Question

An ideal gas turbine operates using air (k=1.4) coming at 375°C and 300 kPa. Find the exit pressure (kPa)  if the air exits at 125 ^oC. Assume the air behaves ideally, properties are constant, and the turbine operates isentropically.

The correct answer is 30.8 kPa

Answer 1

$\\ \textit{\textbf{Solution:}}\\ \\ \qquad \textup{Given Data :-}\\ \\ \qquad T_1=375^oC=648\, \, K \\ P_1=300\, \, kPa \\ T_2 = 125^oC =398\, \, K \\ k=1.4\\ \\ \textup{For an ideal gas under isentropic relation and constant specific } \\ \textup{heat assumption, the temperature ratio is written as:}\\ \\ \therefore \frac{T_2}{T_1}=\left (\frac{P_2}{P_1} \right )^{(k-1)/k} \\ \\ \therefore P_2=P_1 \left ( \frac{T_2}{T_1} \right )^{\frac{k}{k-1}} \\ \\ \therefore P_2=300\left(\frac{398}{648}\right)^{\frac{1.4}{1.4-1}} \\ \\ {\color{DarkBlue} \boxed {\therefore P_2= 54.4752\, \, kPa} }\\$

$\textup{(Note : The correct answer is 54.4752 kPa and the answer}$$\textup{mentioned in problem statement is incorrect.)}$