## Thermodynamic Properties And Thermodynamic State Of A System

**Thermodynamic properties**

The measurable physical quantities by which the dynamic state of a the system can be defined completely are called thermodynamic properties or variables of the system. **Examples:** The pressure (P), temperature (T), volume (V), composition, etc., of a system are the thermodynamic properties or variables of the system because the state of the system can be defined by these variables or properties.

The properties or variables required to define the state of a system are determined by experiment. Although a thermodynamic system may have many properties (like— pressure, volume, temperature, composition, density, viscosity, surface tension, etc.), to define a system we need not mention all of them since they are not independent If we consider a certain number of properties or variables having certain values to define the state of a system, then the other variables will automatically be fixed.

In general, to define the state of a thermodynamic system, four properties or variables are needed. These are the pressure, volume, temperature, and composition of the system. If these variables of a thermodynamic system are fixed then the other variables will also be fixed for that system.

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For a closed system of fixed composition, the state of the system depends upon the pressure (P), temperature (T), and volume (V) of the system. If these three variables of the system (P, V, T) are fixed, then other variables (like density, viscosity, internal energy, etc.) ofthe system automatically become fixed.

**Thermodynamic state of a system**

A system is said to be in a given thermodynamic state ifthe properties (For example pressure, volume, temperature, etc.) determining its state have definite values.

If the thermodynamic properties or variables of a thermodynamic system remain unchanged with time, then the system is said to be in thermodynamic equilibrium. A system is said to be in thermodynamic equilibrium if it attains thermal equilibrium, mechanical equilibrium, and chemical equilibrium simultaneously.

**Thermal equilibrium:**A system is said to be in thermal equilibrium if the temperature throughout the system is the same and is equal to that of its surroundings.**Mechanical equilibrium:**If no imbalanced force exists within a system and also between the system and its surroundings, the system is said to be in mechanical equilibrium.**Chemical equilibrium:**If the chemical composition throughout a system remains the same with time, the system is said to be in chemical equilibrium.

**State function of a thermodynamic system**

The state function of a thermodynamic system is a property whose value depends only on the present state of the system but not on how the system arrived at the present state. **Examples:** Pressure (P), volume (V), temperature (T), internal energy (E or U), enthalpy (H), entropy (S), Gibbs free energy (G), etc., of a thermodynamic system the state functions because the values of these functions depend only on the present state ofa system, not on how the system arrived at that state.

**Change of a state function in a process:** The state of a thermodynamic system at the beginning of a process is called its initial state and the state attained by the system after completion of the process is called its final state. Let X (like P, V, T, etc., of a system) be a state function of a thermodynamic system. The values of X at the beginning and the end of a process are X1 and respectively. So, the change in the value of X in the process, AX = X2-X1.

- Infinitesimal change in x is represented by dx and finite change in x is represented by ax. For example, the infinitesimal change in pressure (p) of a system is dp and the finite change is ap.
- If X is a state function of a thermodynamic system, then dX must be a perfect differential as the integration of dX between two states results in a definite value of X

The state function of a system is a path-independent quantity: A state function of a system depends only on the state of the system.

Consequently, the change in any state function ofa system undergoing a process depends only upon the initial and final states of the system in the process, not on the path of the process. Thus the state function of a system is a path-independent quantity.

**Explanation:** Suppose, a system undergoes a process in which its state changes from A (initial state) to B (final state), and because of this, the value of its state function X changes from XA (value of X at state A ) to XB (value of X at state B). The process can be carried out by following three different paths.

But the change in X, i.e., AX= (XB-XA) will be the same for all three paths. This is because all the paths have identical initial and final states and consequently X has identical initial and final values for these paths.

**Example:** The change in temperature of a system depends only upon the initial and the final stages of the process. It does not depend on the path followed by the system to reach the final state. So the temperature of a system is a state function. Similarly, the change of other state functions like pressure (P), volume (V), internal energy (U), enthalpy (H), entropy (S), etc., (i.e. AP, AV, AU, AH, AS, etc.) does not depend upon the path ofthe process.

**Path-dependent quantity**

Two terms commonly used in thermodynamics are heat (q) and work ( w). These are not the properties ofa system. They are not state functions.

Heat change or work involved in a process depends on the path of the process by which the final state of the system is achieved. Thus, heat and work are the path-dependent quantities.

In general, capital letters are used to denote the state functions (for example, P, V, T, U, etc.), and small letters are used to denote path functions (for example q, w, etc.). q and w are not state functions.

Hence, 5q or 8w (S = delta) are used instead of dq or dw. Unlike dP or dV, which denotes an infinitesimal change in P or V, 8q or 8w does not indicate such kind of change in q or w. This is because q and w like P or F are not the properties of a system. 8q and 8w are generally used to denote the infinitesimal transfer of heat and work, respectively, in a process.