Question

Air expands adiabatically through a turbine from a pressure and temperature of 180 psia,

1600∘R to a pressure of 14.7 psia. If the actual temperature change is 85% of the ideal temperature change, determine the actual temperature of the expanded air and the actual enthalpy and entropy differences across the turbine.

Answer 1

In an adiabatic expansion through a turbine, the actual temperature change is 85% of the ideal temperature change. We can calculate the actual temperature of the expanded air by determining the ideal temperature change and taking 85% of it.

Step-by-step explanation:

In an adiabatic expansion through a turbine, the actual temperature change is 85% of the ideal temperature change. Given that the initial pressure and temperature of the air are 180 psia and 1600∘R, and the final pressure is 14.7 psia, we can determine the actual temperature of the expanded air.

First, we calculate the ideal temperature change using the formula:

T2 = T1 * (P2/P1)^((y-1)/y)

Where T1 and T2 are the initial and final temperatures, P1 and P2 are the initial and final pressures, and y is the ratio of specific heats for air (approximately 1.4).

Plugging in the given values, the ideal temperature change is: T2 = 1600 * (14.7/180)^((1.4-1)/1.4) = 1310.14 ∘R

Now we can calculate the actual temperature change by taking 85% of the ideal temperature change: T_actual = 0.85 * 1310.14 = 1113.62 ∘R

Therefore, the actual temperature of the expanded air is 1113.62 ∘R.