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Section 19.1 The Thermodynamic State

In thermodynamics we study phenomena associated with heating and cooling of macroscopic bodies. Fundamental to our understanding is a concept called thermodynamic state of the system. We use appropriate properties, such as pressure, temperature, volume, magnetization, etc., to define thermodynamic state of the body. We rely on thermodynamic laws obtained from observations or experiments which we apply to understand how thermodynamic state changes by interaction of the body with its environment.

Whenever you place your system in a new environment, thermodynamic properties take time to stabilize. You might say that we are unable to specify the thermodynamic state unless its thermodynamic properties have stopped changing. When values of thermodynamic properties have stabilized, we say that the system has reached a thermodynamic equilibrium and the state corresponding to these conditions are called equilibrium states.

For instance, when you heat some water in a beaker, the bottom part is at a higher temperture than the top part, and hence, you cannot give a unique answer to the question: what is the temperature of water in the beaker? But, if you stop heating and stir the heated water well, you will get the same reading of the temperature throughout, which you can use to specify the state.

Much of what we will study here are ways to characterize equilibrium states and transformation from one equilibrium state to another. For instance, suppose we wish to study thermodynamics of a gas in a tank. The state of the gas will have definite values of pressure, volume, and temperature, say \((p_1,\ V_1,\ T_1)\text{.}\) Now, suppose upon heating the gas, we get to a new state, \((p_2,\ V_2,\ T_2)\text{.}\) Laws of thermodynamics will help us understand the interplay between the mechanical work by the gas and heat flow into the gas.

Mechanical view of thermodynamic phenomena based on the motions of each atom and molecule in the body is addressed by the methods of startistical mechanics and kinetic theory. We will not study statistical mechanics but will study kinetic theory in a later chapter.

Subsection 19.1.1 Thermodynamic Systems

Every macroscopic object or collection of macroscopic objects in the universe is a thermodynamic system. But when we study thermodynamics, we focus on some pure and simple systems. The simplest of all systems is a system that consists of noninteracting particles in a gas state. This is called an ideal gas. The ideal gas is a good model for real gases at low densities when their molecules are far apart. We will have more to say about this model in a separate section.

Following are some examples of thermodynamic systems and ways of specifying their thermodynamic state.

  1. Chemically Pure Homogeneous Fluid. For example, a tank of liquid nitrogen, chemically stable oil in the engine, water in a cooling system of a power plant, etc. The thermodynamic variables here will be pressure (\(p\)), temperature (\(T \)), density (\(\rho\)), volume (\(V\)), and mass (\(M \)).
  2. Chemically Pure Homogeneous Solid. For example, a train track, a concrete slab, wooden block, etc. The thermodynamic variables here will be same as that of chemically pure homogeneous fluid, viz., pressure (\(p\)), temperature (\(T \)), density (\(\rho\)), volume (\(V\)), and mass (\(M \)).
  3. Stable Homogeneous Mixture of Several Chemicals. For example, salty water, chemical reaction products in stationary state, mixture of hydrocarbons, mixture of mixable nonreacting chemicals, etc. The thermodynamic variables here will be pressure (\(p\)), temperature (\(T \)), and concentrations (\(c_i\)) of each of the chemicals.
  4. Systems with Moving Parts. For example, a car that runs on gasoline can be thought of consisting of gasoline, electric circuitry, and moving parts. To specify the state of the car, we will need to specify, not only the amount of gasoline being used, but also energy used in the circuitry and the moving parts.