🔥 Thermodynamics (A Level Physics 9702)

Welcome to Thermodynamics! Don't worry if this topic feels a bit abstract—it’s essentially the study of how energy moves and transforms within systems, especially involving heat and work. Understanding this chapter is crucial because it governs everything from car engines to your refrigerator. We will focus on two key concepts: Internal Energy and the fundamental First Law of Thermodynamics. Let's get started!

16.1 Internal Energy (\(U\))

The Internal Energy of a system (like a gas in a container, or a block of metal) is the total energy stored inside it due to the random motion and arrangement of its molecules.

It is important to remember that internal energy is determined solely by the state of the system (its temperature, pressure, and volume). It doesn't matter how the system reached that state, only what its current state is.

Components of Internal Energy

Internal energy (\(U\)) is the sum of two types of energy associated with the molecules:

  • 1. Random Kinetic Energy (KE):
    This is the energy associated with the random movement (translation, rotation, and vibration) of the molecules.
  • 2. Potential Energy (PE):
    This is the energy associated with the forces between the molecules (intermolecular forces). This energy depends on the separation and arrangement of the molecules.

Analogy: The Class System
Imagine your classroom is the system.

  • KE is the energy of students randomly walking, running, or wiggling in their seats.
  • PE is the energy of attraction or repulsion between the students. If they are packed tightly (like a liquid or solid), the PE component is significant. If they are spread far apart (like an ideal gas), the PE component is negligible.
Internal Energy and Temperature

There is a direct and simple relationship between internal energy and temperature:

  • A rise in temperature of an object is directly related to an increase in its internal energy.
  • Specifically, temperature is a measure of the average random kinetic energy of the molecules.

Did you know? For an Ideal Gas (which we study often in Physics), there are no intermolecular forces, so the Potential Energy component of its internal energy is zero. Therefore, the internal energy of an ideal gas consists only of the total random kinetic energy of its molecules. This makes calculations simpler!

Key Takeaway 1: Internal energy (\(U\)) is the total random KE + PE of the molecules. If the temperature rises, the kinetic part of \(U\) must increase.

16.2 The First Law of Thermodynamics (FLOT)

The First Law of Thermodynamics is essentially the Principle of Conservation of Energy applied to thermodynamic systems. It describes how the internal energy of a system changes when energy is transferred to or from it through heating (q) or work (W).

The law is expressed mathematically as:

\[ \Delta U = q + W \]

Where:

  • \(\Delta U\): The increase in internal energy of the system.
  • \(q\): The energy transferred to the system by heating (often called 'heat').
  • \(W\): The work done on the system.

Don't worry if the equation seems simple at first—the challenge is applying the correct sign conventions!

Understanding Work Done (\(W\))

In the context of gases, work is done when the volume of the gas changes against an external pressure. We focus on changes that occur at constant pressure.

The formula for work done (\(W\)) when the volume of a gas changes is:

\[ W = p \Delta V \]

Where:

  • \(p\) is the constant pressure (in Pa).
  • \(\Delta V\) is the change in volume (in \(\text{m}^3\)).

However, the syllabus requires you to understand the difference between work done on the gas and work done by the gas. This is essential for applying the First Law correctly.

The standard convention used in the equation \(\Delta U = q + W\) assumes \(W\) is the work done ON the system.

Scenario 1: Work Done BY the Gas (Expansion)

If the gas expands (\(\Delta V\) is positive), the gas pushes a piston outwards, doing work on the surroundings. This means the gas loses energy, so the work done ON the gas (\(W\)) is negative.

Example: A balloon inflating.

Scenario 2: Work Done ON the Gas (Compression)

If the gas is compressed (\(\Delta V\) is negative), the surroundings push the piston in, doing work on the gas. This means the gas gains energy, so the work done ON the gas (\(W\)) is positive.

Example: A bicycle pump compressing air.

🚨 Common Mistake Alert!

Sometimes, textbooks use the alternative convention where \(W_{\text{by}}\) is the work done BY the system, and the First Law is written as \(\Delta U = q - W_{\text{by}}\). Stick strictly to the syllabus convention: \(\Delta U = q + W\), where \(W\) is work done ON the system.

Sign Conventions for the First Law

To master the First Law (\(\Delta U = q + W\)), you must memorize the sign rules:

Term Positive (\(+\)) Negative (\(-\))
\(\Delta U\) (Internal Energy Change) Increase in Internal Energy (Temperature Rises) Decrease in Internal Energy (Temperature Drops)
\(q\) (Heating) Energy is transferred TO the system (Heated) Energy is transferred FROM the system (Cooled)
\(W\) (Work Done) Work is done ON the system (Compression) Work is done BY the system (Expansion)

Mnemonic/Memory Aid: Think of the system as a bank account. You want money in.

  • \(\Delta U\) is positive if the balance goes UP.
  • \(q\) is positive if heat transfers INTO the system.
  • \(W\) is positive if work is done ON the system (forcing energy IN).
Step-by-Step FLOT Application

Let's apply the FLOT to common processes:

1. Isothermal Process (\(\Delta U = 0\))

Process at constant temperature.

  • Since temperature is constant, \(\Delta U = 0\).
  • The FLOT becomes: \(0 = q + W\), or \(q = -W\).
  • Meaning: Any work done on the gas must be exactly removed as heat, otherwise the internal energy (and temperature) would rise.
2. Adiabatic Process (\(q = 0\))

Process where no heating transfer occurs (e.g., very fast or heavily insulated).

  • Since there is no heat transfer, \(q = 0\).
  • The FLOT becomes: \(\Delta U = W\).
  • Meaning: If you compress a gas adiabatically (\(W\) is positive), the work done goes entirely into increasing the internal energy, making the gas heat up immediately. (This is how diesel engines work, igniting fuel without a spark plug).
3. Isovolumetric (Isochoric) Process (\(W = 0\))

Process at constant volume (\(\Delta V = 0\)).

  • Since volume doesn't change, no work is done (\(W = p \Delta V = 0\)).
  • The FLOT becomes: \(\Delta U = q\).
  • Meaning: All energy transferred by heating goes directly into increasing the internal energy (and thus the temperature).

Key Takeaway 2: The First Law (\(\Delta U = q + W\)) is a statement of energy conservation. Always ensure \(q\) is heat to the system and \(W\) is work on the system before solving problems.