A farmer is using a tank of 20 $20 ^ { \circ } \mathrm { C }$ C nitrogen pressurized to 540 kPa absolute. It exits the tank out a hose. The hose snaps and the farmer is hit with the expanding nitrogen. Air is primarily
Nitrogen so assuming it is air flowing with no losses, the temperature of the exiting nitrogen is
Nearest:
A) $ -120^{\circ} \mathrm{C} $
B) $ -90^{\circ} \mathrm{C} $
C) $ -70^{\circ} \mathrm{C} $
D) $ -50^{\circ} \mathrm{C} $

Question

A farmer is using a tank of 20 $20 ^ { \circ } \mathrm { C }$ C nitrogen pressurized to 540 kPa absolute. It exits the tank out a hose. The hose snaps and the farmer is hit with the expanding nitrogen. Air is primarily
Nitrogen so assuming it is air flowing with no losses, the temperature of the exiting nitrogen is
Nearest: 
A) $ -120^{\circ} \mathrm{C} $
B) $ -90^{\circ} \mathrm{C} $
C) $ -70^{\circ} \mathrm{C} $
D) $ -50^{\circ} \mathrm{C} $

Quizplus · Accepted Answer

$ -90^{\circ} \mathrm{C} $
The pressure ratio between the exit and the tank is $ p_{e} / p_{0}=100 / 540=0.185 $. From the isentropic flow Table D.1 we find, at $ \mathrm{M}=1.76 $, that
$$
\frac{T}{T_{0}}=\frac{T}{293}=0.6175=181 \mathrm{~K} \text { or } \underline{-92^{\circ} \mathrm{C}} \text { or }-134^{\circ} \mathrm{F}
$$
Such a low temperature would require that the farmer be treated for "burns." The temperature of the nitrogen in the tank is hardly a factor since it would undoubtedly be in the range of $ 10^{\circ} \mathrm{C}<T<35^{\circ} \mathrm{C} $.

A Farmer Is Using a Tank of 20 20∘C20 ^ { \circ } \mathrm { C }20∘C

A Farmer Is Using a Tank of 20 $20 ^ { \circ } \mathrm { C }$