Understanding Latent Heat, Dilatation in Solids, Liquids, and Gases

Posted on Mar 6, 2025 in Physics

Latent Heat of Change of State

The latent heat of change of state, denoted as L, represents the amount of thermal energy transferred to a mass m (in kg) of a pure substance to change its state at a given pressure and temperature. The relationship is expressed as:

Q = m × L

We can distinguish between the latent heat of fusion and the latent heat of vaporization:

Latent Heat of Fusion

In the case of fusion:

Q = m × L_f

Here, L_f is the latent heat of fusion. The difference between fusion and solidification is that energy is supplied to melt a material, while energy is released to the environment as heat when it solidifies.

Latent Heat of Vaporization

In the case of vaporization:

Q = m × L_v

Here, L_v is the latent heat of vaporization. The difference is that energy must be supplied to vaporize a material, while energy is released when it condenses.

Analysis of Phase Changes

Consider the following stages:

1. Stage 1: Ice from t₁ to 0°C (Solid State)
   The amount of heat required to raise the temperature of ice from t₁ (below zero) to 0°C is:

   Q₁ = m × c × (0 – t₁)

2. Stage 2: Ice at 0°C transforms into liquid water at 0°C
   During this stage, a change of state occurs while the temperature remains constant. The amount of heat transferred is:

   Q₂ = m × L_f

3. Stage 3: Liquid water from 0°C to 100°C
   The amount of heat required to raise the temperature of liquid water from 0°C to 100°C is:

   Q₃ = m × c × (100 – 0)

4. Stage 4: Liquid water at 100°C transforms into steam at 100°C
   Again, a change of state occurs: from liquid water at 100°C to steam at 100°C. The amount of heat transferred is:

   Q₄ = m × L_v

The total thermal energy transferred is:

Q_t = Q₁ + Q₂ + Q₃ + Q₄

Dilatation in Solids

Linear dilatation refers to the increase in length experienced by a body when heated. It is given by:

l_t = l₀ (1 + α × t)

Where:

• l₀ = length of the body at 0°C
• t = temperature to which the body is heated
• l_t = resulting length at temperature t
• α = linear coefficient of expansion (change in length per unit length at 0°C for each degree rise in temperature)

The dilatation in a particular dimension is proportional to the baseline of that dimension.

Linear and cubic dilatations occur when the temperature of a body rises.

Superficial Dilatation

Superficial dilatation is the increase in surface area experienced by a body due to heating:

S_t = S₀ (1 + β × t)

Where:

• S₀ = surface area of the body at 0°C
• S_t = resulting surface area at temperature t
• β = superficial coefficient of expansion (change in surface area per unit surface area at 0°C for each degree rise in temperature)

Cubic Dilatation

Cubic dilatation is the increase in volume of a solid when its temperature rises:

V_t = V₀ (1 + γ × t)

Where:

• V₀ = volume of the body at 0°C
• V_t = resulting volume at temperature t
• γ = cubic coefficient of expansion (change in volume per unit volume at 0°C for each degree rise in temperature)

The coefficient of expansion is characteristic of each substance and is measured in °C^-1.

Dilatation in Liquids

In liquids, we distinguish between apparent dilatation and real dilatation. The apparent dilatation is less than the real dilatation due to the expansion of the container. Water exhibits anomalous behavior between 0°C and 4°C, where it contracts instead of expanding, reaching a minimum volume and maximum density at 4°C.

Dilatation in Gases

When the temperature of a gas varies while maintaining constant pressure, the volume changes according to:

V = V₀ (1 + α × t)

Where α = 1/273 °C^-1 (Ley-Gay Lussac’s Law)