11.8. THERMODYNAMIC PROCESSES

Consider a gas in thermal and mechanical equilibrium with its surroundings. The pressure of the gas in that case equals the external pressure and its temperature is the same as that of its surroundings. Suppose that the external pressure is suddenly reduced (say by lifting the weight on the movable piston in the container). The piston will accelerate outward. During the process, the gas passes through states that are not equilibrium states. The non-equilibrium states do not have well-defined pressure and temperature. In the same way, if a finite temperature difference exists between the gas and its surroundings, there will be a rapid exchange of heat during which the gas will pass through non-equilibrium states.

A quasi-static process occurs when the system changes so slowly that it remains in thermal and mechanical equilibrium with its surroundings at each step. This means that the pressure and temperature of the gas remain infinitesimally different from that of the environment as changes are made. If the pressure is suddenly reduced, the piston moves rapidly, and the gas may not equilibrate, leading to undefined values of pressure and temperature during this rapid transition. This is unlike a quasi-static process where every infinitesimal change keeps the gas in equilibrium, allowing for well-defined pressures and temperatures throughout the process.

Imagine filling a balloon with air. If you blow air into the balloon steadily and slowly, the balloon expands uniformly, representing a quasi-static process where the pressure inside the balloon matches the external pressure. Conversely, if you were to quickly exhale hard into the balloon, it would expand suddenly and not uniformly throughout its length, creating regions of varying pressures and temperatures rather than an even distribution.

A process in which the temperature of the system is kept fixed throughout is called an isothermal process. The expansion of a gas in a metallic cylinder placed in a large reservoir of fixed temperature is an example of an isothermal process. In isobaric processes the pressure is constant while in isochoric processes the volume is constant. Finally, if the system is insulated from the surroundings and no heat flows between the system and the surroundings, the process is adiabatic.

Thermodynamic processes can be classified into several types based on their constraints:

1. Isothermal Process: Here, the temperature remains constant. The gas absorbs or releases heat while doing work, maintaining thermal equilibrium with a heat reservoir.
2. Isobaric Process: This process occurs at a constant pressure. When a gas expands or contracts under a constant external pressure, its volume changes while its pressure stays the same.
3. Isochoric Process: Volume remains constant during this type of process, which means no work is done by or on the system. All the supplied heat energy goes into changing the internal energy, thereby increasing the temperature.
4. Adiabatic Process: No heat is exchanged with the surroundings, meaning all energy transfers result from work done on or by the gas, leading to temperature changes without heat exchange.

Think of a pressure cooker. It maintains a constant pressure (isobaric) while cooking food. If you say a pot of water is kept on a stove at a constant temperature (isothermal) while boiling, you can also consider it an isochoric process if the lid is tightly closed, preventing any steam from escaping. In contrast, during its operation, if you rapidly stir the water in a sealed container (adiabatic), it heats up due to the work done on it without heat exchange with the environment.

For an isothermal process (T fixed), the ideal gas equation gives PV = constant, i.e., pressure of a given mass of gas varies inversely as its volume. Suppose an ideal gas goes isothermally (at temperature T) from its initial state (P1, V1) to the final state (P2, V2).

In an isothermal process, the product of pressure and volume for a gas remains constant because the temperature does not change. According to Boyle's Law, if the volume increases, the pressure decreases and vice-versa, as long as the temperature is held constant. So for a gas going from an initial condition of (P1, V1) to a final condition of (P2, V2), the relationship can be expressed by the equation PV = constant. Mathematically, as the gas expands or compresses while keeping temperature constant, its state can be described by this inverse relationship.

A practical analogy would be using a syringe. If you pull back on the plunger (increasing the volume), the pressure inside the syringe decreases. If you push in the plunger without causing the liquid to heat up (isothermal condition), the pressure increases as the volume decreases. No matter how much you change the volume, as long as the liquid remains at a constant temperature, the product of pressure and volume will always equal a constant.

In an adiabatic process, the system is insulated from the surroundings and heat absorbed or released is zero. From Eq. (11.1), we see that work done by the gas results in decrease in its internal energy (and hence its temperature for an ideal gas).

During an adiabatic process, since the system is perfectly insulated, no heat is exchanged with the surroundings. This means any work done by the system (like expanding gases doing work on pistons) reduces its internal energy and results in a decrease in temperature. Conversely, if work is done on the gas (compressing it), its internal energy and therefore temperature increases. This is distinctly different from processes where heat can enter or exit the system.

Think of a bicycle pump. When you compress the air inside the pump, you feel the pump heating up (the work done on the gas increases its temperature)—that's the adiabatic process at work. If the pump were insulated, not only would the air within get hot as you compress it, but if you were to let the gas expand without allowing heat to escape, it would cool down as it expands, demonstrating that work translates directly into internal energy changes.

In a cyclic process, the system returns to its initial state. Since internal energy is a state variable, ∆U = 0 for a cyclic process. From Eq. (11.1), the total heat absorbed equals the work done by the system.

In a cyclic process, the system experiences various transitions but ultimately ends up in the exact same state it began with. Because internal energy is a state variable, the change in internal energy (∆U) during a complete cycle is zero, meaning any energy put in as heat must be transformed into work done by the system. The First Law of Thermodynamics (∆Q = ∆U + ∆W) simplifies here since ∆U is zero, leading to ∆Q = ∆W, indicating all heat added goes into doing work.

Consider a car engine operating on a four-stroke cycle. The engine takes in fuel and mixes it with air (intake), compresses the mixture (compression), ignites it to perform work (power), and expels exhaust gases (exhaust). After completing these four strokes, the process repeats. The engine returns to its starting point at the end of each cycle, meaning the energy transformations in ∆U are reset, while the total energy used remains accountable for work done in that cycle.

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