Thermodynamic State Variables and Equation of State: Class 11 Physics Notes, Definition, Types, and Diagrams

Generally, we define thermodynamic state variables as macroscopic properties (e.g., pressure, volume, temperature) that fully describe a system's equilibrium state. The equation of state is a mathematical relationship connecting these variables.

Importance of Learning Thermodynamic State Variables and Equation of State

From the CBSE syllabus standpoint, thermodynamic state variables in this Physics Class 11 chapter is quite brief. But knowing the applications of the state equation and its related concepts can help you score well in the engineering entrances, including JEE Mains. 

Thermodynamic state variables and the equation of state also continue in undergraduate programmes. It’s part of the B.Sc. Physics syllabus in the third semester. 

Chapter 11 of Physics, in Class 11, provides this explanation of thermodynamic state variables and the equation of state. 

“Thermodynamic state variables describe equilibrium states of systems. The various state variables are not necessarily independent. The connection between the state variables is called the equation of state. For example, for an ideal gas, the equation of state is the ideal gas relation PV=μRT."

In this equation, we have 

P = Pressure 

V = Volume 

μ = Number of moles 

R = Universal gas constant

T = Absolute temperature 

So, as you know, what state variables or properties are by now. But do remember that the state variables, including pressure (P), volume (V), temperature (T), internal energy (U), and mass (m) depend only on the system's state, not its history. Based on this condition, we have two major types of thermodynamic state variables. 

• Extensive Variables: These primarily depend on system size (e.g., V,U,m). Dividing a system into two equal parts halves these values. 
• Intensive Variables: These are independent of size (e.g., P,T, density ()). They remain unchanged when the system is divided.

Here are a few aspects to remember. Find out the difference between state and path variables, what determines equilibrium states, and more. 

• State vs. Path Variables: State variables (e.g., $P,V,T$ ) are path-independent, unlike heat $\left(Q\right)$ and work $\left(W\right)$ , which depend on the process.
•  Equation of State: For an ideal gas, $PV=\mu RT$ , where $\mu$ is the number of moles, $R$ is the universal gas constant ( $8.314\mathrm{J}{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$ ). This relates $P,V$ , and $T$ , with only two being independent for fixed $\mu$ .
• Equilibrium States: State variables describe equilibrium states, where properties are uniform. Non-equilibrium states (e.g., free expansion, chemical reactions) lack welldefined state variables.
• Consistency Check: Thermodynamic equations (e.g., $\mathrm{\Delta }Q=\mathrm{\Delta }U+P\mathrm{\Delta }V$ ) maintain consistency with extensive/intensive classifications, as $P\mathrm{\Delta }V$ (intensive $\times$ extensive) is extensive.

The ideal gas equation, $PV=\mu RT$ , is the simplest equation of state, assuming negligible intermolecular forces. For a fixed amount ( $\mu$ ), it defines relationships like:

Isotherms: At constant $T,P\propto v^1$ , yielding hyperbolic $\mathrm{P}-\mathrm{V}$ curves.

Dependent Variables: Only two of $P,V,T$ are independent, determining the third.

Real gases have more complex equations of state, but the ideal gas model suffices for JEE Main. Learn more about the ideal gas equation, explained simply for all types of exams. 

The thermodynamic state variables and equation of state have applications in various scenarios. 

• Gas Behaviour: The equation of state predicts how gases respond to changes in $P,V$ , or $T$ , guiding applications in engines and compressors. Consider air conditioners, gas cylinders, and other systems whose state behaviour can be calculated using this equation of state.
• Thermodynamic Analysis: State variables enable us to obtain a precise description of equilibrium states in processes such as isothermal or adiabatic changes. In isothermal processes, the temperature is constant, while pressure and volume change. On the other hand, in adiabatic processes, there is no heat exchange with the surroundings, but the temperature, volume, and pressure change together while conserving internal energy. 
• Measurement Standards: Temperature and pressure scales rely on state variables for calibration in thermometry and manometry.