To solve this process it is necessary to consider the concepts related to the relations between pressure and temperature in an adiabatic process.
By definition the relationship between pressure and temperature is given by
[tex](\frac{P_2}{P_1})=(\frac{T_2}{T_1})^{(\frac{\gamma}{\gamma-1})}[/tex]
Here
P = Pressure
T = Temperature
[tex]\gamma =[/tex]The ratio of specific heats. For air normally is 1.4.
Our values are given as,
[tex]P_1 = 15lb/in^2\\T_1= 80\°F = 299.817K\\T_2 =400\°F = 408.15K[/tex]
Therefore replacing we have,
[tex](\frac{P_2}{P_1})=(\frac{T_2}{T_1})^{(\frac{\gamma}{\gamma-1})}[/tex]
[tex](\frac{P_2}{15})=(\frac{408.15}{299.817})^{(\frac{1.4}{1.4-1})}[/tex]
Solving for [tex]P_2,[/tex]
[tex]P_2 = 15*(\frac{408.15}{299.817})^{(\frac{1.4}{1.4-1})}[/tex]
[tex]P_2 = 44.15Lbf/in^2[/tex]
Therefore the maximum theoretical pressure at the exit is [tex]44.15Lbf/in^2[/tex]
