Question

Air enters the compressor of a test facility at 80 °F and 14.5 psia. It is then compressed isentropically to 500 psia and transported to the test cell. At the cell inlet some of the gas is pulled off in a tube for humidity measurements. The tube is maintained at a temperature of 200 °F into the test cell where the sensor is located. Is that line temperature sufficient to ensure a successful measurement of the cell entrance humidity?

Answer 1

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

Explanation:

For isentropic compression, we have;

$\frac{p_{1}}{p_{2}} = \left [\frac{T_{1}}{T_{2}} \right ]^{\frac{\gamma}{\gamma -1}}$

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;

$\frac{14.5}{500} = \left [\frac{299.8167}{T_2 } \right ]^{\frac{1.4}{1.4 -1}}$

$\left [\frac{299.8167}{T_2 } \right ]= 0.364$

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.