Thermodynamics consist of a set of laws that characterise a system based on some physical qualities such as temperature, energy, work done and entropy.

When we say a ‘system’, think of a hob filled with water on the stove. In real life it is more about heat engines and such but let’s just keep it simple.

The 4 Laws of Thermodynamics

At first, there were only 3 laws characterising systems. However, later they added a 0th fundamental law.

So, today we refer to them as the 4 laws of thermodynamics.

Zeroth Law of Thermodynamics

This law is about temperature.

If two systems independently are in equilibrium with a third, then they are in equilibrium with each other. Equilibrium means that one does not heat up the other or cool it down. Simply said, they have the same temperature.

Let’s have 3 systems: A, B and C.

Diagram: Zeroth Law of Thermodynamics

If system A is in thermal equilibrium with C, and also system B is in thermal equilibrium with C, then A and B are in equilibrium with each other.

First Law of Thermodynamics

Energy cannot be created nor destroyed. Only it can be converted from one form to the other.

This law is about the conservation of energy.

We can picture the Universe as a closed system. The energy of the Universe is constant. Always the same. We can’t add or take away.

  • Energy can be transferred from one system to another in 2 ways:
    • heat energy (Q) and
    • work (W).
  • Both measured in Joules (J).

What is Energy and what is Work?

Energy is the ability to do work.

1 Joule of energy is when there is 1 Newton of force moving an object 1 meter away.

Work is the amount of energy that is transferred to the object.

They are closely related and both measured in Jules.

So, heat is a from of energy. Denoted by: Q. The hotter an object or gas is, the faster its particles are moving. Faster moving particles mean higher ability to do work (let’s say if they bump into something). Higher ability to do work means higher Energy.

Picture a kettle with water in it. Let’s put a cork in its nozzle. Now, turn the gas on. The fire from the gas will transfer heat energy to the kettle. Water boils and then turns to steam.

  • As the entire kettle heats up, it will be much hotter than its surroundings (air). Therefore, the kettle will give heat energy (Q) to the air around.
  • But as the steam expands, the internal pressure will push the cork out. The cork being pushed out is the work done (W) by the system.

The First Law of Thermodynamics states, that the net energy change of the system is equal to the heat transferred into the system minus the work done by the system.

Equation: First Law of Thermodynamics: Delta U = Q - W

Where:

ΔU: change in energy;

Q: the net heat transferred into or out the system It is the sum of heat into the system and the heat given by the system to its surrounding. The heat given to the surroundings will be a negative number. If Q is positive, the system is heated up;

W: the sum all work done on or by the system – Done by the system is a positive number, whilst done on a system is a negative number.

Types of Thermodynamic Systems

  • open – a hob without a lid
  • closed – a hob with a lid on
  • isolated – a Thermos

Let’s have a hob filled with hot water.

With no lid on, both heat and matter is transferred to the outside. With lid on, only heat is transferred. Hot water in a Thermos will not transfer anything to the outside.

Second Law of Thermodynamics

This law is about entropy.

Entropy is the measure of disorder. It is a natural process: your room will get messy over time, a nail will be rusty, houses get old and collapse if not being looked after. The messier it is, the higher the entropy is.

  • Isolated systems naturally evolve towards equilibrium
  • Equilibrium has the highest entropy
  • Heat is the highest form of entropy
    • the hotter something is, the faster the particles move, the more the disorder is.

An example:

We’ve got 2 systems below.

There is gas in System 1. For absolute simplicity, this gas has 4 particles: A, B, C and D.

Diagram: Indicating that system in equilibrium has the highest Entropy

We open up the closed pipe between the systems.

Obviously, some of this air will move to System B. How much? Half. Once the gas has moved and we have equal gas ( 2 – 2 particles ) in each system, we have equilibrium. Above we stated that this state, the equilibrium has the highest entropy.

Entropy is disorder, it means something can happen in multiple ways. The way that something happens it is not straight forward. So, the higher the probability, the higher the entropy is. In the drawing above, we have 4 different states showing how these 4 particles can be distributed.

  1. The first state can only happen 1 way: all particles are in System 1.
  2. The second state can happen 4 different ways: A, B, C or D in System 2.
  3. State 3 has 6 possibilities.
  4. The fourth state has 4.

State 3 is the equilibrium and it has the highest possible combinations. Therefore, the entropy is the largest in state 3.

