The *isothermal efficiency* compares the *power requirement for an isothermal compression* with the *actually required power input*.

The *isothermal power** *is the product of *mass flow* and the *mass specific work* required at *ideal isothermal conditions*. The mass flow of the compressor can be obtained by measuring the *volume flow* and the corresponding *thermodynamic conditions, e.g. at suction side*. With additional measurement of the discharge pressure, the *isothermal work* can be calculated.

The **power required**** **is the power input at the clutch, which is obtained by measuring the *torque* and the *revolutions per minute*.

A part of the *power input* is used up as the *mechanical power loss* (*friction* in the *drive mechanism* and at the *sealing elements)*, as well as the work input of *auxiliary aggregates* such as lubricators, cooling pumps etc.).

The *remaining** **internal work***,** which is transmitted by the piston onto the gas, is larger than the *isothermal power***, **see Table 5.8.

**Table 5.8: Calculation of parameters to describe the energy efficiency**

After the experimental evaluation **(***indicating*)** **of the cylinder pressure, which varies with time and crank angle, or by **simulating** the thermodynamic processes by a calculation which comes close to the real conditions, the internal work can be derived by the areas of the *p,V-diagrams* of all working chambers .

The following diagram shows the principle relationship of the *isothermal efficiency* and the *pressure ratio* for air compressors with different number of stages, see Figure 5.6.

**Figure 5.6: Relationship between the isothermal efficiency and the pressure ratio [0]**

For each stage, there is an *optimal pressure ratio from an energy efficiency perspective*. With smaller pressure ratios the *throttling losses* become more important. With larger pressure ratios the additional work due to deviations from the isothermal compression rises. The *maximum achievable efficiency* rises with the *number of stages*, as the approximation to the isothermal process increases.