The First Law of Thermodynamics 🔥❄️

Welcome, students! In this lesson, you will learn one of the most important ideas in physics: the first law of thermodynamics. This law connects heat, work, and energy, and it helps explain everything from a car engine to boiling water to the way a refrigerator keeps food cold. By the end of this lesson, you should be able to explain the meaning of the first law, use it in calculations, and connect it to the bigger topic of thermodynamics.

What the First Law Says

The first law of thermodynamics is a statement of energy conservation for systems that can exchange heat and do work. In simple terms, energy cannot be created or destroyed; it can only be transferred or changed from one form to another. For a thermodynamic system, this is written as $\Delta U = Q - W$.

Here, $\Delta U$ is the change in internal energy of the system, $Q$ is the heat added to the system, and $W$ is the work done by the system. This sign convention matters a lot. If heat flows into the system, then $Q$ is positive. If the system does work on the surroundings, then $W$ is positive. That means the internal energy goes up when heat is added and goes down when the system does work.

Internal energy $U$ is the total microscopic energy inside a substance, including the kinetic energy of its particles and the potential energy from interactions between them. You cannot usually measure $U$ directly, but you can measure changes in it, which is why $\Delta U$ is so useful.

A helpful way to remember the first law is this: energy going into the system as heat can either increase internal energy or leave the system as work. Imagine blowing up a balloon. If air enters the balloon and does work stretching the rubber, some of the energy from the air increases the balloon’s internal energy and some becomes work that expands the balloon 🎈.

Heat, Work, and Internal Energy

To use the first law correctly, students, you need to understand the three key terms.

Heat, represented by $Q$, is energy transferred because of a temperature difference. Heat is not something an object “contains”; it is energy in transit. For example, when a hot mug cools down, thermal energy leaves the mug and enters the surrounding air. That energy transfer is heat.

Work, represented by $W$, is energy transferred when a force causes displacement. In thermodynamics, work often happens when a gas expands or is compressed in a piston. If gas pushes a piston outward, the gas does work on the piston. If the piston compresses the gas, work is done on the gas.

Internal energy, represented by $U$, is a property of the system itself. It depends on the temperature, amount of substance, and microscopic arrangement of particles. For an ideal gas, internal energy depends only on temperature, not pressure or volume alone.

Let’s look at a simple example. Suppose a system absorbs $500\,\text{J}$ of heat and does $200\,\text{J}$ of work on the surroundings. Using $\Delta U = Q - W$, we get

$$\Delta U = 500\,\text{J} - 200\,\text{J} = 300\,\text{J}.$$

So the internal energy increases by $300\,\text{J}$. This means the system gained more energy from heat than it lost through work.

Now suppose the system loses $150\,\text{J}$ of heat and $50\,\text{J}$ of work is done on it by the surroundings. In the sign convention used here, $Q = -150\,\text{J}$ and $W = -50\,\text{J}$ because the system did not do the work. Then

$$\Delta U = -150\,\text{J} - (-50\,\text{J}) = -100\,\text{J}.$$

The internal energy decreases by $100\,\text{J}$. This kind of sign carefulness is a major AP Physics 2 skill.

Applying the First Law with Gas Processes

A large part of thermodynamics involves gases in containers, especially in pistons. When a gas expands or contracts, its volume changes, and that often means work is being done.

For a gas at constant pressure, the work done by the gas can be written as $W = P\Delta V$, where $P$ is pressure and $\Delta V$ is the change in volume. If the gas expands, then $\Delta V > 0$ and $W > 0$. If the gas is compressed, then $\Delta V < 0$ and $W < 0$.

For example, if a gas expands from $2.0\,\text{L}$ to $5.0\,\text{L}$ at a pressure of $1.0\times10^5\,\text{Pa}$, then the change in volume is

$$\Delta V = 3.0\,\text{L} = 3.0\times10^{-3}\,\text{m}^3.$$

So the work done by the gas is

$$W = P\Delta V = \left(1.0\times10^5\,\text{Pa}\right)\left(3.0\times10^{-3}\,\text{m}^3\right) = 300\,\text{J}.$$

If the gas also absorbed $500\,\text{J}$ of heat, then

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

So the gas increased its internal energy by $200\,\text{J}$. This could lead to a higher temperature if the gas behaves ideally.

Real-world example: when you pump air into a bicycle tire, the air is compressed. Work is done on the gas, which can increase its internal energy and temperature. That is why a pump can feel warm after use 🚲.

