Question

Air, modeled as an ideal gas, enters a turbine operating at steady state at 450 kPa, 800 K and exits at 100 kPa. The temperature of the exiting air is 420 K.

a) If the turbine is well insulated and you can ignore kinetic and potential energy effects, determine if the exit temperature can be correct.

b) What if the exit temperature is 550 K? Explain you’re your reasoning. Hint: Find the entropy generation rate first.

Answer 1

The entropy change is given by

is the entropy generation and cannot be negative

The equation can be rearranged

The turbine is insulated, therefore (adiabatic process)

(a) Assuming air as an ideal gas

The equation for entropy change is given by,

The values of R and Cp are

Here the entropy generation becomes negative which is an impossible process, therefor the exit temperature is not correct.

(b) When   using the above equation

Here the entropy generation is positive and greater than zero,

Therefore the exit temperature is correct and the process is feasible.

From the above TS diagram( not for scale), The process 1-2 is an ideal process and isentropic (no change in entropy) and the process 1-2' irreversible process and the entropy is greater than zero. The process 1-2" is an impossible process where the entropy generation becomes negative.