Thermal Physics: Energy Transfer by Heating and Doing Work (A-level Only)

Hello future physicist! Welcome to the heart of Thermal Physics. This chapter connects the mechanical concepts of work you learned earlier with the idea of heat. It’s all about tracking where energy goes when we heat things up, cool them down, or squeeze them! Understanding these principles is crucial for everything from designing efficient engines to understanding climate science. Don't worry if the terminology seems tricky—we'll break down these big ideas into simple, manageable steps.

1. Internal Energy (\(U\)): The Hidden Energy Store

What is Internal Energy?

Every physical object, or system, stores energy internally. This total stored energy is called its Internal Energy (\(U\)). It's made up of two main components related to the particles (atoms or molecules) inside the substance:

1.1 Kinetic Energy (KE) of Particles

The particles in any substance (solid, liquid, or gas) are constantly moving randomly.

  • In a gas, they zoom around freely.
  • In a liquid, they slide past each other.
  • In a solid, they vibrate around fixed points.
The sum of all these random movement energies is the total random kinetic energy of the system. This component is directly related to the substance's temperature.

1.2 Potential Energy (PE) of Particles

Particles interact with each other via forces (like electrical forces). These interactions mean they have potential energy based on their separation and arrangement.

  • PE is high when particles are far apart and forces need to be overcome (e.g., in a gas).
  • PE is low when particles are tightly packed (e.g., in a solid).
This component changes significantly during changes of state (like melting or boiling).

Key Definition:
The Internal Energy (\(U\)) of a body is the sum of the randomly distributed kinetic energies and potential energies of all the particles within it.

Quick Review: Temperature vs. Internal Energy

Temperature is a measure of the average kinetic energy of the particles. Internal Energy (\(U\)) is the total of both KE and PE. Two identical blocks of ice at \(0^\circ\text{C}\) and water at \(0^\circ\text{C}\) have the same average particle KE (same temperature), but the water has higher total PE, meaning the water has a higher overall Internal Energy.

2. The First Law of Thermodynamics: Energy Conservation

The First Law of Thermodynamics is essentially the Principle of Conservation of Energy applied to thermal systems. It tells us how the internal energy of a system changes when energy is transferred to or from it.

Energy Transfer Mechanisms

Internal energy can be increased or decreased through two primary ways:

  1. Heating (\(Q\)): Energy transfer due to a temperature difference between the system and its surroundings (e.g., placing a cold metal block into hot water).
  2. Doing Work (\(W\)): Energy transfer via mechanical means, usually involving a force moving a boundary (e.g., compressing a gas with a piston).

The First Law Equation

The change in internal energy (\(\Delta U\)) is related to the energy transferred by heating (\(Q\)) and the work done (\(W\)) by the equation:

\(\Delta U = Q + W\)

Where:

  • \(\Delta U\) is the change in internal energy (J).
  • \(Q\) is the energy input to the system by heating (J).
  • \(W\) is the work done ON the system (J).

Common Misconception & Sign Convention!

The sign convention is critical and can vary between specifications. For OxfordAQA Physics (9630):

  • \(\Delta U\): Positive if internal energy increases (temp or state change up). Negative if it decreases.
  • \(Q\): Positive if heat flows into the system. Negative if heat flows out of the system.
  • \(W\): Positive if work is done ON the system (e.g., compression). Negative if work is done BY the system (e.g., expansion).
Example: If a gas expands (does work BY the system, \(W\) is negative) and no heat is added (\(Q=0\)), then \(\Delta U\) must be negative, meaning the gas cools down.

Key Takeaway: Energy can be transferred into or out of a system as heat or work, but the total energy (\(U\)) tracks the balance perfectly.

3. Energy Transfer Leading to Temperature Change

When energy is transferred to a body and its temperature changes, the energy input goes primarily into increasing the kinetic energy of the particles (i.e., increasing their vibration/speed). This relationship is quantified by Specific Heat Capacity.

3.1 Specific Heat Capacity (\(c\))

The Specific Heat Capacity (\(c\)) of a substance is defined as the amount of energy required to raise the temperature of one kilogram of the substance by one degree Kelvin (or Celsius).

\(Q = mc \Delta\theta\)

Where:

  • \(Q\) is the heat energy transferred (J).
  • \(m\) is the mass of the substance (kg).
  • \(c\) is the specific heat capacity (\(\text{J kg}^{-1} \text{K}^{-1}\)).
  • \(\Delta\theta\) is the change in temperature (K or \({}^\circ\text{C}\)).