Special Thermodynamic Processes

The first law becomes especially useful when combined with common process types.

In an isothermal process, the temperature stays constant. For an ideal gas, that means the internal energy does not change, so $\Delta U = 0$. The first law then becomes $Q = W$. Any heat added to the gas is exactly balanced by work done by the gas. This is why slow expansion of an ideal gas at constant temperature can transfer energy without changing internal energy.

In an adiabatic process, no heat is exchanged, so $Q = 0$. Then the first law becomes

$$\Delta U = -W.$$

If the gas does work, its internal energy decreases. If work is done on the gas, its internal energy increases. This is common in fast compression, such as in a diesel engine cylinder, where the gas temperature rises because work is done on it.

In an isochoric process, the volume stays constant, so $\Delta V = 0$ and therefore $W = 0$. Then the first law becomes $\Delta U = Q$. Any heat added changes only the internal energy. A sealed rigid container is a good example.

In an isobaric process, the pressure stays constant, so the work can be found with $W = P\Delta V$. This is common when gas is heated in a cylinder with a movable piston.

These process types are important because they help you identify which terms in $\Delta U = Q - W$ are zero or easy to calculate.

Connecting the First Law to Thermodynamics

The first law is central to the topic of thermodynamics because thermodynamics studies energy transfer in systems with temperature, heat, work, and macroscopic properties. The first law gives the energy-accounting rule. Without it, you could not consistently analyze engines, refrigerators, phase changes, or gas behavior.

It also connects to other major ideas in thermodynamics. The second law says that not all energy transfers are equally useful and that entropy tends to increase in isolated systems. Together, the first and second laws explain why heat engines cannot be perfectly efficient and why refrigerators require work input.

For example, a heat engine takes in heat from a hot reservoir, does work, and releases some heat to a cold reservoir. The first law tells us where the energy goes. The second law tells us why some heat must always be rejected. A refrigerator works in the opposite direction: it uses work to move heat from a cold place to a warmer place, like removing heat from food and releasing it into your kitchen.

So the first law is not just a formula. It is the foundation for tracking energy in every thermodynamic system you will study in AP Physics 2.

Example Problem and Reasoning

Let’s work through a full AP-style example, students. A gas in a piston absorbs $800\,\text{J}$ of heat. During the process, it expands and does $500\,\text{J}$ of work on the surroundings. What is the change in internal energy?

First, identify the values: $Q = 800\,\text{J}$ and $W = 500\,\text{J}$. Then use the first law:

$$\Delta U = Q - W.$$

Substitute the values:

$$\Delta U = 800\,\text{J} - 500\,\text{J} = 300\,\text{J}.$$

The internal energy increases by $300\,\text{J}$.

Now think about what this means physically. Because the system absorbed more heat than it used for work, the leftover energy stayed in the gas. That energy could raise the temperature or change the microscopic motion of the particles.

A common AP question may ask you to interpret a graph of pressure versus volume. The area under a $P$-$V$ curve gives the work done by the gas, because $W = \int P\,dV$ for a changing pressure. If a process is shown as a line or curve on a graph, the direction matters. Expansion means positive work by the gas, while compression means negative work by the gas under this convention.

Conclusion

The first law of thermodynamics is a powerful energy law that says the change in internal energy of a system equals heat added to the system minus work done by the system. In symbols, $\Delta U = Q - W$. This law lets you analyze real processes in gases, engines, pistons, and everyday objects. It also connects directly to the larger study of thermodynamics by providing the energy bookkeeping that all thermal processes must obey. If you can track signs carefully and identify heat, work, and internal energy changes, you are well prepared for AP Physics 2 questions on this topic.

Study Notes

The first law of thermodynamics is conservation of energy for thermal systems.
Use $\Delta U = Q - W$ with the AP Physics 2 sign convention.
$Q > 0$ means heat enters the system; $Q < 0$ means heat leaves the system.
$W > 0$ means the system does work on the surroundings; $W < 0$ means work is done on the system.
Internal energy $U$ is the microscopic energy of the system; only changes in $U$ are usually measured.
For a gas at constant pressure, $W = P\Delta V$.
In an isothermal process for an ideal gas, $\Delta U = 0$.
In an adiabatic process, $Q = 0$, so $\Delta U = -W$.
In an isochoric process, $W = 0$, so $\Delta U = Q$.
The first law is essential for understanding engines, refrigerators, pistons, and energy flow in thermodynamics.