Heat Death of the Universe

The Universe is considered to be an isolated system. It is also heading towards an equilibrium where eventually everything ends up at the same temperature. This is referred to as ‘heat death’ of the Universe. It’ll happen in 10^28 years.

Spontaneous, Reversible & Irreversible Processes

We distinguishes between three types of processes:

  • Spontaneous Processes
  • Reversible Processes
  • Irreversible Processes

Reversible Processes

In a reversible process, we can return the system back to its original state by reversing the process. Put water in a freezer it freezes (state 1), take out from the freezer it turns to water (state 2).

  • Reversible Processes are at equilibrium at both states. – So they go from one equilibrium to the other.

Irreversible Processes

As the name suggests, these processes are irreversible. We can’t undo by reversing the process: can’t un-tear a paper and can’t unscramble an egg.

  • Spontaneous processes are all irreversible.

Spontaneous Processes

Happens naturally without any outside intervention. If you tear a piece of paper you can’t un-tear it. Nor can you unscramble an egg.

To understand this, let’s have 2 systems for an example:

Diagram: Hot air from System A transfers energy to the cold air in System B.

System A has hot water in it, B has cold. We connect them together. Note, us connecting them is not an outside intervention.

At the atomic level, if something is hot, it means the particles are moving in a random order, fast. Particles in the cold do not move so fast. So the hot water’s particles will continuously bump into the cold water’s particles when they meet speeding them up. As a result, the cold water gains temperature while the hot water loses. (First Law of Thermodynamics).

  • Naturally, heat flows from hot to cold. It can’t go the other way around.
  • So, System A transfers energy to System B.
  • Spontaneous Processes are only spontaneous in one direction.
  • They can also be temperature dependent: water evaporates above 0C but freezes below.

Note, an air conditioning system pumps cold air into the hot room. But this is done with an outside intervention – the motor.

Change of Entropy Calculation for a Reversible Process

Heat energy can’t be transferred into mechanical energy with 100% efficiency. As a result, there will be some leftover heat left in the gas that has to be discarded through a heat sink. A heat sink is a large piece of metal with large surface area that transfers the heat from the system to the air.

Think about the kettle example – where the heated steam pushes out the cork from the nozzle.

Entropy in terms of energy, is the energy that is not available to do useful work (waste).

Equation: Entropy

Where:

  • ΔS: Change in Entropy (J/K)
  • dQ: The heat added to the system
  • T: The temperature of system the heat is added to

We integrate, because as we add some heat, T increases too. So picture this as adding only a bit of heat at a time. With each addition the system’s temperature will change. Integration is summation which sums up these small steps.

Third Law of Thermodynamics

This law describes a condition when entropy is = 0.

Let’s picture a perfect crystal. It means everything is in order. Although the particles still have microscopic movements causing entropy not being equal to zero.

However, at absolute 0, which is 0 Kelvin or -273C, all particles stop moving. In a case of a perfect crystal at absolute 0 we entropy = 0.

Building such a crystal may be possible but reaching absolute 0 is not.

Efficiency of Heat Engine

First of all, what is a heat engine? It is essentially a general term of engines that we have in a car or steam trains.

Diagram: Operation of Steam Engine

Taking the steam engine for an example, the idea is this:

  • Water is heated in a tank and turns to steam.
  • The steam’s particles are further away from each other due to its gas nature, which results in pressure building up in the tank.
  • The built up steam is controlled by a valve.
  • Steam is fed through a pipe to a piston.
  • Due to the large pressure of the steam the piston is pressed.
  • The piston turns heat energy into mechanical energy by moving the Flywheel.
  • Once the piston has reached its max range, the valve shuts and the steam is let out to the outside air allowing the piston to return.

The Carnot Efficiency

The Carnot Efficiency is maximum efficiency a heat engine can possibly achieve. The efficiency of such system as above is the ratio of the heat actually available to the engine and the heat entering the system.

Derivation: of Carnot efficiency

Where:

  • η: Efficiency
  • Th: Temperature of heat entering the system in Kelvins.
  • Tc: Temperature of heat leaving the system in Kelvins.

Chambadal – Novikov Efficiency

While the Carnot efficiency calculates the maximum efficiency possible, the Chambadal – Novikov efficiency is a much closer approximation to the actual efficiency a heat engine can achieve.

Formula: Chambadal - Novikov Efficiency
  • This efficiency is based on endoreversible thermodynamics – where energy flow is not reversible.
  • This formula is especially close to the reality when it comes to internal combustion engines or simple-cycle turbines.