Did you know? Water has a very high specific heat capacity (\(4200 \text{ J kg}^{-1} \text{K}^{-1}\)). This is why it takes so long to boil a kettle, but also why oceans help regulate the planet's temperature.

3.2 Required Practical 8: Determining Specific Heat Capacity (SHC)

You need to be familiar with the electrical method for determining the SHC of a substance (often a metal block or a liquid in a continuous flow system).

Step-by-Step Electrical Method:

  1. An immersion heater and a thermometer are placed into a known mass (\(m\)) of the substance.
  2. Electrical energy is supplied to the heater for a measured time (\(t\)).
  3. The electrical energy supplied (\(Q\)) is calculated using the power formula: \(Q = P t = I V t\).
  4. The resulting temperature change (\(\Delta\theta\)) is measured.
  5. By rearranging the formula, the SHC can be found: \(c = \frac{Q}{m \Delta\theta} = \frac{I V t}{m \Delta\theta}\).

Memory Aid for SHC: Think of the equation as: Queen Mary Can Delta Theta (Q = m c \(\Delta\theta\)).

Key Takeaway: SHC tells you how resistant a substance is to temperature change when heated. High \(c\) means it takes a lot of energy to heat up.

4. Energy Transfer Leading to Change of State

What happens if you continue to add heat to a substance once it reaches its melting or boiling point? The temperature stops rising! The added energy is not increasing the particle KE; instead, it's increasing the particle potential energy by breaking or forming intermolecular bonds. This energy is called Latent Heat.

4.1 Specific Latent Heat (\(l\))

The Specific Latent Heat (\(l\)) of a substance is the amount of energy required to change the state of one kilogram of the substance without a change in temperature.

\(Q = ml\)

Where:

  • \(Q\) is the heat energy transferred (J).
  • \(m\) is the mass of the substance (kg).
  • \(l\) is the specific latent heat (\(\text{J kg}^{-1}\)).

Two Types of Specific Latent Heat:
  1. Specific Latent Heat of Fusion (\(l_{\text{f}}\)): Energy required to change 1 kg from solid to liquid (melting) or liquid to solid (freezing). This energy is used to break the solid structure bonds.
  2. Specific Latent Heat of Vaporisation (\(l_{\text{v}}\)): Energy required to change 1 kg from liquid to gas (boiling) or gas to liquid (condensing). This energy is used to completely separate the particles.

Analogy: Imagine pulling apart two magnets (particles). You have to do work to increase their separation—this stored energy is the potential energy component of latent heat.

Crucial Point about Phase Change:

During a change of state (e.g., ice melting):

  • Kinetic Energies (KE) are constant (temperature is constant).
  • Potential Energies (PE) are changing (bonds are being broken or formed).
  • Therefore, the heat input (\(Q\)) goes entirely into changing the Potential Energy component of the Internal Energy (\(\Delta U\)).

Key Takeaway: SLH quantifies the energy required to rearrange the particle structure, rather than speed up the particles. Latent heat of vaporisation is almost always higher than fusion because separating particles completely (gas) requires much more energy than just allowing them to slide (liquid).

5. Calculations Involving Energy Transfer

In examination questions, you often have to combine these concepts, especially when a substance moves from one state to another (e.g., heating ice, melting it, then heating the resulting water). You must calculate the energy required for each stage separately and then sum them up.

Step-by-Step Calculation for Changing State and Temperature:
  1. Temperature Change 1: Use \(Q_1 = m c_{\text{substance A}} \Delta\theta_1\).
  2. Phase Change: Use \(Q_2 = m l_{\text{fusion/vaporisation}}\).
  3. Temperature Change 2: Use \(Q_3 = m c_{\text{substance B}} \Delta\theta_2\).
  4. Total Energy: \(Q_{\text{total}} = Q_1 + Q_2 + Q_3 + ...\)

Calculations may also involve continuous flow systems, where the energy supplied by a heater (\(IVt\)) is absorbed by a flowing fluid (like water) that experiences a temperature rise \(\Delta\theta\). If the flow rate is constant, \(Q\) must be replaced by the power \(P\) and mass \(m\) by the mass flow rate (\(\dot{m}\)):

\(P = \dot{m} c \Delta\theta\)

Where \(\dot{m}\) is mass per second (\(\text{kg s}^{-1}\)). This is just a rearrangement of \(Q=mc\Delta\theta\) by dividing both sides by time \(t\).