## Example: Isentropic Expansion in Gas Turbine

Assume an **isentropic expansion** of helium (**3 → 4**) in a **gas turbine**. Since helium behaves almost as an ideal gas, use the ideal gas law to calculate **outlet temperature** of the gas (**T _{4,is}**). In this turbines the high-pressure stage receives gas (point 3 at the figure; p

_{3 }=

**6.7 MPa**;

**T**(917°C)) from a heat exchanger and exhaust it to another heat exchanger, where the outlet pressure is p

_{3}= 1190 K_{4}=

**2.78 MPa**(point 4)

**.**

**Solution:**

The outlet temperature of the gas, T_{4,is}, can be calculated using **p, V, T Relation** for isentropic process (reversible adiabatic process):

In this equation the factor for helium is equal to **κ****=c _{p}/c_{v}=1.66**. From the previous equation follows that the outlet temperature of the gas,

**T**, is:

_{4,is}## Example: Isentropic Expansion in Gas Turbine

Let assume the **ideal Brayton cycle** that describes the workings of a **constant pressure** **heat engine**. **Modern gas turbine** engines and **airbreathing jet engines** also follow the Brayton cycle.

Ideal Brayton cycle consist of four thermodynamic processes. Two isentropic processes and two isobaric processes.

**isentropic compression**– ambient air is drawn into the compressor, where it is pressurized (1 → 2). The work required for the compressor is given by**W**_{C}= H_{2}– H_{1}.**isobaric heat addition**– the compressed air then runs through a combustion chamber, where fuel is burned and air or another medium is heated (2 → 3). It is a constant-pressure process, since the chamber is open to flow in and out. The net heat added is given by**Q**_{add}= H_{3 }– H_{2}**isentropic expansion**– the heated, pressurized air then expands on turbine, gives up its energy. The work done by turbine is given by**W**_{T}= H_{4}– H_{3}**isobaric heat rejection**– the residual heat must be rejected in order to close the cycle. The net heat rejected is given by**Q**_{re}= H_{4 }– H_{1}

As can be seen, we can describe and calculate (e.g. thermal efficiency) such cycles (similarly for **Rankine cycle**) using enthalpies.

See also: Thermal Efficiency of Brayton Cycle

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