Which type of flow corresponds to rapid gas flow through an insulated pipe where no heat is lost or gained by the pipe?

• A. Isothermal
• B. Isobaric
• C. Diffusion
• D. Adiabatic

Answer: (D)

The situation tests the idea of heat transfer boundaries in a flowing gas. If the pipe is insulated and no heat crosses its boundary, the process is adiabatic. In an adiabatic process, Q = 0, so all the energy changes of the gas come from work done on or by the gas, and its internal energy changes accordingly (ΔU = W). For an ideal gas, this leads to relationships like PV^γ = constant and TV^{γ−1} = constant, meaning temperature can change as the gas compresses or expands, even though no heat is exchanged.

Isothermal would require the temperature to stay constant, which would need heat flow to or from the gas to offset any work done, contrary to the insulated, no-heat-transfer setup. Isobaric would imply constant pressure, a condition not dictated by insulation alone. Diffusion describes mass transfer between species, not the thermal boundary condition of the flow.