Isobaric process vs Isothermal process

An isothermal process is a constant temperature process, while an isobaric process is a constant pressure process.

An isothermal process is a thermodynamic process in which the temperature remains constant throughout the process. For an ideal gas undergoing an isothermal process, the change in internal energy (ΔU) is zero because the internal energy of an ideal gas is directly proportional to its temperature.

To explain this point a little more, it may be noted that while real gases have both KE and PE, an ideal gas has only kinetic energy in the absence of intermolecular interactions. Thus, an ideal gas follows the equation: Average KE = ? Kb T [ Kb is Boltzmann constant and T is Kelvin]

This equation does not apply to real gases since the internal energy of real gases is the sum of PE and KE.

?Coming back to the subject, in an isothermal process, the heat transferred (Q) is equal to the work done (W) on the gas. Mathematically, this can be expressed as Q = W.

On the other hand, an isobaric process is a thermodynamic process in which the pressure is held constant. This is typically achieved by allowing heat exchange with the surroundings, such as in the case of a boiler. A boiler is a typical example of an isobaric process.

In an isobaric process, the heat transferred (Q) is equal to the change in internal energy (ΔU) plus the work done (W) by the gas. This can be expressed as

Q = ΔU + W,

where ΔU represents the change in internal energy and W is the work done. It is important to note that in an isobaric process, at constant pressure, the heat transfer is represented not only by the change in internal energy but also by the work done, and this combination is known as enthalpy transfer (H). This is expressed as Q = ΔH, where H represents enthalpy.

Thus, Q = delta W in the case of an isothermal process while for an isobaric process, Q = delta H

To summarize, in an isothermal process, where there is a constant temperature, only work is transferred, and the change in internal energy is zero. In contrast, in an isobaric process, where pressure is held constant, there is a transfer of both internal energy and work, represented as enthalpy transfer. It's essential to understand the distinctions between these processes and their respective equations to analyze and comprehend the behavior of thermodynamic systems accurately.

Typical examples

Condensers work isobarically

A condenser is a crucial component in many heat transfer systems, particularly in refrigeration and power generation. It functions by converting vapor or gas into a liquid state.

The condenser operates isobarically, meaning it maintains a constant pressure during the process.

When the vapor enters the condenser, it contains latent heat, which must be removed to allow the vapor to condense. This occurs at the saturation temperature while the pressure remains constant. As the vapor condenses into liquid, it undergoes compression work, as the gas molecules are compressed into a liquid state. The compression work generates heat and does positive work on the vapor and adds internal energy which gets rejected by the condenser held at constant pressure to the surroundings.

In power plant condensers, throughout this transformation, the vapor transfers its internal energy to the circulating water in the heat exchanger. Finally, the heat is carried to a cooling tower and rejected

Thus the energy transfer in a condenser involves both internal energy and the performance of work, in a manner akin to an isobaric process.

Refrigeration evaporator

The refrigeration evaporator works isobarically. The expansion valve cools the liquid refrigerant from the condenser and maintains a constant pressure downstream while feeding a partially vaporized refrigerant to the evaporator. The constant pressure held in the evaporator ensures a consistent supply of a constant amount of energy to the evaporator despite the expansion of the liquid refrigerant when it converts to gas by absorbing heat from the hot space of the refrigerator. Thus a constant flow of work is maintained.

Steam making in a boiler is another example of a constant pressure process

Let us see how a boiler makes steam. The boiler is an isobaric process where the pressure is held constant by supplying internal energy [heat] from the surroundings despite water expanding into steam by consuming a part of the system's energy. Since the pressure is held constant it keeps compensating energy consumption in the expansion work. Therefore, the steam temperature remains constant.