Heating and work done

Welcome to Thermodynamic Systems!

In this chapter, we are going to dive into the invisible world of atoms and molecules. We’ll explore how energy moves in and out of systems through heating and work. Think of a gas as a busy crowd of people—everything we see on the outside (like temperature and pressure) is just the result of what those "people" are doing on the inside. Understanding this is the key to how everything from car engines to refrigerators works!

1. Internal Energy (\(U\))

Every substance has energy hidden inside it. We call this Internal Energy.

What is it made of?

Internal energy is the sum of a random distribution of microscopic kinetic and potential energies associated with the particles (atoms or molecules) of a system.

• Microscopic Kinetic Energy (\(E_k\)): This comes from the particles moving around (translating, rotating, or vibrating).
• Microscopic Potential Energy (\(E_p\)): This comes from the attractive forces between the particles.

The Temperature Connection

The thermodynamic temperature of a system is directly proportional to the mean (average) microscopic kinetic energy of its particles. Analogy: Think of a dance floor. The higher the "temperature" of the party, the faster the people are dancing (kinetic energy).

Quick Review: If you heat a gas and its temperature rises, its particles are moving faster, meaning its internal energy has increased.

2. Thermal Equilibrium and the Zeroth Law

Why does a hot cup of tea eventually reach room temperature?

Thermal Contact and Heating

When two systems are in thermal contact, energy is transferred from the system at a higher temperature to the system at a lower temperature. We call this energy transfer heating.

This continues until they reach thermal equilibrium. At this point, they are at the same temperature and there is no net energy transfer between them.

The Zeroth Law of Thermodynamics

This law sounds a bit obvious, but it’s the foundation of all temperature measurement: If two systems are both in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other.

Example: If thermometer A says your coffee is 70°C, and the same thermometer A says your tea is 70°C, then the coffee and tea are at the same temperature.

Key Takeaway: Temperature determines the direction of thermal energy flow. Energy always flows from "Hot" to "Cold" until they match.

3. Work Done by a Gas

In thermodynamics, "work" usually involves a gas changing its volume. Imagine a gas trapped in a cylinder with a moveable piston.

Expansion vs. Compression

• Work done BY the gas (Expansion): When the gas pushes the piston out, it uses its own energy to do work. The volume increases (\(\Delta V\) is positive).
• Work done ON the gas (Compression): When you push the piston in, you are transferring energy into the gas. The volume decreases (\(\Delta V\) is negative).

The Formula

To calculate the work done by a gas expanding against a constant external pressure (\(p\)):

\( W = p\Delta V \)

Where:
\(p\) = pressure (in Pascals, \(Pa\))
\(\Delta V\) = change in volume (Final Volume \(-\) Initial Volume, in \(m^3\))

Common Mistake: Always check your units! Volume must be in \(m^3\), not \(cm^3\) or liters, to get the answer in Joules (\(J\)).

4. The First Law of Thermodynamics

This is the most important equation in the chapter! It is essentially the Law of Conservation of Energy applied to thermal systems.

The Equation: \( \Delta U = Q + W \)

• \(\Delta U\): The increase in internal energy of the system.
• \(Q\): The energy transferred to the system by heating.
• \(W\): The work done ON the system.

Don't worry about the signs! Just remember this trick:

Think of the system like a bank account (\(U\)):

• If you add heat (\(Q > 0\)), the balance goes up.
• If you do work ON it (\(W > 0\)), like compressing it, the balance goes up.
• If the system loses heat or does work BY expanding, the balance goes down (negative values).

Key Takeaway: Any change in the internal energy of a system must come from either heating it or doing work on it.

5. Specific Heat Capacity and Latent Heat

When you add energy to a substance, it either gets hotter or it changes state. It usually doesn't do both at the same time!

Specific Heat Capacity (\(c\))

This is the energy required to raise the temperature of 1 kg of a substance by 1 K (or 1°C).

Formula: \( Q = mc\Delta T \)

Example: Water has a high specific heat capacity, which is why it takes a long time to boil a kettle!

Specific Latent Heat (\(L\))

This is the energy required to change the state of 1 kg of a substance without any change in temperature.

Formula: \( Q = mL \)

• Latent Heat of Fusion (\(L_f\)): Used for melting/freezing.
• Latent Heat of Vaporisation (\(L_v\)): Used for boiling/condensing.

Did you know? When ice melts, the energy you add doesn't make the molecules move faster (so temperature stays at 0°C); instead, it's used to break the bonds between the molecules (increasing microscopic potential energy).

Quick Summary Table:
Process: Raising Temp | Energy: \(Q = mc\Delta T\) | Internal Energy Change: \(\Delta E_k\)
Process: Changing State | Energy: \(Q = mL\) | Internal Energy Change: \(\Delta E_p\)

Congratulations! You've covered the core concepts of Heating and Work Done. Keep practicing the sign conventions for the First Law—that is where most students find the challenge!