1.4 Processes and cycles

Thermodynamic Processes: Classification and Characteristics

Definition and Characteristics of Thermodynamic Processes

A thermodynamic process is a change in the state of a system from an initial state to a final state, marked by changes in properties like temperature, pressure, volume, and internal energy. During a process, energy transfers between the system and its surroundings as heat, work, or both.

The path a process follows depends on the constraints placed on the system. For example, you might hold temperature constant, fix the volume, or insulate the system from its surroundings. Each constraint produces a different type of process with different behavior.

The direction of a process depends on the initial and final states and on whether the process is reversible or irreversible.

Classification of Thermodynamic Processes

Processes are often classified by which property stays constant:

• Isothermal (constant temperature): The system exchanges heat with a large thermal reservoir so its temperature doesn't change. Think of a gas slowly expanding while in contact with a heat bath.
• Isobaric (constant pressure): The system expands or compresses while pressure stays fixed. A gas heated in a piston-cylinder device open to the atmosphere is a common example.
• Isochoric (constant volume): The system is heated or cooled inside a rigid container, so volume can't change. Because there's no volume change, no boundary work is done ($W = 0$).
• Adiabatic (no heat transfer): The system is insulated from its surroundings, so $Q = 0$. Any energy change comes entirely from work.

Beyond these, there are two broader categories worth knowing:

• Reversible vs. irreversible processes. A reversible process can be reversed with no net change to the system or surroundings. Irreversible processes involve dissipative effects like friction, unrestrained expansion, or heat transfer across a finite temperature difference, and they can't be fully undone.
• Polytropic processes follow the relationship $PV^n = \text{constant}$, where $n$ is the polytropic index. This is a general form that includes several special cases: $n = 0$ gives an isobaric process, $n = 1$ gives isothermal, $n = \gamma$ (the specific heat ratio) gives an adiabatic process for an ideal gas, and $n \to \infty$ gives isochoric.

Quasistatic vs. Non-Quasistatic Processes

Quasistatic Processes

A quasistatic process occurs slowly enough that the system remains in internal equilibrium at every instant. You can picture it as the system passing through a continuous series of equilibrium states, each only infinitesimally different from the last.

This matters because equilibrium thermodynamics (the equations you use in this course) strictly applies only to equilibrium states. A quasistatic process lets you use those equations at every point along the path, which is why you can plot it as a well-defined curve on a P-V or T-s diagram.

Quasistatic processes are idealizations. Real processes are never truly quasistatic, but many are slow enough to be approximated as such:

• Slow compression or expansion of a gas in a piston-cylinder assembly
• Gradual heating or cooling of a system in thermal contact with a large reservoir

Non-Quasistatic Processes

Non-quasistatic processes happen at a finite rate, fast enough that the system develops internal gradients in temperature, pressure, or other properties. The system is not in equilibrium during the process.

Because of these gradients and dissipative effects (friction, turbulence, heat transfer across finite temperature differences), non-quasistatic processes are always irreversible. They also can't be represented as a single continuous curve on a property diagram, since the system doesn't have a single well-defined state at each moment.

Examples include:

• Rapid compression or expansion of a gas (as in internal combustion engines)
• Sudden mixing of two fluids at different temperatures
• Free expansion of a gas into a vacuum

Thermodynamic Cycles and Their Importance

Definition and Significance of Thermodynamic Cycles

A thermodynamic cycle is a sequence of processes that starts and ends at the same state. After one complete cycle, every property of the system (temperature, pressure, volume, internal energy) returns to its original value.

Cycles are the foundation of how heat engines, refrigerators, and heat pumps work. A heat engine cycle converts heat into net work output; a refrigeration cycle uses net work input to move heat from a cold space to a warm one.

Two key points about cycles on diagrams:

• On a P-V diagram, the net work per cycle equals the area enclosed by the cycle curve. Clockwise cycles produce net work output (heat engines); counterclockwise cycles require net work input (refrigerators/heat pumps).
• Since the system returns to its initial state, the net change in internal energy over a complete cycle is zero. By the first law, this means $W_{net} = Q_{net}$ for a cycle.

Common Thermodynamic Cycles and Their Applications

At this introductory stage, you should recognize these major cycles and know what processes make them up:

• Carnot cycle: Four reversible processes (isothermal expansion → adiabatic expansion → isothermal compression → adiabatic compression). It sets the theoretical maximum efficiency for any heat engine operating between two temperature reservoirs. No real engine can beat it.
• Otto cycle (gasoline engines): Isentropic compression → constant-volume heat addition → isentropic expansion → constant-volume heat rejection.
• Diesel cycle (diesel engines): Isentropic compression → constant-pressure heat addition → isentropic expansion → constant-volume heat rejection. The key difference from the Otto cycle is that heat is added at constant pressure instead of constant volume.
• Brayton cycle (gas turbines, jet engines): Isentropic compression → constant-pressure heat addition → isentropic expansion → constant-pressure heat rejection.
• Rankine cycle (steam power plants): Isentropic compression in a pump → constant-pressure heat addition in a boiler → isentropic expansion in a turbine → constant-pressure heat rejection in a condenser.

Analyzing Processes and Cycles with Diagrams

Property Diagrams for Thermodynamic Analysis

Property diagrams give you a visual way to understand what's happening during a process or cycle. The three most common are:

• P-V diagram (pressure vs. volume): The area under a process curve represents the boundary work done. Area under an expansion curve is positive work (work done by the system); area under a compression curve is negative work (work done on the system).
• T-s diagram (temperature vs. entropy): The area under a process curve represents the heat transfer. Area under a curve where entropy increases is heat added; area under a curve where entropy decreases is heat rejected.
• P-h diagram (pressure vs. enthalpy): Especially useful for analyzing refrigeration and heat pump cycles, where you need to track enthalpy changes across components like compressors, condensers, and evaporators.

Calculating Work, Heat Transfer, and Efficiency Using Diagrams

Property diagrams aren't just qualitative sketches. You can extract quantitative information from them:

1. Work from a P-V diagram: Calculate the boundary work for a process by integrating pressure with respect to volume: $W = \int P \, dV$ For a complete cycle, the net work is the area enclosed by the cycle curve.

2. Heat transfer from a T-s diagram: Calculate heat transfer by integrating temperature with respect to entropy: $Q = \int T \, dS$ For a complete cycle, the net heat transfer equals the net work ($Q_{net} = W_{net}$), since internal energy returns to its starting value.

3. Thermal efficiency: The efficiency of a power cycle is the ratio of net work output to heat input: $\eta = \frac{W_{net}}{Q_{in}}$ On a T-s diagram, this is the ratio of the area enclosed by the cycle to the total area under the heat-addition process curve.

4. Identifying irreversibilities: By comparing an actual cycle to its ideal (reversible) counterpart on a property diagram, you can spot where losses occur. Common sources include heat transfer across large temperature differences, frictional pressure drops, and non-isentropic compression or expansion. These show up as deviations from the ideal cycle shape and represent opportunities for improving efficiency.