Understanding Latent Heat: Definition and Significance

The concept of latent heat plays a crucial role in our understanding of phase transitions in materials, such as the conversion of ice into water or water into steam. This article aims to provide a comprehensive look at what latent heat is, its mathematical representation, and its real-world applications.

What is Latent Heat?

Latent heat is the heat energy required to change the phase of a substance without changing its temperature. This is in contrast to sensible heat, which changes the temperature of a substance but not its phase. The term “latent” comes from the Latin word “latens,” meaning “to lie hidden,” as this heat energy is essentially “hidden” since it doesn’t bring about a temperature change during a phase transition.

Types of Latent Heat

There are two main types of latent heat:

1. Latent Heat of Fusion: This is the heat energy required to change a solid into a liquid at its melting point. For example, the latent heat of fusion for water is approximately \( 334 \, \text{kJ/kg} \).

2. Latent Heat of Vaporization: This is the heat energy required to change a liquid into a gas at its boiling point. For water, the latent heat of vaporization is approximately \( 2260 \, \text{kJ/kg} \).

Mathematical Representation

The amount of latent heat (\( Q \)) involved in a phase transition can be calculated using the formula:

\[

Q = mL

\]

Where:

– \( Q \) is the heat energy absorbed or released,

– \( m \) is the mass of the substance,

– \( L \) is the specific latent heat of the substance (either fusion or vaporization).

Applications of Latent Heat

1. Climate Systems: Latent heat released during the condensation of water vapor helps drive weather systems.

2. Refrigeration: Latent heat is extracted from substances to cool them down in refrigerators and air conditioners.

3. Steam Engines: The latent heat of vaporization of water is harnessed for mechanical work in steam engines.

4. Food Processing: Latent heat is important in processes like freeze-drying, where water is sublimated from food items.

5. Human Physiology: Sweat evaporation utilizes latent heat to cool down the body.

Real-World Example: Ice Packs

A common example of latent heat is the chemical ice pack used for first aid. It consists of water and a packet of ammonium nitrate. When the packet is broken and the substances mix, the ammonium nitrate dissolves in the water, absorbing the latent heat and causing the temperature to drop rapidly.

Conclusion

Understanding latent heat is fundamental to the study of thermodynamics and has wide-ranging applications, from meteorology to engineering. This “hidden” form of heat is responsible for phase changes and plays a crucial role in the natural world and our technological advancements.

**PROBLEMS AND SOLUTIONS**

1. What is latent heat?

Solution: Latent heat is the heat energy required to change the phase of a substance without changing its temperature.

2. How is latent heat different from sensible heat?

Solution: Sensible heat changes the temperature of a substance but not its phase, whereas latent heat changes the phase but not the temperature.

3. What is the latent heat of fusion?

Solution: It is the heat energy required to change a solid into a liquid at its melting point.

4. What is the latent heat of vaporization?

Solution: It is the heat energy required to change a liquid into a gas at its boiling point.

5. Why is the term “latent” used?

Solution: The term “latent” comes from Latin, meaning “to lie hidden,” as this heat energy is essentially “hidden” since it doesn’t cause a temperature change during a phase transition.

6. Calculate the heat energy required to melt 2 kg of ice at \(0^\circ\) C. The latent heat of fusion for water is \(334 \, \text{kJ/kg}\).

Solution:

\[

Q = mL = 2 \, \text{kg} \times 334 \, \text{kJ/kg} = 668 \, \text{kJ}

\]

7. How much heat is needed to vaporize 1.5 kg of water at \(100^\circ\) C? The latent heat of vaporization for water is \(2260 \, \text{kJ/kg}\).

Solution:

\[

Q = mL = 1.5 \, \text{kg} \times 2260 \, \text{kJ/kg} = 3390 \, \text{kJ}

\]

8. If 500 kJ of heat is added to 3 kg of ice at \(0^\circ\) C, how much of the ice will melt?

Solution:

\[

m = \frac{Q}{L} = \frac{500 \, \text{kJ}}{334 \, \text{kJ/kg}} = 1.5 \, \text{kg}

\]

9. A 2 kg block of aluminum at its melting point absorbs 800 kJ of heat. What is the latent heat of fusion for aluminum?

Solution:

\[

L = \frac{Q}{m} = \frac{800 \, \text{kJ}}{2 \, \text{kg}} = 400 \, \text{kJ/kg}

\]

10. How much heat is needed to convert 5 kg of water at \(100^\circ\) C to steam?

Solution:

\[

Q = mL = 5 \, \text{kg} \times 2260 \, \text{kJ/kg} = 11300 \, \text{kJ}

\]

11. If 1200 kJ of heat is added to 2 kg of water at \(100^\circ\) C, how much of it will be converted to steam?

Solution:

\[

m = \frac{Q}{L} = \frac{1200 \, \text{kJ}}{2260 \, \text{kJ/kg}} = 0.53 \, \text{kg}

\]

12. A substance has a latent heat of fusion of \(250 \, \text{kJ/kg}\). How much heat is required to melt 4 kg of this substance?

Solution:

\[

Q = mL = 4 \, \text{kg} \times 250 \, \text{kJ/kg} = 1000 \, \text{kJ}

\]

13. How much heat is required to vaporize 1 kg of a liquid with a latent heat of vaporization of \(1800 \, \text{kJ/kg}\)?

Solution:

\[

Q = mL = 1 \, \text{kg} \times 1800 \, \text{kJ/kg} = 1800 \, \text{kJ}

\]

14. A 3 kg sample of a substance at its boiling point absorbs 2700 kJ of heat. What is its latent heat of vaporization?

Solution:

\[

L = \frac{Q}{m} = \frac{2700 \, \text{kJ}}{3 \, \text{kg}} = 900 \, \text{kJ/kg}

\]

15. If 1600 kJ of heat is added to 2 kg of a substance at its boiling point, how much of it will be converted to gas?

Solution:

\[

m = \frac{Q}{L} = \frac{1600 \, \text{kJ}}{900 \, \text{kJ/kg}} = 1.78 \, \text{kg}

\]

16. A substance has a latent heat of fusion of \(200 \, \text{kJ/kg}\). How much heat would be required to freeze 3 kg of this substance?

Solution:

\[

Q = mL = 3 \, \text{kg} \times 200 \, \text{kJ/kg} = 600 \, \text{kJ}

\]

17. If 900 kJ of heat is removed from 4 kg of a liquid at its freezing point, how much of it will be converted to a solid?

Solution:

\[

m = \frac{Q}{L} = \frac{900 \, \text{kJ}}{200 \, \text{kJ/kg}} = 4.5 \, \text{kg}

\]

18. A metal requires 500 kJ of heat to completely melt. If the metal weighs 10 kg, what is its latent heat of fusion?

Solution:

\[

L = \frac{Q}{m} = \frac{500 \, \text{kJ}}{10 \, \text{kg}} = 50 \, \text{kJ/kg}

\]

19. If 3500 kJ of heat is added to 5 kg of a substance at its boiling point, what would be its latent heat of vaporization?

Solution:

\[

L = \frac{Q}{m} = \frac{3500 \, \text{kJ}}{5 \, \text{kg}} = 700 \, \text{kJ/kg}

\]

20. A substance has a latent heat of vaporization of \(1200 \, \text{kJ/kg}\). If 1.5 kg of this substance vaporizes, how much heat is absorbed?

Solution:

\[

Q = mL = 1.5 \, \text{kg} \times 1200 \, \text{kJ/kg} = 1800 \, \text{kJ}

\]