### Summary

### 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.

### 3.3 First Law of Thermodynamics

- 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.

### 3.4 Thermodynamic Processes

- 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: $\text{\Delta}{E}_{\text{int}}=0,Q=W;$ (b) adiabatic: $Q=0,\text{\Delta}{E}_{\text{int}}=\text{\u2212}W;$ (c) isobaric: $\text{\Delta}{E}_{\text{int}}=Q-W;$ and (d) isochoric: $W=0,\text{\Delta}{E}_{\text{int}}=Q.$

### 3.5 Heat Capacities of an Ideal Gas

- For an ideal gas, the molar capacity at constant pressure ${C}_{p}$ is given by ${C}_{p}={C}_{V}+R=dR\text{/}2+R$, 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 ${C}_{p}\simeq {C}_{V}+R.$

### 3.6 Adiabatic Processes for an Ideal Gas

- 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.