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Thermodynamic Processes

09th Apr 2022 @ 5 min read

Physical Chemistry

In thermodynamics, we often encounter various terminologies and processes. It is always better to acquaint ourselves with such names. In this article, we will go through various types of processes in thermodynamics.

Reversible process

In thermodynamics, a reversible process is a process whose direction can be reversed to its initial state by infinitesimal changes in thermodynamic variables. In a reversible process, the system is always in thermodynamic equilibrium with its surrounding throughout the change. Since a perfect reversible process takes an infinite amount of time and an infinite number of steps to complete, in the real world, reversible processes are fictional and do not exist. However, we can approximate many worldly processes to a reversible process. 

A classical depiction of a reversible process is an isothermal expansion of a piston as shown below.

isothermal expansion of a piston

In the above diagram, the first process is an irreversible expansion. The system moves from P1, V1 to P2, V2 in a single spontaneous expansion. The spontaneity is accompanied by heat loss in the form of friction between the piston and the wall of the container. Heat loss is a permanent loss; we cannot restore the system and its surrounding to the original thermodynamic state. Thus, we qualify the process as irreversible.

The work done in an irreversible process is given by W = −P2 (ΔV) = −P2 (V2 − V1). The negative sign indicates the work is done by the system on the surrounding; the system loses internal energy. In the graph, the work done is represented by the red rectangle.

For a reversible process, the piston has to be moved by an infinitesimal displacement against external pressure (P1 + ΔP) from P1. In every step, there is an infinitesimal increase in volume and an infinitesimal decrease in pressure. And also the system remains in thermodynamic equilibrium with the surrounding. There is no friction between the piston and the wall, so no heat loss in a reversible process.

The work done by the system in a reversible process is ∫ {from V1 to V2} −PdV. In the graph, it is the area under the PV isotherm.

It is clear that from the graph, the work done in an irreversible process is a subset of the work done in a reversible process. Thus, the maximum work is always obtained in a reversible process.

Adiabatic process

In an adiabatic process, the flow of heat or mass between the system and its surrounding is prohibited. The flow of heat from or in the system can be restricted by an insulation wall between the system and its surrounding. Despite the insulation, the internal energy of the system can be changed by mechanical work. The adiabatic process does not restrict the system to exchange energy in the form of work. The system can decrease its internal energy by doing work on its surroundings, or the internal energy can be gained when the work is done on the system.

The internal energy for a closed system by the first law of thermodynamics is expressed as:

ΔU = Q+W = Q−PΔV

For an adiabatic process, Q = 0. So, ΔU = W = −PΔV.

A true adiabatic process does not exist in nature, but many phenomena in the real world can be approximated close to an ideal adiabatic process. Below are some examples:

  1. The compression of the fuel vapor in the diesel engine is considered adiabatic. The fuel is compressed so rapidly in the engine cylinder that the heat dissipation via conduction is negligible in the compression stroke of the diesel cycle. Adiabatic compression causes the rise in temperature of the system.
  2. The air moving over rising terrain cools adiabatically. The parcel of air mass expands by doing work on its surroundings. This expansion causes cooling of the air parcel and can lead to the formation of clouds and further precipitation.

Isothermal process

The isothermal process occurs at a constant temperature. If the system changes from one thermodynamic state to another while keeping its temperature constant, we call it an isothermal process.

In an isothermal process, ΔT = 0. For an ideal gas, the internal energy is solely dependent on the temperature of the system. Thus, ΔU = 0 for an isothermal ideal-gas system.

The system can maintain its temperature if it is in constant contact with a heat reservoir. Any rise or fall in the temperature during the state change can be accommodated by the heat flow from or to the heat reservoir.

In an ideal gas system undergoing an isothermal change, ΔT = 0 and ΔU = 0. So, 0 = ΔU = Q + W.

Thus, Q = −W = PΔV.

From the above equation, for an isothermal ideal-gas system, all the work done in compression or expansion of the system will be exchanged with the heat reservoir in the form of heat flow.

