5.2.1. Work

First of all, let us concentrate on the nature of work a system can do. We will consider only mechanical work i.e., pressure-volume work.

In thermodynamics, work refers to how energy is transferred to or from a system. This section focuses specifically on mechanical work, which can be understood in the context of gases confined in a cylinder with a piston. When the gas expands or is compressed, it performs work according to the changes in pressure and volume. This mechanical work is crucial in understanding how energy transfer occurs during physical and chemical processes.

Consider a bicycle pump. When you push down the pump, you are compressing air inside it. The work you do on the pump is converted to pressure that forces air into the tire. Similarly, when a gas in a cylinder is compressed by pushing down a piston, it leads to an increase in pressure, which can be quantified as work done on the gas.

For understanding pressure-volume work, let us consider a cylinder which contains one mole of an ideal gas fitted with a frictionless piston. Total volume of the gas is Vi and pressure of the gas inside is p. If external pressure is pex which is greater than p, piston is moved inward till the pressure inside becomes equal to pex.

In this scenario, we analyze the work done on an ideal gas when it is compressed. The initial volume (Vi) and pressure (p) of the gas are essential to calculate changes when an external pressure (pex) is applied. As the piston moves inward, the gas is compressed, and this compression results in work being done on the gas. The work can be described mathematically using the formula: w = -pex(Vf - Vi), where Vf is the final volume and Vi is the initial volume.

Imagine a syringe filled with air. As you push the plunger (similar to moving the piston), you compress the air inside. The work done on the air increases its pressure. If we could quantify this compression, we would find it directly relates to the volume of the air that has decreased as you push in the plunger.

If the pressure is not constant at every stage of compression, but changes in number of finite steps, work done on the gas will be summed over all the steps. If the pressure is not constant but changes during the process such that it is always infinitesimally greater than the pressure of the gas, then, at each stage of compression, the volume decreases by an infinitesimal amount, dV.

When pressure varies during compression, we can still calculate the work done using an integral approach. In such cases, we consider infinitesimal changes, meaning we look at tiny steps of compression where pressure at each step is just slightly greater than the gas pressure. By continuously summing these small changes, we derive a comprehensive expression for the total work done. The relationship becomes more useful during reversible processes, which are ideal and occur so slowly that the system remains in equilibrium.

Think of gradually inflating a balloon. If you apply pressure evenly and slowly, the balloon fills smoothly. This situation mimics a reversible process. On the other hand, if you rapidly blow air into the balloon, the change in pressure and volume occurs too quickly to maintain this equilibrium, emulating an irreversible process.

A process or change is said to be reversible, if a change is brought out in such a way that the process could, at any moment, be reversed by an infinitesimal change. A reversible process proceeds infinitely slowly by a series of equilibrium states such that system and the surroundings are always in near equilibrium with each other.

Reversible processes are characterized as ideal scenarios where the system can be returned to its original state without any net change in the surroundings. This requires an incredibly slow approach to changes, allowing the system to adjust and maintain equilibrium throughout the process. In contrast, irreversible processes happen rapidly and cannot return to the initial state without external work being performed.

Consider the melting of an ice cube in a glass of water. If the conditions are just right, and the ice melts slowly, you could refreeze the water and restore the original situation. But if you spill the water or let it evaporate, the process becomes irreversible — you cannot bring back the ice cube without additional actions.

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