Conservation of Energy (HSC SSCE Physics): Revision Notes

Conservation of Energy

Understanding energy systems

In thermodynamics, we need to understand two important types of systems:

Closed system: A closed system is one where matter cannot enter or leave the system, but energy can be transferred into or out of the system through work or heat processes. Think of a sealed bottle of hot water - the water molecules stay inside, but thermal energy can escape through the bottle walls.

Isolated system: An isolated system is one where neither energy nor matter can enter or leave. In reality, perfectly isolated systems don't exist (except perhaps the universe itself), but we can model systems as isolated when energy losses are negligible, such as in well-insulated calorimeter experiments.

The conservation of energy principle

Within an isolated system, the total amount of energy always remains constant. Although energy can be converted from one form to another, and can be transferred from place to place, the total energy within the isolated system never changes.

Energy transfer occurs when energy flows from one object or substance to another. For example, heat flowing from hot water to a cooler container.

Energy transformation occurs when energy changes from one form to another. When you switch on a torch, the battery's stored chemical energy transforms into electrical energy, which then transforms into both light energy and thermal energy. The battery converts chemical energy to electrical energy, while the globe or LED converts electrical energy into light and heat.

First law of thermodynamics

State changes

Pure substances undergo state changes at specific temperatures. A pure solid begins to change state to a liquid at its melting point. A pure liquid begins to change state to a gas at its boiling point.

Types of state changes

There are six main types of state changes:

• Melting: Solid → Liquid (requires energy input)
• Vaporization: Liquid → Gas (requires energy input)
• Condensation: Gas → Liquid (releases energy)
• Solidification (Freezing): Liquid → Solid (releases energy)
• Sublimation: Solid → Gas directly (requires energy input)
• Deposition: Gas → Solid directly (releases energy)

Evaporation vs vaporization

These two processes are often confused, but they are distinctly different:

Evaporation occurs below the boiling point at the surface of a liquid. Particles with relatively high kinetic energy that are less tightly bound at the surface can escape into the vapour phase. Some particles may lose energy and return to the liquid.

Vaporization occurs when a liquid changes to gas at the boiling point. Bubbles form below the surface and throughout the liquid. Importantly, no temperature change occurs during vaporization, even though energy is being continuously added.

Latent heat

When a substance undergoes a state change, energy must be added or removed, but the temperature remains constant during the change. This energy is called latent heat (from the Latin word meaning "hidden").

Specific latent heat of fusion

The specific latent heat of fusion of a substance is the energy required to change the state of $1 \text{ kg}$ of the substance from its solid state to its liquid state without any change in temperature.

For water, the specific latent heat of fusion is $334 \text{ kJ} \cdot \text{kg}^{-1}$.

In the solid state, water particles are held tightly together in a rigid structure. To separate them enough to form a liquid requires a large amount of energy. This energy is supplied from an external source and increases the average separation between particles, not their kinetic energy. Therefore, the internal energy increases, but since there's no increase in average kinetic energy, the temperature remains constant and a thermometer cannot detect this energy change.

Specific latent heat of vaporization

The specific latent heat of vaporization of a substance is the heat required to change the state of $1 \text{ kg}$ of the substance from its liquid state to its gaseous state.

For water, the specific latent heat of vaporization is $2260 \text{ kJ} \cdot \text{kg}^{-1}$.

This value is much larger than the latent heat of fusion because it requires significantly more energy to completely separate the particles from each other to form a gas.

Why latent heat matters

Both melting and vaporization are reversible processes. When steam at $100°\text{C}$ condenses to liquid water at $100°\text{C}$, it releases the latent heat of vaporization to its surroundings. This is why steam burns are far more severe than burns from the same mass of liquid water at $100°\text{C}$ - the steam releases additional energy as it condenses on your skin.

Application: Cloud formation

Condensation and latent heat release play a crucial role in cloud formation. When a pocket of moist air rises into cooler regions (because it's less dense than the surrounding dry air), the water vapour condenses to form clouds. During condensation, the latent heat of vaporization is released into the surrounding air, warming it. This warmer air becomes even less dense and continues rising. Eventually, the rising air reaches the boundary of the troposphere (the weather zone's "ceiling"), and cloud formation continues horizontally rather than vertically. This creates the distinctive anvil-shaped clouds often seen at the tops of thunderclouds, particularly in tropical regions.

Calculating energy changes during state changes

Deriving the formula

Through experimental investigation, scientists have found a direct proportionality between the energy required for a state change and the mass of substance changing state:

$Q \propto m$

To convert this proportionality to an equation, we introduce a constant, $L$ (the latent heat):

$Q = mL$

Rearranging this equation to find the latent heat:

$L = \frac{Q}{m}$

where:

• $Q$ is the energy transferred (in joules, J)
• $m$ is the mass (in kilograms, kg)
• $L$ is the specific latent heat (in joules per kilogram, $\text{J} \cdot \text{kg}^{-1}$)

Investigating latent heat

A student investigated the relationship between mass and energy during the melting of ice. Different masses of ice at $0°\text{C}$ were dried to remove any liquid water, then heated at a steady rate of $1000 \text{ J} \cdot \text{s}^{-1}$ until the ice had just melted. The time was recorded for each mass. The investigation was designed to minimize external heat gains or losses.

Mass of water produced (kg)	Time (s)	Energy (kJ)
0.10	33	33
0.22	71	71
0.39	88	88
0.51	175	175
0.64	217	217
0.90	300	300

The graph clearly shows a direct proportional relationship between energy input and mass. From the graph, the gradient equals $334$, which represents the latent heat of fusion in units of $\text{J} \cdot \text{kg}^{-1}$. This matches the known value of $334 \text{ kJ} \cdot \text{kg}^{-1}$ for water.

Investigation: Latent heat of fusion of solids

This investigation can be adapted to measure the latent heat of fusion for various solids including ice and other substances that melt at similar temperatures.

Basic principle

When crushed ice at $0°\text{C}$ is added to water at a known temperature, the ice melts and the water cools. By measuring the temperature change of the water and knowing the masses involved, you can calculate the latent heat of fusion of ice.

Experimental design considerations

Aim: To determine the latent heat of fusion of ice by calorimetry.

Materials needed:

• Calorimeter (or well-insulated container)
• Thermometer
• Crushed ice at $0°\text{C}$ (dried to remove surface water)
• Water at room temperature
• Balance for measuring mass

Analysis approach

The energy lost by the warm water equals the energy gained by the ice:

Energy lost by water = Energy to melt ice + Energy to warm melted ice to final temperature

Using: $Q_{\text{water lost}} = Q_{\text{latent}} + Q_{\text{ice warmed}}$

This can be written as:

$m_{\text{water}}c\Delta T_{\text{water}} = m_{\text{ice}}L + m_{\text{ice}}c\Delta T_{\text{melted ice}}$

By measuring masses and temperatures, you can solve for $L$, the latent heat of fusion.