Thermodynamic processes and polytropic index

In a nutshell, thermodynamic processes involve different types of heat and work transfer. Typically, there are four thermodynamic processes. [1] isobaric or constant pressure process [2] isothermal or constant temperature process [3] adiabatic process; [4] isochoric or constant volume process. The constant pressure process uses heat from outside to keep the pressure constant. Isothermal processes maintain a constant temperature by absorbing heat from the surroundings and returning it to the surroundings, whereas adiabatic processes use their internal energy in the process. Internal energy increases in the isobaric process, it remains constant in the isothermal process and decreases in the adiabatic process. No work in the isochoric process.

The change in internal energy of a system is the sum of the heat transferred and the work done.

Thermodynamic processes follow the equation PV^n=C. In this case, P is pressure, V is volume, n is the polytropic index, and C is a constant.

What does the polytropic equation signify?

Polytropic index ‘n’ signifies the PV work. The polytropic process equation can be used to describe a variety of expansion and compression processes, including heat transfer.

Polytropic work transfer

n = 0, constant pressure or isobaric process, W = P [ V2-V1]

n = 1, constant temperature or isothermal process, W = Q = RT ln V2/V1

n = y, reversible adiabatic process, W = P1V1 – P2V2 / Y – 1

n = infinity, constant volume or isochoric process, W = 0

Isobaric vs isothermal process

Between constant pressure or isobaric process and isothermal process, in the isobaric process pressure is maintained constant by supplying additional heat that increases the internal energy of the gas.?Therefore, the work done by an isobaric process is purely a function of pressure and not limited to atmospheric pressure as in the case of the isothermal process. In the isothermal process, the internal energy stays constant.

Isothermal vs adiabatic process

An infinite amount of heat is available from the surroundings to maintain a constant temperature. This means that the system can exchange as much heat as needed to keep the temperature constant, allowing for unlimited work to be done. On the other hand, in an adiabatic process, no heat is exchanged with the surroundings. The work done in an adiabatic process is limited by the available internal energy or the specific heats (Cp and Cv) of the gas. This limitation on the available energy means that the adiabatic process can do only as much work as the internal energy allows, making it less than the theoretical maximum for the isothermal process.

Isochoric process

As explained, there is no work in the isochoric process.

Finally, the work done by Isobaric process > Isothermal process > Adiabatic process.