Answer:
The temperature difference between the tube temperature and compressed air temperature of 457.979 K is very large which can impact on the accuracy of the humidity measurement such as error magnification and sensitivity to rapid changes
Step-by-step explanation:
For isentropic compression, we have;
![(p_(1))/(p_(2)) = \left [(T_(1))/(T_(2)) \right ]^{(\gamma)/(\gamma -1)}](https://img.qammunity.org/2021/formulas/physics/college/a5t7rgvdn69j9pm13rqfxt6siwlgyjol03.png)
Where:
p₁ = Initial pressure = 14.5 psia
p₂ = Final pressure = 500 psia
T₁ = Initial temperature = 80 °F = 299.8167 K
T₂ = Final temperature (Required)
Tube temperature = 200 °F = 366.4833 K
γ = The ratio of the specific heats of the gas, cp/cv = 1.4 for air.
Plugging in the values we have;
![(14.5)/(500) = \left [(299.8167)/(T_2 ) \right ]^{(1.4)/(1.4 -1)}](https://img.qammunity.org/2021/formulas/physics/college/a9b8lzgfp2mnw751vqc5gpetpk583k01h0.png)
![\left [(299.8167)/(T_2 ) \right ]= 0.364](https://img.qammunity.org/2021/formulas/physics/college/mugxae8ujisi1nju30fact1ffz34ksel4r.png)
T₂ =824 K
Therefore, the temperature difference between the tube temperature and compressed air temperature which is 824.46 K - 366.48 K = 457.979 K is very large which can impact on the accuracy of the humidity measurement such as error magnification and sensitivity to rapid changes.