A farmer is applying compressed nitrogen to a field from a tank originally at $800 \mathrm { kPa }$. The temperature of the nitrogen as it leaves the tank is approximately:
A) $- 140 ^ { \circ } \mathrm { C }$
B) $- 120 ^ { \circ } \mathrm { C }$
C) $- 100 ^ { \circ } \mathrm { C }$
D) $- 80 ^ { \circ } \mathrm { C }$

Question

Quizplus · Accepted Answer

$- 120 ^ { \circ } \mathrm { C }$
Assume the nitrogen is an ideal gas which undergoes an isentropic process so that
$$T _ { 2 } = T _ { 1 } \left( \frac { p _ { 2 } } { p _ { 1 } } \right) ^ { ( k - 1 ) / k } = ( 273 + 10 ) \left( \frac { 100 } { 800 } \right) ^ { 0.4 / 1.4 } = 156 \mathrm {~K} \text { or } \underline { - 117 ^ { \circ } \mathrm { C } }$$
The assumption of a constant entropy process as the nitrogen expands is quite acceptable since there is no heat transfer and the process is relatively frictionless.

A Farmer Is Applying Compressed Nitrogen to a Field from a Tank