Thermodynamics

Thermodynamic State

Question

What is the state of a thermodynamic system? Explain the meaning of state, property and variable in thermodynamics.

Definition of State

State is the condition of a system at an instant of time as described or measured by its properties.

In other words, each unique condition of a system is called a state.

\boxed{ \text{State} = \text{Condition of a system at an instant of time} }

The state of a system is described using its thermodynamic properties such as temperature, pressure and other measurable quantities.

State and Properties

Each property has a single value at a particular state. Therefore, when a state is specified, the values of its properties are fixed.

\boxed{ \text{One state} \rightarrow \text{One definite value of each property} }

If two systems are in identical states, their corresponding properties have identical values.

Detailed Answer

1. What Is the State of a System?

The state of a system represents its condition at a particular instant of time.

This condition is described using the values of the properties of the system.

For example, if the temperature and pressure of a gas are known along with the required information needed to describe its condition, the state of the gas can be specified.

\boxed{ \text{State is described by the values of properties} }

2. State Has a Single Value for Each Property

From the definition of state, each property has a single value at each state.

This means that a particular state cannot have two different values of the same property at the same time.

For example, if the temperature of a system at a specified state is \(T\), its temperature has one definite value for that state.

\boxed{ \text{A given state} \rightarrow \text{single value of a property} }

3. Identical States

If two systems are in identical states, all their corresponding properties have identical values.

Therefore, state provides a complete description of the condition of a system through its properties.

\boxed{ \text{Identical states} \Rightarrow \text{Identical values of corresponding properties} }

4. What Is a Variable?

A variable is a property if, and only if, it has a single value at each equilibrium state.

\boxed{ \text{Variable is a property with a single value at each equilibrium state} }

This definition connects the ideas of a thermodynamic property, variable and equilibrium state.

5. Change in a Variable

A variable is a property if the change in its value between any two prescribed equilibrium states is single-valued.

\boxed{ \Delta X = X_2-X_1 }

Here \(X_1\) and \(X_2\) represent the values of the variable in two equilibrium states.

Therefore, once the initial and final equilibrium states are specified, the change in a property is uniquely determined.

6. Property and State

A property describes the condition of a system at a particular state. It does not depend on the route followed to reach that state.

Therefore, when the same final state is reached, the value of a property at that state is fixed.

\boxed{ \text{Property} \rightarrow \text{depends on state} }

This is why thermodynamic properties are useful for describing and comparing equilibrium states.

7. Equilibrium State

The source defines a variable in relation to an equilibrium state. At an equilibrium state, the system has a definite condition and the properties used to describe it have definite values.

Therefore, a thermodynamic variable must have one definite value at each equilibrium state.

\boxed{ \text{Equilibrium state} \rightarrow \text{Definite property values} }

8. Easy Example

Consider a gas in a container.

Suppose the gas is in a particular equilibrium state with a definite temperature and pressure.

The temperature has one definite value.
The pressure has one definite value.
Each property has a single value for that state.

If the system moves to another equilibrium state, the values of its properties may change. The new equilibrium state will then have its own definite property values.

9. State vs Variable

These two terms are related but they are not the same.

\boxed{ \begin{array}{c|c} \text{Term} & \text{Meaning}\\ \hline \text{State} & \text{Condition of the system}\\ \text{Property} & \text{Characteristic used to describe the state}\\ \text{Variable} & \text{A property having a single value at each equilibrium state} \end{array} }

10. Key Relationship

The complete idea can be remembered as a chain:

\boxed{ \text{System} \rightarrow \text{State} \rightarrow \text{Properties} \rightarrow \text{Variables} }

A system has a particular condition called its state. That state is described using properties, and a variable is a property satisfying the stated single-valued condition at equilibrium states.

11. Important Points to Remember

State is the condition of a system at an instant of time.
A state is described or measured by the properties of the system.
Each property has a single value at a particular state.
Identical states have identical values of their corresponding properties.
A variable is a property if it has a single value at each equilibrium state.
A variable is a property when its change between prescribed equilibrium states is single-valued.

12. Exam-Oriented Understanding

If the question asks for the definition of state, focus on the condition of the system at an instant of time and the properties used to describe it.

If the question asks for a variable, remember the key phrase:

\boxed{ \text{Single value at each equilibrium state} }

If the question asks when a variable is a property, mention that its change between any two prescribed equilibrium states must be single-valued.

Final Answer

State is the condition of a system at an instant of time as described or measured by its properties. Each property has a single value at each state. If two systems are in identical states, all their corresponding properties have identical values.

A variable is a property if and only if it has a single value at each equilibrium state. A variable is also a property when its change between any two prescribed equilibrium states is single-valued.

\boxed{ \text{State} \rightarrow \text{Properties} \rightarrow \text{Single-valued variables} }

Quick Revision

State

\boxed{ \text{Condition of a system at an instant of time} }

Property

\boxed{ \text{Characteristic used to describe the state} }

Variable

\boxed{ \text{Property with a single value at each equilibrium state} }

Change between two states

\boxed{ \Delta X=X_2-X_1 }

Exam Tip

Do not confuse state with property.

Think of it this way:

\boxed{ \text{State = condition} } \] \[ \boxed{ \text{Property = characteristic describing that condition} }

For the definition of a variable, the phrase "single value at each equilibrium state" is the key point to remember.

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