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State Functions
A property whose value is not dependent upon the path that it takes to reach a specific value is known as a state function or point function. The opposite of state function is path function, in which the values are dependent upon the path it takes. The factors upon which the final values of state function depend include the state of the substance, such as its pressure, temperature, type, or amount of the substance. Thus, state functions do not take into account how that state was established.
State function examples include the density of an object. Since the density is not affected by how that substance was created, it is a state function. When deciding whether an object is a state function or not, one must keep a simple rule in mind – ask whether the value of the property has been affected by the path or way it was established. In case the answer is yes, then the property is not a state function, and if it is no, then it is indeed a state function.
The mathematics of state functions
State functions are considered integrals since integrals are dependent upon three things: the upper limit, lower limit, and function. Thus state functions are also dependent upon three things: the initial value, the property, and the final value. In other words, integrals show how state functions are dependent only upon the initial and final values, and not on the history of the object or the path which it took to reach the final value from the initial value.
For instance, if there is an integral of enthalpy H, in which t0 is supposed to represent the initial state, whereas t1 shall represent the final state, then the formula shall be
∫t1t0 H (t) dt = H (t1) – H (t0)
This equation is quite similar to that of the equation of enthalpy
ΔH = Hfinal − Hinitial
Thus you will observe from the example above that enthalpy is basically a state function since its value is dependent only upon the initial and final conditions.
Difference between state and path functions
As we mentioned earlier, state function thermodynamics is a property whose value is not dependent upon the path that it takes to reach that particular value or function. On the other hand, path functions are dependent upon the path that it takes to reach that particular value.
State function | Path function |
Not dependent upon the path that it takes to reach the final value. | Dependent upon the path that it takes to reach the final value. |
It can integrate itself using initial and final values. | It needs numerous integrals and integration limits in order to integrate itself. |
No matter how many steps are involved, they will reach the same value. | May reach different values based upon the number of steps involved. |
It depends upon the state of the property established. (e.g., its pressure, temperature, amount, or identity as a system) | It depends upon the steps based on which the state of the property was established. |
List of state functions
- Pressure
Pressure can be defined as a way to measure the force that is exercised by the constituent molecules per unit area upon the walls of a container. Since pressure is not dependent on the course of molecules, it is classified as a state function.
- Temperature
Temperature can be defined as a way to measure the average kinetic energy of the molecules or atoms in a particular system. Thus temperature is a state function since it is not dependent upon how that state was reached.
- Volume
Volume can be defined as the physical space which is occupied by a substance. Since it is not dependent upon the path it follows, it is a state function.
- Mass
Mass can be defined as the amount of matter that an object occupies. It is measured in grams or kilograms. Since mass is not dependent upon either the location of the matter in the universe or its gravitational force, it can be classified as a state function.
- Internal energy
Internal energy is defined as the total sum of the energy of molecular motions. Since it is only dependent upon temperature in the case of ideal gases, and volume, pressure, and temperature, in the case of real gases, which are all state functions, the internal energy is also a state function.
- Gibb’s free energy
The enthalpy of a system at any point is subtracted by the product of the temperature, along with the entropy of the system.
G = H – TS
It is a state system since it is defined in thermodynamic terms which include state functions.
- Entropy
Entropy can be defined as a measure of a system’s imbalance, and it is independent of the path through which the final state is achieved by the system, thus making it a state function.
Conclusion
These notes on State Functions can prove to be quite useful for state-based and other competitive exams as well, such as banking PO, SSC, and so on. A state function thermodynamics is a property of a system that depends on the state of the system. Pressure ,temperature ,volume, density etc. are few examples of state functions .Path function is a property of a system depend on path taken .Work and heat are examples of path function.
