*Thermodynamics is the study of the relationships
between heat, work, and energy in systems.* A perfect gas is an idealized gas
that follows the ideal gas law, which describes the relationship between
pressure, volume, and temperature. In this chapter, we will explore the
thermodynamic processes of perfect gases, including isobaric, isochoric,
isothermal, and adiabatic processes.

**Isobaric
Process:**

An isobaric process is a thermodynamic process that occurs at a constant pressure. During an isobaric process, the volume of the gas changes while the pressure remains constant. The work done by the gas is given by the equation:

**W
= PÎ”V**

** **

where W is the work done by the gas, P is the constant pressure, and Î”V is the change in volume of the gas. The heat added to or removed from the gas is given by the equation:

**Q
= Î”H = CpÎ”T**

** **

where Q is the heat added to or removed from the gas, Î”H is the change in enthalpy of the gas, Cp is the specific heat at constant pressure, and Î”T is the change in temperature of the gas. The first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred, is applicable to isobaric processes.

**Isochoric
Process:**

** **

An isochoric process is a thermodynamic process that occurs at a constant volume. During an isochoric process, the pressure and temperature of the gas may change, but the volume remains constant. The work done by the gas is zero because there is no change in volume. The heat added to or removed from the gas is given by the equation:

**Q
= Î”U = CvÎ”T**

** **

where Q is the heat added to or removed from the gas, Î”U is the change in internal energy of the gas, Cv is the specific heat at constant volume, and Î”T is the change in temperature of the gas. The first law of thermodynamics is also applicable to isochoric processes.

**Isothermal
Process:**

** **

An isothermal process is a thermodynamic process that occurs at a constant temperature. During an isothermal process, the pressure and volume of the gas change, but the temperature remains constant. The work done by the gas is given by the equation:

**W
= -nRT ln(V2/V1)**

** **

where W is the work done by the gas, n is the number of moles of gas, R is the gas constant, V1 is the initial volume of the gas, and V2 is the final volume of the gas. The heat added to or removed from the gas is given by the equation:

**Q
= Î”H = 0**

** **

because the enthalpy of the gas remains constant during an isothermal process. The second law of thermodynamics, which states that the total entropy of a closed system always increases, is applicable to isothermal processes.

**Adiabatic
Process:**

** **

An adiabatic process is a thermodynamic process that occurs without the transfer of heat between the system and its surroundings. During an adiabatic process, the temperature, pressure, and volume of the gas may change. The work done by the gas is given by the equation:

**W
= -Î”E**

** **

where W is the work done by the gas, and Î”E is the change in internal energy of the gas. The heat added to or removed from the gas is zero because the process is adiabatic. The adiabatic index, Î³, relates the specific heat at constant pressure, Cp, to the specific heat at constant volume, Cv, as discussed earlier in this book.