# What is a physio-emotional process

## What is an adiabatic process - definition

### Example: efficiency of isentropic turbines

Take oneisentropic expansion of helium (3 → 4) in a gas turbine. In these turbines, the high pressure stage receives gas (point 3 in the figure; p3 = 6.7 MPa ; T3 = 1190 K (917 ° C)) from a heat exchanger and diverts it to another heat exchanger, where the output pressure is p4 = 2.78 MPa (Point 4)The temperature (for the isentropic process) of the gas at the exit of the turbine is T4s = 839 K (566 ° C).

Calculate the work done by this turbine and the actual temperature at the exit of the turbine when theEfficiency theisentropic turbineηT = 0,91 (91%) amounts.

Solution:

From the first law of thermodynamics, the work of the turbine in an isentropic process can be calculated from:

W.T = h3 - Hs → WTs = cp (T3 - Ts )

From the ideal gas law we know that the molar specific heat of a monatomic ideal gas is:

C.v = 3 / 2R = 12.5 J / mol K and C.p = Cv + R = 5 / 2R = 20.8 J / mol K.

We transfer the specific heat capacities in units ofJ / kg K over:

cp = Cp . 1 / M (molar weight of helium) = 20.8 x 4.10 &min;³ = 5200 J / kg K.

The work of the gas turbine in the isentropic process is then:

W.T, s = cp (T3 - Ts ) = 5200 × (1190-839) = 1.825 MJ / kg

The actual work of the gas turbine in the adiabatic process is then:
W.T, real = cp (T3 - T4s ). ηT= 5200 x (1190 - 839) x 0.91 = 1.661 MJ / kg