In everyday life, when we think of “work”, we might imagine physical efforts, projects or activities. However, in a **thermodynamic context** , “ **work** ” takes on a particular meaning. It represents a means by which **energy is transferred between a system and its environment** , often leading to observable changes that can manifest in various forms, such as motion or temperature changes.

Thermodynamic work can be thought of as an energy bridge. Imagine compressing a spring: the effort you exert is converted into potential energy in the spring. Similarly, when a gas expands in a cylinder by pushing a piston, the gas does “work” on the piston, transferring energy in the form of motion. These transformations of energy, from one form to another, are at the heart of the notion of work in thermodynamics.

Applications of this concept are everywhere around us. When we pump air into a bicycle, when an internal combustion engine moves an automobile, or when a steam engine powers a generator, we are experiencing, in various forms, thermodynamic work in action. Let’s find out more about **thermodynamic work** together !

## Thermodynamic work in an isobaric transformation

To understand how **work** varies in an **isobaric transformation,** let’s take our cylinder once again (containing perfect gas, heated by a flame placed underneath, and with a piston that closes it).

We slowly heat the gas contained in the cylinder so that it expands at **constant pressure** and let the **volume** of the gas increase in a **quasi-static** manner. As the piston rises, the system does **positive work**.

Just think: you could use this mechanism to lift an object via a pulley.

From a quantitative point of view, the **work** W that the system performs is equal to the product of the **force** $F$, which pushes the piston upwards, and the **displacement** $h$of the piston: W = F h. From this consideration, it can be deduced that, in any **transformation**, the **work** is equal to the **area** of the rectangle between the **volume** axis and the **graph** of the **transformation** in question.

## Thermodynamic work in an isochoric transformation

Now that you know the characteristics of an **isochoric transformation** , calculating the **work** in a **transformation** of this type will be very easy. In fact, since the **work** is equal to the **area** underneath the **transformation ****graph** , and since the **graph** in question is a **vertical segment** , it is intuitive that in **isochore transformations** :

## Thermodynamic work in a cyclic transformation

Expansion

Compression

Cyclic transformation

When a gas expands, during an expansion, the **volume changes** $ΔV_$is positive, therefore the **work** $W$it’s **positive. **During compression, however, the **volume changes** $ΔV_$is negative, and consequently, **work** $W$it is **negative** .

During a **cyclic transformation** of the type shown in the image, there is an expansion and a compression phase. During the **expansion** phase the **system** performs **positive work** equal to the **area** of the part of the plane shaded in red. **During the compression** phase the **system** performs **negative ****work**, the absolute value of which is given by the gray shaded **area . **The **total work** done is equal to the algebraic sum of the two works.

## Work in thermodynamics is not a state function

Example – Transformation 1

Example – Transformation 2

Let us consider two **quasistatic transformations** that cause a system to pass from the same **initial state** TO the same **final state** $B$following two different paths.

The **work** $W_{1}$accomplished in the first **transformation** is different from **work** TOaccomplished in the second. Therefore the **work** done in a **transformation** does not only depend on the **initial** and **final** states , but also on the particular **transformation** followed in passing from$TO$to$B$.

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