Which of the following is/are state function/functions? 1. q + w 2. q 3. w 4. H - TS Select the correct answer using the code given below.
1 and 4 only
Understanding State Functions in Thermodynamics
In thermodynamics, a state function (or state variable) is a property of a system that depends only on the current state of the system, not on the path taken to reach that state. Think of it like your altitude on a mountain; it only depends on where you are right now, not how you got there (whether you hiked straight up or took a winding trail).
Conversely, a path function is a property that depends on the specific way the change was carried out. Heat (\(q\)) and work (\(w\)) are classic examples of path functions because the amount of heat absorbed or work done by a system can vary greatly depending on the process (e.g., whether a gas expands against a constant pressure or expands reversibly).
Analyzing Each Given Expression
- \(\mathbf{q + w}\): This expression relates to the change in internal energy (\(\Delta U\)) according to the First Law of Thermodynamics, which is often written as \(\Delta U = q + w\) (using the convention where work done *on* the system is positive). Internal energy (\(U\)) is a fundamental state function. Since \(\Delta U\) represents the difference in internal energy between the final and initial states, it depends only on the initial and final states, not the path taken. Therefore, \(q+w\) (representing \(\Delta U\)) is a state function.
- \(\mathbf{q}\): This represents heat transferred to or from the system. Heat (\(q\)) is a path function. The amount of heat exchanged depends on the specific process followed between two states. For example, heating a substance from temperature T1 to T2 can involve different amounts of heat depending on whether the process occurs at constant pressure or constant volume.
- \(\mathbf{w}\): This represents work done by or on the system. Work (\(w\)) is also a path function. The amount of work done depends on the specific path taken between two states. For instance, the work done during the expansion of a gas from a certain initial volume to a final volume is different for an isothermal reversible expansion compared to an irreversible expansion against a constant external pressure.
- \(\mathbf{H - TS}\): This expression is the definition of Gibbs free energy (\(G\)), i.e., \(G = H - TS\). Enthalpy (\(H\)), temperature (\(T\)), and entropy (\(S\)) are all well-known state functions. A combination of state functions, like \(H - TS\), also results in a state function. Therefore, Gibbs free energy (\(G\)) is a state function.
Identifying the State Functions
Based on our analysis:
- Statement 1 (\(q+w\)) is a state function (\(\Delta U\)).
- Statement 2 (\(q\)) is NOT a state function (it's a path function).
- Statement 3 (\(w\)) is NOT a state function (it's a path function).
- Statement 4 (\(H - TS\)) is a state function (\(G\)).
Thus, the expressions that represent state functions are 1 and 4.
Conclusion
The state function expressions among the given options are \(q+w\) (which is \(\Delta U\)) and \(H-TS\) (which is \(G\)). Therefore, options 1 and 4 are state functions.
Revision Table: State vs. Path Functions
| Property | Type | Depends On | Example |
|---|---|---|---|
| Internal Energy (U) | State Function | Current state of the system | \(q+w = \Delta U\) |
| Enthalpy (H) | State Function | Current state of the system | \(H = U + PV\) |
| Entropy (S) | State Function | Current state of the system | — |
| Gibbs Free Energy (G) | State Function | Current state of the system | \(G = H - TS\) |
| Heat (q) | Path Function | Process/Path taken | Heat transferred depends on constant V vs constant P process. |
| Work (w) | Path Function | Process/Path taken | Work done depends on reversible vs irreversible process. |
Additional Information on State Functions
State functions are crucial in thermodynamics because they allow us to define the change in a system's properties simply by knowing the initial and final states, without needing to know the intricate details of the process that occurred between them. This simplifies many thermodynamic calculations.
Other important state functions include pressure (P), volume (V), and temperature (T). Any property that can be uniquely defined for a given state, regardless of how that state was achieved, is a state function.
The First Law of Thermodynamics (\(\Delta U = q + w\)) is a fundamental principle that connects the change in a state function (\(\Delta U\)) to two path functions (\(q\) and \(w\)). This law highlights that while heat and work are path-dependent individually, their sum, representing the change in internal energy, is path-independent.
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