# How do external irreversibilities decrease the efficiency of thermodynamic cycles?

In gas power cycles, one mentioned that:

The Carnot cycle is both externally and internally reversible. Therefore making the Carnot cycles more efficient than other practical cycles.

## Question:

How do external and internal irreversibilities affect the efficiency of a Thermodynamic cycle?

## Irreversible process

In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics.

In thermodynamics, a change in the thermodynamic state of a system and all of its surroundings cannot be precisely restored to its initial state by infinitesimal changes in some property of the system without expenditure of energy.

A system that undergoes an irreversible process may still be capable of returning to its initial state. However, the impossibility occurs in restoring the environment to its own initial conditions. (Wikipedia)

Then here it comes:

All complex natural processes are irreversible. (Lucia, U (1995). "Mathematical consequences and Gyarmati's principle in Rational Thermodynamics".)

## The Carnot Cycle

The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. It provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference (e.g. refrigeration) by the application of work to the system. It is not an actual thermodynamic cycle but is a theoretical construct. (Wikipedia)

Which is a theoretical cycle in order to determine the upper limit of a practical thermodynamic cycle.

The External and Internal Irreversibilities, Decreases the efficiency of a Thermodynamic Cycle.

Here is how; First I strongly suggest you to read this simple introduction from Wikipedia.

This limiting value is called the Carnot cycle efficiency because it is the efficiency of an unattainable, ideal, reversible engine cycle called the Carnot cycle. No device converting heat into mechanical energy, regardless of its construction, can exceed this efficiency. (Wikipedia)

In thermodynamic cycle, the processes that are applied to the mass that runs the cycle is irreversible. That is the law of entropy.

The Carnot efficiency formulas are based on simple idealized mathematical models of engines, with no friction and working fluids that obey simple thermodynamic rules called the ideal gas law.

Real engines have many departures from ideal behavior that waste energy, reducing actual efficiencies far below the theoretical values given above. (Wikipedia)

Examples are:

• friction of moving parts
• inefficient combustion
• heat loss from the combustion chamber
• departure of the working fluid from the thermodynamic properties of an ideal gas
• aerodynamic drag of air moving through the engine
• energy used by auxiliary equipment like oil and water pumps.
• inefficient compressors and turbines
• imperfect valve timing

Then for further reading, you can take a look at this topic too.

A Carnot cycle is a theoretical limit. The irreversibility of a real cycle is always expressed in addition to the expression of the Carnot efficiency of the cycle.

In this regard, inefficiencies, whether internal (gas interactions) or external (loss of heat to friction) become an additional term of irreversibility. The real efficiency of any cycle is a multiplication of the irreversible term with the Carnot efficiency.

$$\varepsilon_{actual} = \varepsilon_{irr}\ \varepsilon_{Carnot}$$

A system that is operating at a Carnot efficiency of 0.8 but is only 60% efficient at doing so has an actual efficiency of 48%.