Isentropic Process Formula

Pv k constant.

Isentropic process formula. Isentropic process is characterized by constant entropy of the system. Notice the important role that the mach number plays in all the equations on the right side of this slide. It is a special case of the adiabatic processes defined as a reversible adiabatic process. Isentropic processes for ideal gases an isentropic process of ideal gases on a t s diagram.

The starred conditions occur when the flow is choked and the mach number is equal to one. A a 1 m2 gam 12 gam1 gam 12 gam12 gam1 gam 12 m. Displaystyle dudelta wdelta q. S2 s1 cp ln t2 t1 r ln p2 p1 where the numbers 1 and 2 denote the states at the beginning and end of the compression process s is the entropy t is the temperature p is the pressure and ln denotes the natural logarithm function.

Thermodynamic work done on a system undergoing isentropic process is given by. In an irreversible process of transfer of energy as work entropy is produced within the system. One for constant pressure c p and one for constant volume c v. The isentropic process a special case of adiabatic process can be expressed with the ideal gas law as.

Now we use the equation we have derived for the entropy of a gas. P 1 v 1 k p 2 v 2 k. From the previous equation follows that the outlet temperature of the gas t 4is is. For an isentropic process which by definition is reversible there is no transfer of energy as heat because the process is adiabatic dq 0.

Pv k constant. The isentropic process a special case of adiabatic process can be expressed with the ideal gas law as. Consequently in order to maintain constant entropy within the system energy must be removed from the system as heat during the process. One for constant pressure c p and one for constant volume c v.

In which k c p c v is the ratio of the specific heats or heat capacities for the gas. P 1 v 1 k p 2 v 2 k. Derivation of the isentropic relations. For a closed system the total change in energy of a system is the sum of the work done and the heat added d u d w d q.

For an ideal gas undergoing isentropic process or. In this equation the factor for helium is equal to kc p c v 166. 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. Isentropic compression ambient air is drawn into the compressor where it is pressurized 1 2.

The work required for the compressor is given by wc h2 h1. In which k c p c v is the ratio of the specific heats or heat capacities for the gas.