True or False: In all adiabatic flows, the temperature of the gas when it exits the pipe will be higher than when it entered the pipe.

True or False: In all adiabatic flows, the temperature of the gas when it exits the pipe will be higher than when it entered the pipe.

• A. True
• B. Sometimes higher
• C. Always lower
• D. False

Answer: (D)

In adiabatic flow, no heat enters or leaves the fluid, so energy can only move between internal energy and kinetic energy. The stagnation temperature is conserved along a streamline when there’s no external heat transfer or shaft work, written as h0 = h + v^2/2 = constant. For an ideal gas, h = c_p T, so c_p T0 = c_p T + v^2/2, which rearranges to T = T0 − v^2/(2 c_p). This shows that static temperature depends on how velocity changes from entry to exit. If the flow speeds up, the static temperature drops; if it slows down, the static temperature rises. Therefore the exit temperature being higher than the entry temperature is not guaranteed in adiabatic flow; it can be higher, lower, or the same depending on the velocity change.

In adiabatic flow, no heat enters or leaves the fluid, so energy can only move between internal energy and kinetic energy. The stagnation temperature is conserved along a streamline when there’s no external heat transfer or shaft work, written as h0 = h + v^2/2 = constant. For an ideal gas, h = c_p T, so c_p T0 = c_p T + v^2/2, which rearranges to T = T0 − v^2/(2 c_p). This shows that static temperature depends on how velocity changes from entry to exit. If the flow speeds up, the static temperature drops; if it slows down, the static temperature rises. Therefore the exit temperature being higher than the entry temperature is not guaranteed in adiabatic flow; it can be higher, lower, or the same depending on the velocity change.