Thermodynamics studies the relationship between heat, work, temperature, and energy, focusing on how energy is transferred and transformed. Thermodynamic properties are categorized based on whether their value depends only on the initial and final states (path independent) or if they are influenced by the specific process taken between those states (path dependent). This distinction between path dependence and path independence is central to understanding energy transfer.
Defining Properties of a State Function
A state function is a property of a system whose value depends only on its current state, defined by variables like temperature, pressure, and volume. The value of a state function is completely independent of the process or path taken to reach that state. For example, the altitude of a mountain climber is a state function. If a climber begins at sea level and ends at a 5,000-foot summit, the change in altitude is exactly 5,000 feet, regardless of the specific path taken.
The final change in any state function is calculated simply by subtracting the initial value from the final value. This path independence is a powerful tool in thermodynamics because it allows for the calculation of property changes without needing to know the complex intermediate steps of a process. Key state functions include temperature, pressure, volume, and composition.
Understanding Thermodynamic Work
Thermodynamic work represents energy transferred across the boundary between a system and its surroundings. This transfer occurs when a force causes a displacement, and it is not a property contained within the system itself. The most common and illustrative example is pressure-volume (P-V) work, which involves the expansion or compression of a gas.
Consider a gas confined in a cylinder fitted with a movable piston. If the gas expands, it pushes the piston against an external pressure, thereby performing work on the surroundings. Conversely, if the surroundings push the piston inward, work is done on the gas. The calculation of this work is generally represented by the integral of pressure with respect to the change in volume, showing that the amount of work done is inherently connected to the mechanical process that takes place.
Why Work Depends on the Process Path
Work is not a state function; it is classified as a path function because the quantity of work exchanged between a system and its surroundings is dependent on the specific sequence of steps followed. This is demonstrated by comparing two different ways of expanding a gas from the same initial volume and pressure to the same final volume and pressure.
In the first scenario, a gas might expand in a single, irreversible step against a constant external pressure. In the second scenario, the same gas might expand in two or more separate steps, where the external pressure is allowed to drop to a different intermediate value after each step.
Even though both processes start and end at the identical state points, the total work done in the multi-step expansion will be different from the work done in the single-step expansion. This difference arises because the pressure term used in the work calculation changes along the path. On a pressure-volume diagram, the work done is represented by the area under the curve connecting the initial and final states. Since different paths trace different curves, they enclose different areas, proving that work is path-dependent.
State Functions That Contrast With Work
The distinction between work and a state function is fundamental to the First Law of Thermodynamics. This law states that the change in a system’s internal energy (\(\Delta U\)) is equal to the heat (\(Q\)) added to the system plus the work (\(W\)) done on the system (\(\Delta U = Q + W\)). Internal Energy (\(U\)) is a state function, meaning its value only depends on the system’s current state.
Internal energy is the total energy stored within a system, encompassing the kinetic and potential energies of its molecules. Because \(\Delta U\) is path-independent, the combination of heat and work must always result in the same change in internal energy, regardless of how much of the energy transfer was due to \(Q\) and how much was due to \(W\).
Enthalpy (\(H\)) is another state function, defined as the internal energy of the system plus the product of its pressure and volume (\(H = U + PV\)). Like internal energy, the change in enthalpy is independent of the path taken between states. The fact that the sum of two path-dependent quantities (heat and work) yields a path-independent quantity (internal energy) is a defining feature of energy conservation in thermodynamic systems.