Question

Would you expect the temperature of air to drop as it undergoes a steady-flow throttling process? Explain.

Short answer

Answer: Yes, the temperature of air would be expected to drop during a steady-flow throttling process due to its deviation from ideal gas behavior and its positive Joule-Thomson coefficient.

Step-by-step solution

Understanding the throttling process and Ideal Gas Law

A throttling process typically involves a fluid passing through a valve, nozzle, or other restriction that results in changes to its pressure, temperature, and/or velocity without doing any work or transferring any heat to the surroundings. For an ideal gas, we can use the Ideal Gas Law equation: PV=nRT, where P is the pressure, V is the volume, n is the amount of substance, R is the gas constant, and T is the temperature. In this process, the specific enthalpy (h) will remain constant.

Applying the constant enthalpy principle

In a steady-flow throttling process, the specific enthalpy (h) remains the same before and after the process. For an ideal gas, the specific enthalpy can be expressed as h = cpT, where cp is the specific heat at constant pressure and T is the temperature. Since the specific enthalpy remains constant, cpT1 = cpT2, which simplifies to T1 = T2.

Analyzing the change in temperature for an ideal gas

For an ideal gas undergoing a throttling process, we found that the temperature should remain constant (T1 = T2). This means that the temperature of an ideal gas would not be expected to drop during a steady-flow throttling process.

Considering the behavior of a real gas

Real gases deviate from ideal gas behavior due to intermolecular forces and non-zero molecular sizes. One of the parameters that can help us understand the deviation from ideality is the Joule-Thomson coefficient (µ), which describes the rate of change of temperature with pressure during a throttling process. For air, the Joule-Thomson coefficient is positive, which means that the temperature decreases as pressure decreases during a throttling process.

Answering the question

By analyzing the behavior of both ideal and real gases, we can conclude that the temperature of air would be expected to drop as it undergoes a steady-flow throttling process. This is due to the fact that, as a real gas, air deviates from the ideal gas behavior, and its positive Joule-Thomson coefficient indicates that its temperature would decrease as its pressure decreases during the throttling process.