How to Derive the Dimensions and Units of Latent Heat in Physics
Latent heat is a fundamental concept in thermodynamics, representing the amount of heat energy absorbed or released by a substance during a phase change at constant temperature and pressure. Understanding its dimensional formula is essential for dimensional analysis and for solving problems in heat and thermodynamics at the JEE level.
Definition and Physical Meaning of Latent Heat
Latent heat refers to the heat required for a substance to undergo a phase transition, such as melting or vaporization, without a change in its temperature. It is typically measured in joules per kilogram in SI units.
Mathematical Expression for Latent Heat
Latent heat $(L)$ is mathematically defined as the ratio of the heat energy $(Q)$ absorbed or released to the mass $(m)$ of the substance undergoing the phase change, i.e., $L = \dfrac{Q}{m}$.
Dimensional Analysis of Latent Heat
To find the dimensional formula of latent heat, consider the dimensions of heat energy $(Q)$ and mass $(m)$. The heat energy has the dimensions of work, which are $[M^1L^2T^{-2}]$, and mass has dimensions $[M^1]$.
Therefore,
$L = \dfrac{Q}{m} = \dfrac{[M^1L^2T^{-2}]}{[M^1]} = [M^0L^2T^{-2}]$
| Quantity | Dimensional Formula |
|---|---|
| Latent Heat (L) | $[M^0L^2T^{-2}]$ |
Interpretation of the Dimensions of Latent Heat
The dimensional formula $[M^0L^2T^{-2}]$ indicates that latent heat is dimensionally equivalent to energy per unit mass. It has no dependence on mass in its dimensional representation.
Understanding the dimensions of latent heat aids in verifying units and checking the consistency of equations in thermodynamics. For more on phase changes and heat transfer, see Defining Latent Heat.
Relation to Specific Latent Heat and Latent Heat of Fusion/Vaporization
Specific latent heat is defined as the amount of heat required to change the phase of one kilogram of a substance. Its dimensional formula is the same as that of latent heat: $[M^0L^2T^{-2}]$.
Latent heat of fusion and latent heat of vaporization are special cases of latent heat, corresponding respectively to melting and vaporization processes. Their dimensional formulas remain $[M^0L^2T^{-2}]$.
Comparison with Related Physical Quantities
Latent heat should not be confused with latent heat capacity or specific heat, which involve different physical definitions and dimensional formulas. For broader thermodynamic principles relevant to latent heat, refer to Thermodynamics Overview.
| Physical Quantity | Dimensional Formula |
|---|---|
| Latent Heat (L) | $[M^0L^2T^{-2}]$ |
| Specific Heat (c) | $[M^0L^2T^{-2}\Theta^{-1}]$ |
| Heat Capacity (C) | $[M^1L^2T^{-2}\Theta^{-1}]$ |
Application of Dimensional Formula in Problem Solving
The dimensional formula for latent heat is often used to check the consistency of equations, analyze derived units, and solve advanced thermodynamic problems. This technique helps avoid calculation errors in both theoretical and experimental contexts.
Concepts of latent heat are fundamental in evaluating heat pump performance. Learn more at Understanding Heat Pumps.
Thermodynamic Laws Involving Latent Heat
Latent heat plays a vital role in the application of the first and second laws of thermodynamics, especially during phase changes at constant temperature. The energy absorbed or released corresponds to work done or internal energy changes, according to thermodynamic principles.
Detailed analysis of these laws can be found in First Law of Thermodynamics and Second Law of Thermodynamics.
Associated Concepts: Thermal Expansion and Energy Conservation
Although latent heat concerns phase change at constant temperature, related concepts such as thermal expansion involve changes in the physical dimensions of substances with temperature. Dimensional considerations are important in all such thermodynamic calculations.
For additional study on related thermal properties, visit Exploring Thermal Expansion.
FAQs on What Are the Dimensions of Latent Heat?
1. What is the dimensional formula of latent heat?
Latent heat is the amount of thermal energy required to change the state of a unit mass of a substance without any temperature change. The dimensional formula of latent heat is [L2T–2], as it is defined as the amount of energy (ML2T–2) per unit mass (M).
Key points:
- Latent heat = Energy / Mass
- Dimensional formula of energy: [ML2T–2]
- Divided by mass (M), so: [ML2T–2] / [M] = [L2T–2]
2. What is latent heat in physics?
Latent heat refers to the heat energy required to change the phase of a substance (such as melting or boiling) without changing its temperature.
Key points:
- It's measured in joules per kilogram (J/kg)
- No temperature change occurs during the phase change
- Types include latent heat of fusion (solid to liquid) and vaporization (liquid to gas)
3. How is latent heat calculated?
Latent heat is calculated by multiplying the substance's mass by its specific latent heat.
Formula:
Latent heat (Q) = mass (m) × specific latent heat (L)
- Q = m × L
- Q unit: joule (J)
- L unit: joule per kilogram (J/kg)
4. What are the types of latent heat?
Latent heat comes in two main types in the CBSE syllabus:
- Latent heat of fusion: Heat required to convert a solid into liquid at constant temperature
- Latent heat of vaporization: Heat required to convert a liquid into gas at constant temperature
5. What is the SI unit of latent heat?
The SI unit of latent heat is joule per kilogram (J/kg).
Details:
- Heat energy measured in joules (J)
- Per unit mass (kg)
- Indicates energy needed for phase change per kilogram
6. Explain the significance of latent heat in daily life.
The concept of latent heat is essential for understanding many everyday phenomena involving phase changes.
Examples:
- Melting of ice: Ice absorbs latent heat to become water, keeping drinks cold without raising temperature until it melts completely.
- Steaming clothes: Steam releases latent heat on condensing, helping remove wrinkles effectively.
- Boiling water: Water absorbs latent heat to boil, enabling efficient cooking and sterilization.
7. Why does temperature remain constant during the change of state?
During a change of state, the supplied heat is used as latent heat to break intermolecular forces, so temperature remains constant until the entire substance changes its phase.
- Heat energy goes into changing state, not raising temperature
- Applies for melting (solid to liquid) and boiling (liquid to gas)
8. State the difference between specific heat and latent heat.
Specific heat is the heat required to raise the temperature of a unit mass by 1°C, whereas latent heat is the heat required for phase change at constant temperature.
Main differences:
- Specific heat: Raises temperature, no phase change
- Latent heat: Causes phase change, no temperature rise
9. What is the dimensional formula of specific latent heat?
The dimensional formula of specific latent heat is [L2T–2], since it is defined as energy per mass.
- Derived the same way as for latent heat
- Unit: J/kg, which equates to [L2T–2]
10. What is the formula for latent heat of fusion?
The latent heat of fusion is calculated using:
- Q = m × Lf
- Q = heat energy absorbed/released (Joules)
- m = mass of the substance (kg)
- Lf = specific latent heat of fusion (J/kg)
It measures the amount of heat needed to convert a solid into a liquid at constant temperature.
