Uniform Cross-Section Pipe Flow

When a gas flows through a very long pipe of uniform cross-section, the flow is approximately isothermal.

Reasoning

The gas flowing through the pipe experiences friction with the walls of the pipe, resulting in a loss of energy. This loss of energy takes the form of heat, which causes the gas to warm up. However, the pipe is very long, and the heat generated is dissipated over the entire length of the pipe. As a result, the gas temperature remains relatively constant along the length of the pipe, making the flow approximately isothermal.

Explanation

Isothermal flow refers to a flow process in which the temperature of the fluid remains constant throughout the process. In practice, it is impossible to achieve perfectly isothermal flow, but in some cases, the flow can be approximated as isothermal if the temperature changes are small.

In the case of a gas flowing through a pipe of uniform cross-section, the temperature changes are relatively small because the pipe is very long. As a result, the heat generated by frictional losses is dissipated over the entire length of the pipe, resulting in a relatively constant gas temperature. This makes the flow approximately isothermal.

The other options (isentropic, isobaric, adiabatic, and isochoric) are not applicable to this situation because they either assume no heat transfer or no change in specific volume, which is not the case for a gas flowing through a pipe with frictional losses.

Conclusion

In conclusion, when a gas flows through a very long pipe of uniform cross-section, the flow is approximately isothermal because the heat generated by frictional losses is dissipated over the entire length of the pipe, resulting in a relatively constant gas temperature.