt in different conditions.

Example Problems on Latent Heat Formula

Problem 1: Calculating Energy for Melting Ice

Question: How much energy is required to melt 500 grams of ice at 0°C? The latent heat of fusion for ice is 334,000 joules/kg.

Solution:

Identify the given values:

Mass, 𝑚 = 500 grams = 0.5 kg (since 1 kg = 1000 grams)

Latent heat of fusion, 𝐿 = 334,000 joules/kg

Apply the latent heat formula:𝑄=𝑚 x 𝐿

Q=mL

Q = 0.5 kg × 334,000 J/kg

𝑄=167,000 joules

Explanation: To melt 0.5 kg of ice, 167,000 joules of energy are needed. This energy goes into breaking the molecular bonds in the ice without raising its temperature.

Problem 2: Energy Released During Condensation

Question: Calculate the amount of energy released when 2 kg of steam at 100°C condenses into water at the same temperature. The latent heat of vaporization of water is 2,260,000 joules/kg.

Solution:

Identify the given values:

Mass, 𝑚 = 2 kg

Latent heat of vaporization, 𝐿 = 2,260,000 joules/kg

Apply the latent heat formula:

𝑄=𝑚𝐿

𝑄 = 2 kg × 2,260,000 J/kg

𝑄 = 4,520,000 joules

Explanation: When 2 kg of steam condenses, it releases 4,520,000 joules of energy. This released energy can significantly warm the surroundings, as the steam transfers its hidden heat to the environment.

FAQs

What is L in Latent Heat?

L represents the latent heat capacity, measuring energy per unit mass required for a phase change, expressed in joules per kilogram (J/kg).

How to Calculate Latent Heat of Vaporization?

Multiply the mass of the substance by its latent heat of vaporization value: 𝑄=𝑚𝐿, where 𝐿 is specific to vaporization.

How to Calculate Latent Heat of Ice?

Use the formula 𝑄=𝑚𝐿, substituting 𝐿 with the latent heat of fusion specific to ice to determine the required energy.