 # State Functions

## What is State Function in Thermodynamics?

A property whose value doesn’t depend on the path taken to reach that specific value is known to as state functions or point functions. In contrast, those functions which do depend on the path from two points are known as path functions. State functions are the values which depend on the state of the substance like temperature, pressure or the amount or type of the substance. as a matter of fact, state functions do not depend on how the state was reached or established.

For example, density is a state function, because a substance’s density is not affected by how the substance is obtained. To decide whether certain property is a state function or not, keep this rule in mind: is this property or value affected by the path or way taken to establish it? If the answer is yes then it is not a state function and if the answer is no, then the property is a state function.

State functions can be considered as integrals. This is because, integrals depend on only three things: the function, lower limit and its upper limit. Similarly, state functions also depend on three things: the property, initial value and its final value.

Thus, it is evident that state functions depend only on the initial and final value of the property.

For example, the integral of enthalpy H, where t0 represents the initial state and t1 represents the final state is given by,

$\int_{t_{0}}^{t_{1}} H(t)dt = H(t_{1}) – H(t_{0})$

This equation is similar to the equation of enthalpy, which is:

ΔH = Hfinal Hinitial

As seen in the above example, enthalpy is a state function because its value depends only on initial and final conditions.

## Difference Between State Function And Path Function

As defined earlier, state functions are properties whose values do not depend on the path taken to reach that specific function or value.

All functions that depend on the path taken to reach that specific value are known as path functions.

 State function Path function Independent of the path taken to reach the property or value Dependent on the path taken to establish the property or value Capable of integrating using initial and final values Requires multiple integrals and limits of integration in order to integrate any number of steps results in the same value Different steps result in different values Based on the established state of system (temperature, pressure, amount, and identity of a system). It is based on how the state of the system was established.

## List of State Functions

### Pressure:

Pressure is a measure of the average force exerted by the constituent molecules per unit area on the container walls. pressure does not depend on the path of the molecules and thus it is a state function.

### Temperature:

Temperature is defined as the measure of the average kinetic energy of the atoms or molecules in the system. Temperature measures a property of a state of a system irrespective of how it got there and thus it is a state function.

### Volume:

Volume is the amount of physical space occupied by a substance and it will not be dependent on the path followed. Thus, the volume is a state function

### Mass:

The measure of the amount of matter in an object is known as mass and is usually measured in grams (g) or kilograms (kg). Mass measures the quantity of matter regardless of both its location in the universe and the gravitational force applied to it and thus it is a state function.

### Internal energy:

It can be defined as the sum of all kind of energy associated with molecular motions.

The internal energy of ideal gases is a function of temperature only (Joule’s law) and internal energy of real gases is a function of temperature, pressure and volume (temperature and volume being the dominating quantities and effect of pressure are negligible), So it can be seen that since internal energy depends on quantities like P, T, V which are state functions, the internal energy is also a state function.

### Gibb’s free energy:

The enthalpy of the system at any point minus the product of the temperature times the entropy of the system is Gibb’s free energy of the system

G = H – TS

The Gibbs free energy of the system is a state function because it is defined in terms of thermodynamic properties that are state functions.

### Entropy:

entropy is the measure of imbalance in the system and it’s totally independent of the path through which the system has achieved that state also it’s unique to the current state of the system

### Important Questions

1. Among the following, state functions are

• Internal energy
• Reversible expansion work
• Irreversible expansion work
• Molar enthalpy

2. Which of the following statement is false?

• Work is a state function
• Work appears at the boundary of a system
• Temperature is a state function
• Change in the state is completely defined when the initial and final states are specified.

3. Why is heat not a state function?

4. Why is energy a path function yet heat and work are not?

5. Is heat capacity a state function?

6. Why is internal energy a state function?

7. State whether entropy is a state function or not. Justify your answer.

8. Two moles of an ideal gas undergo isothermal reversible expansion from 2 L to 8 L at 300 K. The enthalpy change of the gas is

• 4.8 KJ
• 11.4 KJ
• Zero
• -11.4 KJ

9. Standard molar enthalpy of formation of CO2 is

• the standard molar enthalpy of combustion of gaseous carbon.
• the sum of standard molar enthalpies of formation of CO and O2.
• the standard molar enthalpy of combustion of graphite.
• Zero

10. For which of the following equations is ΔrH equal to ΔfH?

• CH4(g) + Cl2(g) ——-> CH2Cl2(l) + 2HCl(g)
• Xe(g) + 2F2(g) ——–> XeF4(g)
• 2CO(g) + O2(g)  ——–> 2CO2(g)
• N2(g) + O3(g) ———> N2O3(g)

11. Why is the enthalpy change in one reaction path is equal to that in another path?