3.1 Thermodynamic Systems

A thermodynamic system, its boundary, and its surroundings must be defined with all the roles of the components fully explained before we can analyze a situation.
Thermal equilibrium is reached with two objects if a third object is in thermal equilibrium with the other two separately.
A general equation of state for a closed system has the form $f (p, V, T) = 0,$ with an ideal gas as an illustrative example.

3.2 Work, Heat, and Internal Energy

Positive (negative) work is done by a thermodynamic system when it expands (contracts) under an external pressure.
Heat is the energy transferred between two objects (or two parts of a system) because of a temperature difference.
Internal energy of a thermodynamic system is its total mechanical energy.

The internal energy of a thermodynamic system is a function of state and thus is unique for every equilibrium state of the system.
The increase in the internal energy of the thermodynamic system is given by the heat added to the system less the work done by the system in any thermodynamics process.

The thermal behavior of a system is described in terms of thermodynamic variables. For an ideal gas, these variables are pressure, volume, temperature, and number of molecules or moles of the gas.
For systems in thermodynamic equilibrium, the thermodynamic variables are related by an equation of state.
A heat reservoir is so large that when it exchanges heat with other systems, its temperature does not change.
A quasi-static process takes place so slowly that the system involved is always in thermodynamic equilibrium.
A reversible process is one that can be made to retrace its path and both the temperature and pressure are uniform throughout the system.
There are several types of thermodynamic processes, including (a) isothermal, where the system’s temperature is constant; (b) adiabatic, where no heat is exchanged by the system; (c) isobaric, where the system’s pressure is constant; and (d) isochoric, where the system’s volume is constant.
As a consequence of the first law of thermodymanics, here is a summary of the thermodymaic processes: (a) isothermal: $Δ E_{int} = 0, Q = W;$ (b) adiabatic: $Q = 0, Δ E_{int} = − W;$ (c) isobaric: $Δ E_{int} = Q - W;$ and (d) isochoric: $W = 0, Δ E_{int} = Q .$

For an ideal gas, the molar capacity at constant pressure $C_{p}$ is given by $C_{p} = C_{V} + R = d R / 2 + R$ , where d is the number of degrees of freedom of each molecule/entity in the system.
A real gas has a specific heat close to but a little bit higher than that of the corresponding ideal gas with $C_{p} ≃ C_{V} + R .$

A quasi-static adiabatic expansion of an ideal gas produces a steeper pV curve than that of the corresponding isotherm.
A realistic expansion can be adiabatic but rarely quasi-static.