The First Law of Thermodynamics

Welcome, students 👋 In this lesson, you will learn one of the most important ideas in thermodynamics: the first law of thermodynamics. This law helps us keep track of energy in systems like engines, kettles, turbines, refrigerators, and even the human body. By the end of this lesson, you should be able to explain what the first law means, use the main terms correctly, and apply the law to simple real-world situations.

What the first law is really saying

The first law of thermodynamics is a statement of energy conservation. Energy cannot be created or destroyed; it can only be transferred or changed from one form to another. In thermodynamics, we usually study a system and everything around it, called the surroundings. The surface that separates the system from the surroundings is the boundary.

The first law tells us how the energy of the system changes when heat and work cross the boundary. A common form of the law is:

$$\Delta E = Q - W$$

Here, $\Delta E$ is the change in the total energy of the system, $Q$ is heat added to the system, and $W$ is work done by the system. In many thermofluids situations, the total energy $E$ includes internal energy $U$, and sometimes also kinetic and potential energy. If those extra energy forms are negligible, the law becomes:

$$\Delta U = Q - W$$

This is one of the most used equations in Thermofluids 1.

Why this matters

Imagine heating water in a sealed container. The water may gain energy from the heater, and some of that energy may increase the water’s internal energy. If the container can move, part of the energy may also become work. The first law gives a clear accounting system for what happens to the energy.

Systems, surroundings, and boundaries

To use the first law well, you must first define the system. The system is the part of the universe you are studying. The surroundings are everything outside the system. The boundary is the real or imagined surface that separates them.

There are different types of systems:

Closed system: mass does not cross the boundary, but energy can cross as heat or work.
Open system: both mass and energy can cross the boundary.
Isolated system: neither mass nor energy crosses the boundary.

For the first law, closed systems are often the easiest starting point because we only need to track heat and work. A sealed piston-cylinder device is a classic example. If gas inside the cylinder is heated, energy enters as heat, and the gas may push the piston upward, doing work on the surroundings.

Example: a sealed bottle in sunlight ☀️

If a sealed bottle is left in the sun, heat can pass through the bottle walls and warm the air or liquid inside. Since the bottle is sealed, no mass enters or leaves. The system gains energy through heat transfer, so its internal energy changes.

Properties and state variables

A property is a measurable characteristic of a system, such as temperature $T$, pressure $P$, volume $V$, density $\rho$, and internal energy $U$. A state is the condition of the system described by these properties.

Some properties are state variables, which means they depend only on the current state, not on how the system got there. Internal energy $U$ is a state variable. Pressure, temperature, and volume are also state variables.

This is important because heat and work are not properties of a system. They are path functions, meaning they depend on the process used to move from one state to another.

For example, gas can go from state 1 to state 2 by being heated slowly or by being compressed in a different way. The change in internal energy $\Delta U$ is the same for both paths if the initial and final states are the same, but the values of $Q$ and $W$ can be different.

Real-world idea

Think about climbing a hill. Your change in height depends only on where you start and finish, not the route taken. That is like a state variable. But the amount of effort you spend on the way may change depending on the route. That is like heat and work, which depend on the process.

Heat, work, and internal energy

The first law uses three major energy ideas: heat, work, and internal energy.

Heat $Q$

Heat is energy transferred because of a temperature difference. If a hotter object touches a colder one, energy flows from hot to cold. Heat is measured in joules $\mathrm{J}$.

Work $W$

Work is energy transferred when a force causes displacement at the boundary of the system. In thermodynamics, a common example is boundary work, such as a gas pushing a piston. When the gas expands, it may do work on the surroundings.

Internal energy $U$

Internal energy is the microscopic energy stored within the system. It includes molecular motion and molecular interactions. If a substance gets hotter, its internal energy usually increases.

The sign convention used in many engineering courses is:

$Q > 0$ when heat enters the system
$W > 0$ when work is done by the system

With that convention, the first law for a closed system is:

$$\Delta U = Q - W$$

If $Q$ is larger than $W$, the internal energy increases. If $W$ is larger than $Q$, the internal energy decreases.

Applying the first law step by step

When solving a thermodynamics problem, follow these steps:

Define the system clearly.
Decide whether it is open, closed, or isolated.
Identify heat transfer $Q$ and work transfer $W$.
Write the first law.
Use property data or physical reasoning to find unknowns.

Example 1: Heating a rigid tank

Suppose a rigid tank contains gas and is heated. Because the tank is rigid, its volume does not change, so boundary work is zero:

$$W = 0$$

Then the first law becomes:

$$\Delta U = Q$$

This means all the heat added goes into increasing the internal energy of the gas. If the gas warms up, its temperature usually rises too.

Example 2: Gas in a piston-cylinder

Now imagine gas in a piston-cylinder device. If the gas is heated, it may expand and push the piston upward. In that case, some of the heat added becomes work done by the gas.

If the system receives $Q = 500\,\mathrm{J}$ and does $W = 200\,\mathrm{J}$ of work, then:

$$\Delta U = Q - W = 500 - 200 = 300\,\mathrm{J}$$

So the internal energy increases by $300\,\mathrm{J}$.

Example 3: Compression

If a gas is compressed, work may be done on the system. Under the sign convention used here, work done by the system is negative. That means $W < 0$.

If $Q = 0$ and $W = -150\,\mathrm{J}$, then:

$$\Delta U = 0 - (-150) = 150\,\mathrm{J}$$

The internal energy increases because the surroundings did work on the gas.

How the first law fits into Thermodynamic Basics

The first law connects directly to the main ideas in Thermodynamic Basics: systems, surroundings, boundaries, properties, state variables, heat, work, and internal energy. It is the rule that tells us how energy moves across boundaries and how that movement changes a system’s state.

It also helps explain everyday devices:

Engines convert heat into work
Refrigerators use work to move heat from cold to hot
Boilers add heat to fluids to raise internal energy
Compressors use work to increase fluid pressure and energy

In thermofluids, this law is the starting point for analyzing more advanced processes. Whether you are studying flow through turbines or heating in a tank, the same energy accounting idea applies. The first law is not just a formula; it is a framework for thinking clearly about energy.

Conclusion

The first law of thermodynamics is a statement of energy conservation for thermodynamic systems. It shows how heat $Q$ and work $W$ change the system’s total energy, especially its internal energy $U$. To use it correctly, students, you must define the system, understand the boundary, identify the process, and choose the correct sign convention. Once you do that, the first law becomes a powerful tool for solving real problems in Thermofluids 1 🔧

Study Notes

The first law of thermodynamics is based on energy conservation.
A system is the part studied; surroundings are everything outside; the boundary separates them.
A closed system exchanges energy but not mass.
A property describes the state of a system, such as $T$, $P$, $V$, and $U$.
State variables depend only on the current state, not on the path taken.
Heat $Q$ is energy transfer due to temperature difference.
Work $W$ is energy transfer caused by force acting through distance.
Internal energy $U$ is microscopic energy stored in a system.
Common sign convention: $Q > 0$ into the system, $W > 0$ done by the system.
For a closed system, the first law is often written as $\Delta U = Q - W$.
If volume is constant, then $W = 0$ and $\Delta U = Q$.
The first law is a foundation for understanding engines, refrigerators, compressors, and many other thermofluid devices.