The isothermal process can be explained on a PV graph.

PV graph of isothermal process

In the above diagram, the system expands isothermally from state 1 (P1, V1) to state 2 (P2, V2). Assuming an ideal gas system, we can apply the ideal gas law, PV = nRT. And the equation of the isotherm becomes P = nRT/V.

The work done is given as ∫ {from V1 to V2} −PdV = ∫ {from V1 to V2} −nRT/V dV = −nRT ln (V2/V1).

Isobaric process

A thermodynamic process in which the pressure of the system remains constant throughout the change is called an isobaric process. So, for an isobaric process, P = constant or ΔP = 0.

In an isothermal process, the system has to be in constant touch with a heat reservoir, while in an isobaric, the contact has to be with a constant-pressure reservoir. The best example of a constant-pressure reservoir is the atmosphere. The atmosphere is so vast that the effect of any external pressure on it is insignificant. You can imagine a system with flexible boundaries. So, any change in the pressure of the system is balanced by the expansion or relaxation of the boundaries.

The work done in an isobaric process is given by W =  ∫ {from V1 to V2} −PdV

Since P is constant, we can take it out of the integral.

W = −P ∫ {from V1 to V2} dV = −PΔV.

Assuming the ideal gas law, ΔV = nRΔT/P or PΔV = nRΔT

W = −nRΔT.

work done in Isobaric process

In the above graph, state 1 and state 2 are two thermodynamic states. The work done to move the system from 1 to 2 is the rectangular portion under the isobar P = constant.

Isochoric process

For an isochoric process, the volume of the system remains constant throughout the thermodynamic state change. The isochoric process is also called the isometric process or the isovolumetric process.

The volume remains constant, so ΔV = 0.

The system can maintain its volume if the boundaries of the system are rigid or inflexible. It means the system cannot expand or compress. A simple example of an isochoric process will be a metal can set under fire. The can cannot expand because of the rigid metal body. All the heat supply is utilized to raise the temperature of the fluid in the can.

The mechanical work done in an isochoric process is zero since ΔV = 0.

W =  ∫ {from V to V } −PdV = 0

The internal energy of the system is given by ΔU = Q + W = Q + 0 = Q

Thus, we can say all the heat supply to the system is added to the internal energy of the system.

work in Isochoric process

In the above PV graph, the change of state from 1 to 2 is a straight vertical line. And the mechanical work done, the area under the line, is zero.

Isentropic process

An isentropic process is a constant-entropy process. In an isentropic process, the change in state is both adiabatic and reversible. The adiabatic ensures there is no transfer of heat from and to the system. And reversibility means the system is always in thermodynamic equilibrium with its surrounding.

The change in the entropy of the system is given by ΔS = Q/T + Ṡ. 

Here Q is the heat flow across the system’s boundaries and Ṡ is entropy production.

In a reversible process, no entropy is produced; Ṡ = 0.

ΔS = Q/T + 0 = Q/T

In an adiabatic process, heat exchange is zero, so Q = 0.

Thus, ΔS = 0/T = 0 for an isentropic process.

The internal energy of the isentropic system is ΔU = Q + W = 0 + W =  −∫ {from V1 to V2} PdV.

In the natural world, the isentropic process is hardly seen, but it is often found in engineering applications, especially thermodynamic cycles, like the Otto cycle, diesel cycle, Rankine cycle, Brayton cycle. 

The isentropic process on the TS graph will be a straight line as shown in the below diagram.

work done in Isentropic process

Isenthalpic process

The isenthalpic process is a process of constant enthalpy. Enthalpy is represented by the symbol H. So, for an isenthalpic process, ΔH = 0. One common useful application of the isenthalpic process is throttling, an important part of the refrigeration system.

The enthalpy is H = U + PV. 

When fluid is passed through a throttling device (valve), the fluid expands. The expansion increases the PV term in the equation. To have a constant H, the value of U needs to be decreased. The decrease in U means fall in the temperature of the fluid or cooling of the fluid.

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